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Номер 15, страница 14 - гдз по математике 5 класс учебник Бунимович, Дорофеев
Авторы: Бунимович Е. А., Дорофеев Г. В., Суворова С. Б., Кузнецова Л. В., Минаева С. С., Рослова Л. О.
Тип: Учебник
Серия: сферы
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: оранжевый с компасом
ISBN: 978-5-09-105798-0
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Глава 1. Линии. 2. Прямая. Части прямой. Ломаная - номер 15, страница 14.
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" => 534154 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-15" "field_display_title" => "15" "field_outside_task" => null "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 534063 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Линии" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => 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 } "field_page_start" => "7" "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 {#1086 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 59 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Математика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "математику" "field_creative_case" => "математикой" "field_dative_case" => "математике" "field_genitive_case" => "математики" "field_nominative_case" => "математика" "field_prepositional_case" => "математике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "matematika" ] #original: array:10 [ "id" => 6484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Математика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "математику" "field_creative_case" => "математикой" "field_dative_case" => "математике" "field_genitive_case" => "математики" "field_nominative_case" => "математика" "field_prepositional_case" => "математике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "matematika" ] #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_class" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #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" => 5445 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "5" "field_cases" => array:6 [ "field_accusative_case" => "пятый" "field_creative_case" => "пятым" "field_dative_case" => "пятому" "field_genitive_case" => "пятого" "field_nominative_case" => "пятый" "field_prepositional_case" => "пятом" ] "field_translit" => "pjatyj" ] #original: array:6 [ "id" => 5445 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "5" "field_cases" => array:6 [ "field_accusative_case" => "пятый" "field_creative_case" => "пятым" "field_dative_case" => "пятому" "field_genitive_case" => "пятого" "field_nominative_case" => "пятый" "field_prepositional_case" => "пятом" ] "field_translit" => "pjatyj" ] #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_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #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_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:6 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "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 {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "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 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "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 => "*" ] } 3 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "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 => "*" ] } 4 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "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 => "*" ] } 5 => App\Models\Term {#1062 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "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 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #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_country" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #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_city" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #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_series" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #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" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1076 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null …1 ] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #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_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с компасом" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "941" "field_priority" => "10" "field_default_folder" => "/matematika_05/bunimovich-u23/" "field_isbn" => "978-5-09-105798-0" "field_cover" => array:1 [ 0 => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399" "alt" => "" "width" => "1200" "height" => "1604" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_url" => "/5-klass/matematika/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Term {#1083 #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" => 50 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "оранжевый" "field_cases" => array:6 [ …6] "field_translit" => "oranzhevyy" ] #original: array:6 [ "id" => 50 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "оранжевый" "field_cases" => array:6 [ …6] "field_translit" => "oranzhevyy" ] #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 "breadcrumbs" => array:3 [ "class" => 376 "subject" => 544 "class_subject" => 398 ] ] #original: array:50 [ "id" => 59 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1063} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_country" => Illuminate\Database\Eloquent\Collection {#1066} "field_city" => Illuminate\Database\Eloquent\Collection {#1068} "field_series" => Illuminate\Database\Eloquent\Collection {#1070} "field_umk" => Illuminate\Database\Eloquent\Collection {#1072} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1073} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1075} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1078} "field_under_the_edition_degree" => null "field_cover_description" => "с компасом" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "941" "field_priority" => "10" "field_default_folder" => "/matematika_05/bunimovich-u23/" "field_isbn" => "978-5-09-105798-0" "field_cover" => array:1 [ 0 => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399" "alt" => "" "width" => "1200" "height" => "1604" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1079} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1080} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1081} "field_url" => "/5-klass/matematika/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1082} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 376 "subject" => 544 "class_subject" => 398 ] ] #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 {#1084 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534063 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Линии" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "7" "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 {#1086} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1084} ] #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 {#1121 #items: array:2 [ 0 => App\Models\Branch {#1129 #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" => 534063 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Линии" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "7" "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534063 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Линии" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "7" "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132} ] #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 {#1133 #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" => 534065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Прямая. Части прямой. Ломаная" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "12" "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 {#1135 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Прямая. Части прямой. Ломаная" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134} "field_page_start" => "12" "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 {#1135} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1136} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1112 #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" => 646083 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Edition {#1111 #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" => 1542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ …1] #escapeWhenCastingToString: false } "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" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 1542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110} "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" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1108} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106} "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" => "534154" "type" => "task" ] "text" => "<p><strong>15</strong> Начертите две пересекающиеся прямые $a$ и $b$ и обозначьте точку их пересечения буквой $D$. Проведите через точку $D$ ещё одну прямую, отличную от $a$ и $b$. Сколько получилось лучей с началом в точке $D$? Сколько можно построить прямых, проходящих через точку $D$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "15-1.jpg" "alt" => null "width" => "2078" "height" => 321 "path" => "/media/matematika_05/bunimovich-u23/0-00/15-1.webp?ts=1737374009" ] ] ] #original: array:7 [ "id" => 646083 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102} "task" => array:2 [ "refs" => "534154" "type" => "task" ] "text" => "<p><strong>15</strong> Начертите две пересекающиеся прямые $a$ и $b$ и обозначьте точку их пересечения буквой $D$. Проведите через точку $D$ ещё одну прямую, отличную от $a$ и $b$. Сколько получилось лучей с началом в точке $D$? Сколько можно построить прямых, проходящих через точку $D$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "15-1.jpg" "alt" => null "width" => "2078" "height" => 321 "path" => "/media/matematika_05/bunimovich-u23/0-00/15-1.webp?ts=1737374009" ] ] ] #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 {#1104 #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" => 1468495 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Edition {#1105 #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" => 5408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ …1] #escapeWhenCastingToString: false } "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" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1100} "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" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099} "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" => "534154" "type" => "task" ] "text" => "<p><strong>Сколько получилось лучей с началом в точке D?</strong></p><p>По условию, мы имеем две пересекающиеся прямые $a$ и $b$. Точка их пересечения — $D$. Затем через точку $D$ мы проводим еще одну, третью прямую (назовем ее $c$), которая не совпадает с первыми двумя.</p><p>Каждая прямая, проходящая через точку, делится этой точкой на два луча. Лучи, исходящие из одной точки и лежащие на одной прямой, называются дополнительными.</p><ul><li>Прямая $a$ проходит через точку $D$ и образует два луча с началом в этой точке.</li> <li>Прямая $b$ проходит через точку $D$ и также образует два луча с началом в этой точке.</li> <li>Третья прямая $c$ проходит через точку $D$ и добавляет еще два луча.</li></ul><p>Так как все три прямые различны, то и все образованные ими лучи будут различными. Чтобы найти общее количество лучей, нужно умножить количество прямых на количество лучей, которые образует каждая прямая:</p><p>$3 \text{ прямые} \times 2 \text{ луча/прямая} = 6 \text{ лучей}$</p><p>Таким образом, получилось 6 лучей с началом в точке $D$.</p><p>Ответ: 6 лучей.</p><p><strong>Сколько можно построить прямых, проходящих через точку D?</strong></p><p>Через любую одну точку на плоскости можно провести бесконечное множество прямых. Это одна из аксиом геометрии.</p><p>Можно представить себе точку $D$ как центр, из которого исходят прямые во всех возможных направлениях. Вращая прямую вокруг точки $D$, мы каждый раз будем получать новую прямую, проходящую через эту же точку. Поскольку существует бесконечно много положений для такой вращающейся прямой, то и количество прямых, которые можно провести через точку $D$, бесконечно.</p><p>Ответ: Бесконечно много.</p>" ] #original: array:6 [ "id" => 1468495 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096} "task" => array:2 [ "refs" => "534154" "type" => "task" ] "text" => "<p><strong>Сколько получилось лучей с началом в точке D?</strong></p><p>По условию, мы имеем две пересекающиеся прямые $a$ и $b$. Точка их пересечения — $D$. Затем через точку $D$ мы проводим еще одну, третью прямую (назовем ее $c$), которая не совпадает с первыми двумя.</p><p>Каждая прямая, проходящая через точку, делится этой точкой на два луча. Лучи, исходящие из одной точки и лежащие на одной прямой, называются дополнительными.</p><ul><li>Прямая $a$ проходит через точку $D$ и образует два луча с началом в этой точке.</li> <li>Прямая $b$ проходит через точку $D$ и также образует два луча с началом в этой точке.</li> <li>Третья прямая $c$ проходит через точку $D$ и добавляет еще два луча.</li></ul><p>Так как все три прямые различны, то и все образованные ими лучи будут различными. Чтобы найти общее количество лучей, нужно умножить количество прямых на количество лучей, которые образует каждая прямая:</p><p>$3 \text{ прямые} \times 2 \text{ луча/прямая} = 6 \text{ лучей}$</p><p>Таким образом, получилось 6 лучей с началом в точке $D$.</p><p>Ответ: 6 лучей.</p><p><strong>Сколько можно построить прямых, проходящих через точку D?</strong></p><p>Через любую одну точку на плоскости можно провести бесконечное множество прямых. Это одна из аксиом геометрии.</p><p>Можно представить себе точку $D$ как центр, из которого исходят прямые во всех возможных направлениях. Вращая прямую вокруг точки $D$, мы каждый раз будем получать новую прямую, проходящую через эту же точку. Поскольку существует бесконечно много положений для такой вращающейся прямой, то и количество прямых, которые можно провести через точку $D$, бесконечно.</p><p>Ответ: Бесконечно много.