Answer:
f(x) = 4x + 4
Step-by-step explanation:
When a line is parallel to another line, the slopes are always equal. Therefore, the coefficient for x has to be four. If you multiply the y-coordinate by 4, you get 4. To get 8, you have to add four, so the equation is simply f(x) = 4x+4.
Area of pool edge = Area of big rectangle - Area of the pool
Area of pool edge = Area of the pool = 40 × 60 = 2400 ft²
2400 = Area of big rectangle - 2400
Area of big rectangle = 2400 + 2400
Area of big rectangle = 4800
Length × width = 4800
From the diagram, we need the length to be [x + x] more than the length of the pool, where x is the distance from the pool edge to the patio edge.
We also need the width of the big rectangle to be [[x + x] more than the width of the pool.
Length = 60 + 2x
Width = 40 + 2x
Length × Width = [60+2x] × [40+2x]
4800 = 2400 + 120x + 80x + 4x²
0 = 4x² + 200x - 2400
0 = 4[x² + 50x - 600]
0 = x² + 50x - 600
0 = [x - 60] [x + 10]
x - 60 = 0 OR x + 10 = 0
x = 60 OR x = -10
We can only use the positive value of x since the context is length
Hence, x = 60
B. Negative exponent flip from denominator to numerator and numerator to denominator.
B is the second option.
Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume