Question

1. Спростіть вираз (7а+2b)^2-(за-b) (4а +5b). 2. Розкладіть на множники:1) 36m^2n^3-49m^4n;2) 50+20х+2х^2.3. Графік функції у = kx + b перетинає осі координат у точ- ках А (2; 0) і В (0; -4). Знайдіть значення k i b.4. Розв'яжіть систему рівнянь {3x-y=17{2x+3y=-7.5. Знайдіть чотири послідовних натуральних числа таких, що добуток другого та четвертого із цих чисел на 31 біль- ший за добуток першого та третього.6. Розв'яжіть рівняння x^2 + y^2 -8х+12y+52=0. +1​ Смотреть ответ shabelnik83 shabelnik83 1. Спростіть вираз (7а+2b)^2-(за-b) (4а +5b). Розкриваємо квадрат: (7а+2b)^2 = (7а)^2 + 2 * (7а) * (2b) + (2b)^2 = 49а^2 + 28ab + 4b^2 Розкриваємо дужки: (49а^2 + 28ab + 4b^2) - (4а + 5b) = 49а^2 + 28ab + 4b^2 - 4а - 5b 2. Розкладіть на множники: 1) 36m^2n^3-49m^4n: 36m^2n^3-49m^4n = (6mn)^2 - (7mn)^2 = (6mn - 7mn)(6mn + 7mn) = (mn)(-mn)(13mn) = -13m^2n^3 2) 50+20х+2х^2: 2х^2 + 20х + 50 = 2(х^2 + 10х + 25) = 2(х + 5)^2 3. Графік функції у = kx + b перетинає осі координат у точ- ках А (2; 0) і В (0; -4). Знайдіть значення k і b. Точка А (2; 0) належить графіку функції, отже підставимо значення (2, 0) у рівняння функції: 0 = 2k + b Точка В (0; -4) належить графіку функції, отже підставимо значення (0, -4) у рівняння функції: -4 = 0 + b b = -4 Замінюємо значення b у першому рівнянні: 0 = 2k - 4 2k = 4 k = 2 Отже, значення k = 2 і b = -4. 4. Розв'яжіть систему рівнянь: {3x-y=17 {2x+3y=-7 Можна використати метод заміщення або метод додавання. Використаємо метод додавання: 3 * (2x + 3y) = -7 * 3 6x + 9y = -21 2 * (3x - y) = 17 * 2 6x - 2y = 34 При додаванні отримаємо: 6x + 9y + 6x - 2y = -21 + 34 12x + 7y = 13 Після розв'язування цього рівняння отримаємо: 12x = 13 - 7y x = (13 - 7y)/12 Підставимо значення х у одне з початкових рівнянь: 3 * (13 - 7y)/12 - y = 17 39 - 21y - 12y = 204 -33y = 165 y = -5 Підставимо значення y у вираз для х: x = (13 - 7*(-5))/12 x = 2 Отже, розв'язок системи рівнянь x = 2 і y = -5. 5. Знайдіть чотири послідовних натуральних числа таких, що добуток другого та четвертого із цих чисел на 31 більший за добуток першого та третього. Позначимо послідовні числа як n, n+1, n+2, n+3. За умовою задачі: (n+1)(n+3) - n(n+2) = 31 (n^2 + 4n + 3) - (n^2 + 2n) = 31 4n + 3 - 2n = 31 2n = 28 n = 14 Чотири послідовних натуральних числа: 14, 15, 16, 17. 6. Розв'яжіть рівняння x^2 + y^2 -8x+12y+52=0. Перетворимо рівняння, щоб отримати квадратичний тричлен у вигляді повного квадрату: x^2 - 8x + y^2 + 12y + 52 = 0 (x^2 - 8x + 16) + (y^2 + 12y + 36) + 52 - 16 - 36 = 0 (x - 4)^2 + (y + 6)^2 = 0 Отже, розв'язком рівняння є точка (4, -6). Новые вопросы в Алгебра 4. Найдите сумму многочленов. 1) 0, 2x ^ 2 + 0, 4y ^ 2 * va + 0, 3x ^ 2 + 0, 5y ^ 2 3) 5a ^ 2 * b - a * b ^ 2 * va - 3a ^ 2 * b + 4a * b ^ 2 2) 0,6x4 … +0,7y va 1, 8x ^ 4 - 4, 3y ^ 5 4) - 4a ^ 3 * b + 5a ^ 4 * b ^ 2 va 6a ^ 3 * b - 7a ^ 4 * b ^ 2 5) 2 1/3 * a ^ 2 - 4 3/5 * b ^ 2 * va * 6 2/3 * a ^ 2 + 7 2/5 * b ^ 2 6) 3/4 * a ^ 4 - 2/5 * b ^ 4 * va - 2/5 * a ^ 4 + 1/4 * b ^ 4 Знайдіть суму й різницю многочленів: 1)-2x2+x+13 i-3x²+x-15; 2) 7x-2xy+3y i-8xy+7x-3y, 3) 5xy²+2xyi-24 x⁴y²-3xy4. 4) d26c² i d+5c2. x^2=5x-6 найти корень найдите множество точек координатной плоскости, которое задано системой неравенств: y≥ x^2 - 2y - x ≤ 2​ помогите пожалуйста ​ Предыдущий Следующий Вместе мы знаем больше КОМПАНИЯ Блог Карьера Условия пользования Авторское право Политика конфиденциальности Предпочтения cookie-файлов СООБЩЕСТВО Сообщество Brainly Brainly для школ и учителей Сообщество родителей Кодекс чести Правила сообщества Brainly Insights Стань помощником ПОМОЩЬ Зарегистрируйся Центр помощи Центр 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Answer 1

2 * (3x - y) = 17 * 2 6x - 2y = 34

Now, we can add the two equations together:

(6x + 9y) + (6x - 2y) = (-21) + 34 12x + 7y = 13

Now, we have a new equation:

12x + 7y = 13

Let's solve this equation for one variable and then substitute it back to find the other variable. We can isolate y:

7y = 13 - 12x y = (13 - 12x)/7

Now, we can substitute this expression for y into one of the original equations to find the value of x. Let's use the first equation:

3x - y = 17 3x - [(13 - 12x)/7] = 17

Now, solve for x:

21x - 13 + 12x = 119

Combine like terms:

33x - 13 = 119

Add 13 to both sides:

33x = 132

Divide by 33:

x = 132/33 x = 4

Now that we have found the value of x, we can substitute it back into the expression for y:

y = (13 - 12x)/7 y = (13 - 12(4))/7 y = (13 - 48)/7 y = (-35)/7 y = -5

So, the solution to the system of equations is:

x = 4 y = -5

5. To find four consecutive natural numbers such that the product of the second and fourth is 31 greater than the product of the first and third, we can set up an equation. Let the first number be "n," then the four consecutive numbers are n, n+1, n+2, and n+3.

According to the problem, the product of the second and fourth is 31 greater than the product of the first and third:

(n + 1)(n + 3) = 31 + n(n + 2)

Now, let's solve this equation:

n^2 + 4n + 3 = 31 + n^2 + 2n

Subtract n^2 from both sides to simplify:

4n + 3 = 31 + 2n

Subtract 2n from both sides:

2n + 3 = 31

Subtract 3 from both sides:

2n = 28

Divide by 2:

n = 14

So, the first number is 14. The consecutive numbers are 14, 15, 16, and 17.

6. To solve the equation x^2 + y^2 - 8x + 12y + 52 = 0, complete the square for both x and y:

x^2 - 8x + y^2 + 12y + 52 = 0

Now, complete the square for x and y separately:

For x: x^2 - 8x = (x^2 - 8x + 16) - 16

For y: y^2 + 12y = (y^2 + 12y + 36) - 36

Add the completed square terms to both sides:

(x^2 - 8x + 16) + (y^2 + 12y + 36) - 16 - 36 + 52 = 0

Now, simplify:

(x - 4)^2 + (y + 6)^2 - 16 - 36 + 52 = 0

(x - 4)^2 + (y + 6)^2 - 0 = 0

Now, the equation is in the form of the equation of a circle:

(x - 4)^2 + (y + 6)^2 = 0

The center of the circle is at (4, -6), and the radius is 0. So, this represents a single point:

(x, y) = (4, -6)