</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" => "534155" "type" => "task" ] "previous" => array:2 [ "refs" => "534153" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1117 #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" => 949308 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-14" "field_display_title" => "14" "field_folder" => "1" "field_image_name" => "14" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1095 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Element {#1043 #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" => 1124590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1124590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 …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" => "949309" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949307" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:7 [ 0 => App\Models\Task {#1209 #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" => 534153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1210 …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 {#1211 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1212 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1213 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1221 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1210 …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 {#1211 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1212 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1213 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1221 …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 {#1216 #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" => 534154 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-15" "field_display_title" => "15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1223 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1219 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217 …2} "content" => Illuminate\Database\Eloquent\Collection {#1220 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1218 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534154 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-15" "field_display_title" => "15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1223 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1219 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217 …2} "content" => Illuminate\Database\Eloquent\Collection {#1220 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1218 …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 {#1228 #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" => 534155 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-16" "field_display_title" => "16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null 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"edition_groups" => Illuminate\Database\Eloquent\Collection {#1230 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1232 …2} "content" => Illuminate\Database\Eloquent\Collection {#1234 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1240 …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 {#1235 #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" => 534156 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[] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1247 #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" => 534157 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-18" "field_display_title" => "18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239 …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 {#1254 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1250 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1264 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534157 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-18" "field_display_title" => "18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239 …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 {#1254 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1250 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1264 …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 {#1259 #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" => 534158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null 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+timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1271 #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" => 534159 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-20" "field_display_title" => "20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 …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 {#1278 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1272 …2} "content" => Illuminate\Database\Eloquent\Collection {#1273 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1288 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534159 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-20" "field_display_title" => "20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 …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 {#1278 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1272 …2} "content" => Illuminate\Database\Eloquent\Collection {#1273 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1288 …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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 949308 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-14" "field_display_title" => "14" "field_folder" => "1" "field_image_name" => "14" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1097} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090} "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 {#1095} "content" => Illuminate\Database\Eloquent\Collection {#1041} "next" => array:2 [ "refs" => "949309" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949307" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1195} ] #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" => 534154 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "14" 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#dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№15 (с. 14)
Условие. №15 (с. 14)
скриншот условия
15 Начертите две пересекающиеся прямые $a$ и $b$ и обозначьте точку их пересечения буквой $D$. Проведите через точку $D$ ещё одну прямую, отличную от $a$ и $b$. Сколько получилось лучей с началом в точке $D$? Сколько можно построить прямых, проходящих через точку $D$?
Решение 2. №15 (с. 14)
Сколько получилось лучей с началом в точке D?
По условию, мы имеем две пересекающиеся прямые $a$ и $b$. Точка их пересечения — $D$. Затем через точку $D$ мы проводим еще одну, третью прямую (назовем ее $c$), которая не совпадает с первыми двумя.
Каждая прямая, проходящая через точку, делится этой точкой на два луча. Лучи, исходящие из одной точки и лежащие на одной прямой, называются дополнительными.
- Прямая $a$ проходит через точку $D$ и образует два луча с началом в этой точке.
- Прямая $b$ проходит через точку $D$ и также образует два луча с началом в этой точке.
- Третья прямая $c$ проходит через точку $D$ и добавляет еще два луча.
Так как все три прямые различны, то и все образованные ими лучи будут различными. Чтобы найти общее количество лучей, нужно умножить количество прямых на количество лучей, которые образует каждая прямая:
$3 \text{ прямые} \times 2 \text{ луча/прямая} = 6 \text{ лучей}$
Таким образом, получилось 6 лучей с началом в точке $D$.
Ответ: 6 лучей.
Сколько можно построить прямых, проходящих через точку D?
Через любую одну точку на плоскости можно провести бесконечное множество прямых. Это одна из аксиом геометрии.
Можно представить себе точку $D$ как центр, из которого исходят прямые во всех возможных направлениях. Вращая прямую вокруг точки $D$, мы каждый раз будем получать новую прямую, проходящую через эту же точку. Поскольку существует бесконечно много положений для такой вращающейся прямой, то и количество прямых, которые можно провести через точку $D$, бесконечно.
Ответ: Бесконечно много.
Другие задания:
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