Answer:
121
Step-by-step explanation:
Given
f(x) = - (x + 8)(x - 14) ← expand factors using FOIL
= - (x² - 6x - 112) ← distribute by - 1
= - x² + 6x + 112
Given a quadratic in standard form. y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= - 
f(x) = - x² + 6x + 112 ← is in standard form
with a = - 1 and b = 6, thus
= - 
= 3
Substitute x = 3 into f(x) for corresponding value of y
f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121
vertex = (3, 121 ) ← with y = 121
Answer:
3/2x+2y-7/2
Step-by-step explanation:
Answer:
Step-by-step explanation:
(3,4) ; (6,-1)
slope = y₂ - y₁ / x₂-x₁
= -1 - 4 / 6-3
= -5/3
Answer: 16 men
32 women
38 children
Step-by-step explanation:
Let x represent the number of men in the group.
Let y represent the number if women in the group.
Let z represent the number of children in the group.
A group of 86 people consist of men women and children. This means that
x + y + z = 86 - - - - - - - - - - - - 1
There are twice as many women than there are men. It means that
x = y/2
There are 6 more children than there are women. This means that
z = y + 6
Substituting x = y/2 and z = y + 6 into equation 1, it becomes
y/2 + y + y + 6 = 86
multiplying through by 2, it becomes
y + 2y + 2y + 12 = 172
5y = 172 - 12 = 160
y = 160/5 = 32
x = y/2 = 32/2
x = 16
z = y + 6 = 32 + 6
z = 38
Answer:
B
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = area of triangular face × length
Area of triangle = 
bh ( b is the base and h the height )
Here b = 6 and h = 8, thus
Area = × 6 × 8 = 3 × 8 = 24 units², thus
V = 24 × 20 = 480 units³ → B
