Answer:
y = -63
Step-by-step explanation:
y - 15 = -78
Add 15 on both sides to get y alone:
y - 15 + 15 = -78 + 15
y = -63
Answer:
x = 3
Step-by-step explanation:
Given y varies directly as x², then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 27 when x = 3 , then
27 = k × 3² = 9k ( divide both sides by 9 )
3 = k
y = 3x² ← equation of variation
When y = 81, then
81 = 3x² ( divide both sides by 3 )
27 = x² ( take the square root of both sides )
x = 
= 
= 3
Answer: 14x² - 4x - 17
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be
Area = (5x + 4)(3x - 2)
Area = 15x² - 10x + 12x - 8
= 15x² + 2x - 8
The formula for determining the area of a square is expressed as
Area = length²
Length of square patio = x + 3
Area of square patio = (x + 3)(x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
The expression for the area of grass that will be left in the back yard after the patio is built is
15x² + 2x - 8 - (x² + 6x + 9)
= 15x² + 2x - 8 - x² - 6x - 9
= 15x² - x² + 2x - 6x - 8 - 9
= 14x² - 4x - 17
Answer:
2580n -43n^3 - 10000
Step-by-step explanation:
From the question:
q= assembled product
n = Number of employees
q(f) = 60n - n^3
p=g(q)= 43q - 10000
P(q)= 43(60n - n^3) - 10000
P(q) = 2580n - 43n^3 - 10000
Answer:
Step-by-step explanation:
15 ≤ x-2
