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Номер 898, страница 249 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
Повторение курса алгебры 7-9 классов. Числовые и алгебраические выражения и их преобразования - номер 898, страница 249.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => "250" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-898" "field_display_title" => "898" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:2 [ 0 => App\Models\Branch {#1069 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Book {#1073 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1102 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Числовые и алгебраические выражения и их преобразования" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Book {#1105 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => 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"978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1134 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 …2} ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Числовые и алгебраические выражения и их преобразования" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1104} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:3 [ 0 => App\Models\Element {#1166 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1277253 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175 #items: array:1 [ 0 => App\Models\Edition {#1167 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108653" "type" => "task" ] "text" => "<p><strong>898. a)</strong> Яблоки подешевели на 20 %. Сколько килограммов яблок можно купить за те же деньги, на которые прежде можно было купить 2,8 кг яблок?</p><p><strong>б)</strong> Для покраски пола в комнате израсходовали 2 кг краски. Хватит ли 1,5 кг такой краски для покраски пола в комнате, длина которой в 1,5 раза меньше, а ширина такая же?</p>" "img" => array:2 [ 0 => array:5 [ "name" => "898-1.jpg" "alt" => null "width" => "1543" "height" => 291 "path" => "/media/algebra_09/soltan-u19/0-1/898-1.webp?ts=1752834875" ] 1 => array:5 [ "name" => "898-2.jpg" "alt" => null "width" => "1456" "height" => 282 "path" => "/media/algebra_09/soltan-u19/0-1/898-2.webp?ts=1752834875" ] ] ] #original: array:7 [ "id" => 1277253 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175} "task" => array:2 [ "refs" => "1108653" "type" => "task" ] "text" => "<p><strong>898. a)</strong> Яблоки подешевели на 20 %. Сколько килограммов яблок можно купить за те же деньги, на которые прежде можно было купить 2,8 кг яблок?</p><p><strong>б)</strong> Для покраски пола в комнате израсходовали 2 кг краски. Хватит ли 1,5 кг такой краски для покраски пола в комнате, длина которой в 1,5 раза меньше, а ширина такая же?</p>" "img" => array:2 [ 0 => array:5 [ "name" => "898-1.jpg" "alt" => null "width" => "1543" "height" => 291 "path" => "/media/algebra_09/soltan-u19/0-1/898-1.webp?ts=1752834875" ] 1 => array:5 [ "name" => "898-2.jpg" "alt" => null "width" => "1456" "height" => 282 "path" => "/media/algebra_09/soltan-u19/0-1/898-2.webp?ts=1752834875" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1173 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1278544 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Edition {#1174 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108653" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "898-1.jpg" "alt" => null "width" => "1400" "height" => 1091 "path" => "/media/algebra_09/soltan-u19/1-1/898-1.webp?ts=1752831710" ] ] ] #original: array:6 [ "id" => 1278544 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1183} "task" => array:2 [ "refs" => "1108653" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "898-1.jpg" "alt" => null "width" => "1400" "height" => 1091 "path" => "/media/algebra_09/soltan-u19/1-1/898-1.webp?ts=1752831710" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1181 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1554499 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191 #items: array:1 [ 0 => App\Models\Edition {#1182 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108653" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Пусть $P_1$ — первоначальная цена яблок за килограмм, а $M_1$ — первоначальное количество яблок, которое можно было купить. Тогда общая сумма денег, потраченная на покупку, составляет $C = P_1 \times M_1$. По условию, $M_1 = 2,8$ кг, значит, $C = P_1 \times 2,8$.</p><p>Цена яблок понизилась на 20%. Новая цена $P_2$ составит $100\% - 20\% = 80\%$ от первоначальной цены. Таким образом, $P_2 = P_1 \times (1 - 0,20) = 0,8 \times P_1$.</p><p>Теперь нужно найти, какое количество яблок $M_2$ можно купить за ту же сумму денег $C$ по новой цене $P_2$.</p><p>$C = P_2 \times M_2$</p><p>Приравняем два выражения для стоимости $C$:</p><p>$P_1 \times 2,8 = P_2 \times M_2$</p><p>Подставим выражение для $P_2$:</p><p>$P_1 \times 2,8 = (0,8 \times P_1) \times M_2$</p><p>Сократим обе части уравнения на $P_1$ (так как цена не равна нулю):</p><p>$2,8 = 0,8 \times M_2$</p><p>Отсюда найдем $M_2$:</p><p>$M_2 = \frac{2,8}{0,8} = \frac{28}{8} = \frac{7}{2} = 3,5$ кг.</p><p><strong>Ответ:</strong> за те же деньги можно купить 3,5 кг яблок.</p><p><strong>б)</strong></p><p>Расход краски прямо пропорционален площади окрашиваемой поверхности. Пусть $L_1$ и $W_1$ — длина и ширина первой комнаты, а $S_1$ — её площадь. Тогда $S_1 = L_1 \times W_1$. На покраску этой площади израсходовали 2 кг краски.</p><p>У второй комнаты длина $L_2$ в 1,5 раза меньше, а ширина $W_2$ такая же, как у первой. То есть:</p><p>$L_2 = \frac{L_1}{1,5}$</p><p>$W_2 = W_1$</p><p>Площадь второй комнаты $S_2$ равна:</p><p>$S_2 = L_2 \times W_2 = \frac{L_1}{1,5} \times W_1 = \frac{L_1 \times W_1}{1,5} = \frac{S_1}{1,5}$</p><p>Таким образом, площадь второй комнаты в 1,5 раза меньше площади первой комнаты.</p><p>Следовательно, и краски на её покраску потребуется в 1,5 раза меньше. Рассчитаем необходимое количество краски $K_2$:</p><p>$K_2 = \frac{2 \text{ кг}}{1,5} = \frac{2}{3/2} = 2 \times \frac{2}{3} = \frac{4}{3} \approx 1,33$ кг.</p><p>В наличии есть 1,5 кг краски. Сравним необходимое количество с имеющимся:</p><p>$1,5 \text{ кг} > \frac{4}{3} \text{ кг}$ (поскольку $1,5 = \frac{3}{2} = \frac{9}{6}$, а $\frac{4}{3} = \frac{8}{6}$)</p><p>Так как имеющееся количество краски (1,5 кг) больше, чем необходимое (≈1,33 кг), краски хватит.</p><p><strong>Ответ:</strong> да, хватит.</p>" ] #original: array:6 [ "id" => 1554499 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191} "task" => array:2 [ "refs" => "1108653" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Пусть $P_1$ — первоначальная цена яблок за килограмм, а $M_1$ — первоначальное количество яблок, которое можно было купить. Тогда общая сумма денег, потраченная на покупку, составляет $C = P_1 \times M_1$. По условию, $M_1 = 2,8$ кг, значит, $C = P_1 \times 2,8$.</p><p>Цена яблок понизилась на 20%. Новая цена $P_2$ составит $100\% - 20\% = 80\%$ от первоначальной цены. Таким образом, $P_2 = P_1 \times (1 - 0,20) = 0,8 \times P_1$.</p><p>Теперь нужно найти, какое количество яблок $M_2$ можно купить за ту же сумму денег $C$ по новой цене $P_2$.</p><p>$C = P_2 \times M_2$</p><p>Приравняем два выражения для стоимости $C$:</p><p>$P_1 \times 2,8 = P_2 \times M_2$</p><p>Подставим выражение для $P_2$:</p><p>$P_1 \times 2,8 = (0,8 \times P_1) \times M_2$</p><p>Сократим обе части уравнения на $P_1$ (так как цена не равна нулю):</p><p>$2,8 = 0,8 \times M_2$</p><p>Отсюда найдем $M_2$:</p><p>$M_2 = \frac{2,8}{0,8} = \frac{28}{8} = \frac{7}{2} = 3,5$ кг.</p><p><strong>Ответ:</strong> за те же деньги можно купить 3,5 кг яблок.</p><p><strong>б)</strong></p><p>Расход краски прямо пропорционален площади окрашиваемой поверхности. Пусть $L_1$ и $W_1$ — длина и ширина первой комнаты, а $S_1$ — её площадь. Тогда $S_1 = L_1 \times W_1$. На покраску этой площади израсходовали 2 кг краски.</p><p>У второй комнаты длина $L_2$ в 1,5 раза меньше, а ширина $W_2$ такая же, как у первой. То есть:</p><p>$L_2 = \frac{L_1}{1,5}$</p><p>$W_2 = W_1$</p><p>Площадь второй комнаты $S_2$ равна:</p><p>$S_2 = L_2 \times W_2 = \frac{L_1}{1,5} \times W_1 = \frac{L_1 \times W_1}{1,5} = \frac{S_1}{1,5}$</p><p>Таким образом, площадь второй комнаты в 1,5 раза меньше площади первой комнаты.</p><p>Следовательно, и краски на её покраску потребуется в 1,5 раза меньше. Рассчитаем необходимое количество краски $K_2$:</p><p>$K_2 = \frac{2 \text{ кг}}{1,5} = \frac{2}{3/2} = 2 \times \frac{2}{3} = \frac{4}{3} \approx 1,33$ кг.</p><p>В наличии есть 1,5 кг краски. Сравним необходимое количество с имеющимся:</p><p>$1,5 \text{ кг} > \frac{4}{3} \text{ кг}$ (поскольку $1,5 = \frac{3}{2} = \frac{9}{6}$, а $\frac{4}{3} = \frac{8}{6}$)</p><p>Так как имеющееся количество краски (1,5 кг) больше, чем необходимое (≈1,33 кг), краски хватит.</p><p><strong>Ответ:</strong> да, хватит.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108654" "type" => "task" ] "previous" => array:2 [ "refs" => "1108652" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1163 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: 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13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1140 #connection: "mysql" #table: "terms" 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#escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1148} "field_class" => Illuminate\Database\Eloquent\Collection {#1149} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1153} "field_author" => Illuminate\Database\Eloquent\Collection {#1150} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_country" => Illuminate\Database\Eloquent\Collection {#1144} "field_city" => Illuminate\Database\Eloquent\Collection {#1143} "field_series" => Illuminate\Database\Eloquent\Collection {#1155} "field_umk" => Illuminate\Database\Eloquent\Collection {#1162} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1164} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1160} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1161} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1159} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\BookPage {#1199 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1097991 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-249" "field_display_title" => "249" "field_folder" => "folder1" "field_image_name" => "249" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Book {#1163} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Element {#1212 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1261142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1261142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1097992" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097990" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1370 #items: array:6 [ 0 => App\Models\Task {#1382 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108648 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-893" "field_display_title" => "893" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1383 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1384 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1385 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1386 …2} "content" => Illuminate\Database\Eloquent\Collection {#1412 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1413 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108648 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-893" "field_display_title" => "893" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1383 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1384 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1385 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1386 …2} "content" => Illuminate\Database\Eloquent\Collection {#1412 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1413 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1411 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108649 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-894" "field_display_title" => "894" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1414 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1415 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1416 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1417 …2} "content" => Illuminate\Database\Eloquent\Collection {#1435 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1442 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108649 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-894" "field_display_title" => "894" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1414 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1415 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1416 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1417 …2} "content" => Illuminate\Database\Eloquent\Collection {#1435 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1442 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1426 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108650 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-895" "field_display_title" => "895" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1427 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1428 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1433 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1432 …2} "content" => Illuminate\Database\Eloquent\Collection {#1440 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1456 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108650 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-895" "field_display_title" => "895" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1427 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1428 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1433 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1432 …2} "content" => Illuminate\Database\Eloquent\Collection {#1440 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1456 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1423 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108651 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-896" "field_display_title" => "896" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1421 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1422 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1439 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1443 …2} "content" => Illuminate\Database\Eloquent\Collection {#1454 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1470 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108651 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-896" "field_display_title" => "896" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1421 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1422 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1439 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1443 …2} "content" => Illuminate\Database\Eloquent\Collection {#1454 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1470 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1419 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-897" "field_display_title" => "897" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1418 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1420 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1453 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1457 …2} "content" => Illuminate\Database\Eloquent\Collection {#1468 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1484 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-897" "field_display_title" => "897" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1418 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1420 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1453 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1457 …2} "content" => Illuminate\Database\Eloquent\Collection {#1468 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1484 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1429 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => "250" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-898" "field_display_title" => "898" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1431 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1430 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1467 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1471 …2} "content" => Illuminate\Database\Eloquent\Collection {#1469 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1452 …2} …1 ] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1097991 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-249" "field_display_title" => "249" "field_folder" => "folder1" "field_image_name" => "249" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1203} "content" => Illuminate\Database\Eloquent\Collection {#1213} "next" => array:2 [ "refs" => "1097992" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097990" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1370} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1108653 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => "250" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-898" "field_display_title" => "898" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1138} "content" => Illuminate\Database\Eloquent\Collection {#1156} "next" => array:2 [ "refs" => "1108654" "type" => "task" ] "previous" => array:2 [ "refs" => "1108652" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195} "page" => array:2 [ "refs" => "1097991" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№898 (с. 249)
Условие. №898 (с. 249)
скриншот условия
898. a) Яблоки подешевели на 20 %. Сколько килограммов яблок можно купить за те же деньги, на которые прежде можно было купить 2,8 кг яблок?
б) Для покраски пола в комнате израсходовали 2 кг краски. Хватит ли 1,5 кг такой краски для покраски пола в комнате, длина которой в 1,5 раза меньше, а ширина такая же?
Решение. №898 (с. 249)
Решение 2 (rus). №898 (с. 249)
а)
Пусть $P_1$ — первоначальная цена яблок за килограмм, а $M_1$ — первоначальное количество яблок, которое можно было купить. Тогда общая сумма денег, потраченная на покупку, составляет $C = P_1 \times M_1$. По условию, $M_1 = 2,8$ кг, значит, $C = P_1 \times 2,8$.
Цена яблок понизилась на 20%. Новая цена $P_2$ составит $100\% - 20\% = 80\%$ от первоначальной цены. Таким образом, $P_2 = P_1 \times (1 - 0,20) = 0,8 \times P_1$.
Теперь нужно найти, какое количество яблок $M_2$ можно купить за ту же сумму денег $C$ по новой цене $P_2$.
$C = P_2 \times M_2$
Приравняем два выражения для стоимости $C$:
$P_1 \times 2,8 = P_2 \times M_2$
Подставим выражение для $P_2$:
$P_1 \times 2,8 = (0,8 \times P_1) \times M_2$
Сократим обе части уравнения на $P_1$ (так как цена не равна нулю):
$2,8 = 0,8 \times M_2$
Отсюда найдем $M_2$:
$M_2 = \frac{2,8}{0,8} = \frac{28}{8} = \frac{7}{2} = 3,5$ кг.
Ответ: за те же деньги можно купить 3,5 кг яблок.
б)
Расход краски прямо пропорционален площади окрашиваемой поверхности. Пусть $L_1$ и $W_1$ — длина и ширина первой комнаты, а $S_1$ — её площадь. Тогда $S_1 = L_1 \times W_1$. На покраску этой площади израсходовали 2 кг краски.
У второй комнаты длина $L_2$ в 1,5 раза меньше, а ширина $W_2$ такая же, как у первой. То есть:
$L_2 = \frac{L_1}{1,5}$
$W_2 = W_1$
Площадь второй комнаты $S_2$ равна:
$S_2 = L_2 \times W_2 = \frac{L_1}{1,5} \times W_1 = \frac{L_1 \times W_1}{1,5} = \frac{S_1}{1,5}$
Таким образом, площадь второй комнаты в 1,5 раза меньше площади первой комнаты.
Следовательно, и краски на её покраску потребуется в 1,5 раза меньше. Рассчитаем необходимое количество краски $K_2$:
$K_2 = \frac{2 \text{ кг}}{1,5} = \frac{2}{3/2} = 2 \times \frac{2}{3} = \frac{4}{3} \approx 1,33$ кг.
В наличии есть 1,5 кг краски. Сравним необходимое количество с имеющимся:
$1,5 \text{ кг} > \frac{4}{3} \text{ кг}$ (поскольку $1,5 = \frac{3}{2} = \frac{9}{6}$, а $\frac{4}{3} = \frac{8}{6}$)
Так как имеющееся количество краски (1,5 кг) больше, чем необходимое (≈1,33 кг), краски хватит.
Ответ: да, хватит.
Другие задания:
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