Answer:
g(-2) = -7
Step-by-step explanation:
To find g(-2), plug -2 into g(x).
g(x) = -4x² + 3x + 15
g(-2) = -4(-2)² + 3(-2) + 15
g(-2) = -4(4) + 3(-2) + 15
g(-2) = -16 + (-6) + 15
g(-2) = -1 + (-6)
g(-2) = -7
Answer:
Step-by-step explanation:
10, 24 and 38 are composite numbers.
(10 can be divided by 5 and 2; 24 can be divided by 8, 3, 12 and 2; 38 can be divided by 19 and 2).
The others are prime numbers.
Answer:
(-5, 2)
Step-by-step explanation:
<u>plug x into the equation x - 5y = -15</u>
-5 - 5y = -15
add 5 to both sides: -5y = -10
divide by -5: y = 2
Answer:
10m x 15m
Step-by-step explanation:
You are given some information.
1. The area of the garden: A₁ = 150m²
2. The area of the path: A₂ = 186m²
3. The width of the path: 3m
If the garden has width w and length l, the area of the garden is:
(1) A₁ = l * w
The area of the path is given by:
(2) A₂ = 3l + 3l + 3w + 3w + 4*3*3 = 6l + 6w + 36
Multiplying (2) with l gives:
(3) A₂l = 6l² + 6lw + 36l
Replacing l*w in (3) with A₁ from (1):
(4) A₂l = 6l² + 6A₁ + 36l
Combining:
(5) 6l² + (36 - A₂)l +6A₁ = 0
Simplifying:
(6) l² - 25l + 150 = 0
This equation can be factored:
(7) (l - 10)*(l - 15) = 0
Solving for l we get 2 solutions:
l₁ = 10, l₂ = 15
Using (1) to find w:
w₁ = 15, w₂ = 10
The two solutions are equivalent. The garden has dimensions 10m and 15m.
