Step-by-step explanation:
25 - 2(5 + 4x)
= 25 - 10 - 8x (Distributive Property)
= 15 - 8x.
Hourly wages.
She worked for 75 hours and makes $9 per hour.
Multiply:
You are correct, $675 is our answer.
Simplify n + -2 to n - 2
(n - 2)(n + 4) = 27
Expand
n^2 + 4n - 2n - 8 = 27
Simplify n^2 + 4n - 2n - 8 to n^2 + 2n - 8
n^2 + 2n - 8 = 27
Move all terms to one side
n^2 + 2n - 8 - 27 = 0
Simplify n^2 + 2n - 8 - 27 to n^2 + 2n - 35
n^2 + 2n - 35 = 0
Factor n^2 + 2n - 35
(n - 5)(n + 7) = 0
Solve for n
<u>n = 5, -7</u>
The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.
The dimensions of your box will be 8 ft square by 4 ft high.
_____
If the base dimension is x ft, the area (quantity of material) is
... a = x² + 4x(256/x²)
... a = x² + 1024x⁻¹
Then the derivative of area with respect to x is
... a' = 2x -1024x⁻²
Setting this derivative to zero and solving for x gives the value of x for minimum area.
... 0 = 2x -1024/x²
... 512 = x³
... x = 8 . . . . . . . . same as above.
Answer: 124
Step-by-step explanation: 7^2=49; 13^2=169; 19^2=361. Only 124 cannot be expressed as a square of an integer.
