Answer:
a = 2, b = - 3, c = - 8
Step-by-step explanation:
Expand f(x) = a(x + b)² + c and compare coefficients of like terms, that is
a(x + b)² + c ← expand (x + b)² using FOIL
= a(x² + 2bx + b²) + c ← distribute parenthesis by a
= ax² + 2abx + ab² + c
Compare like terms with f(x) = 2x² - 12x + 10
Compare coefficients x² term
a = 2
Compare coefficients of x- term
2ab = - 12, substitute a = 2
2(2)b = - 12
4b = - 12 ( divide both sides by 4 )
b = - 3
Compare constant term
ab² + c = 10 , substitute a = 2, b = - 3
2(- 3)² + c = 10
18 + c = 10 ( subtract 18 from both sides )
c = - 8
Then a = 2, b = - 3, c = - 8
1 gallon = 16 cups. She is making 2 gallons so needs 32 total cups.
The ratio is 4:3:1
Add the ratios: 4+ 3 + 1 = 8
Divide total cups by total ratio:
32/8 =4
Now multiply that by each portion of the ratio:
Grape juice = 4 x 4 = 16 cups
Pineapple juice = 3x4 = 12 cups
Cider = 1x 4 = 4 cups
She needs 12 cups of pineapple juice.
Answer:
Step-by-step explanation:
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
x² + 9x - 22
Factors of c (-22):
1 × -22 or -1 × 22
2 × -11 or -2 × 11
Sum of factors:
1 + (-22) = -21 or -1 + 22 = 21
2 + (-11) = -9 or -2 + 11 = 9
Table:
Hope this helps!
Select 4 from 9, and 3 from 8. Multiply together.
C(9,4)*C(8,3)
=9!/(4!5!) * 8!/(3!5!)
=7056
Answer:
When sides are doubled, the area of new triangle will always be 4 times the original, the change in area will be 3 times. Hence the % change will always be 300% irrespective of the type of triangle.
Step-by-step explanation:
