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10 questions
You are drawing a rectangle with side lengths of (3 – x) inches and (x – 7) inches.
What is the value of x that will maximize this drawing?
What is the maximum area that can be obtained from this drawing?
x = 3
max area = 7 in^{2}
x = 5
max area = 4 in^{2}
x = 7
max area = 3 in^{2}
x = 4
max area = 5 in^{2}
An open box is to be made from a 2-foot by 3-foot rectangular piece of material by cutting equal squares from the corners and turning up the sides. Find the volume of the largest box that can be made in this manner.
0.392 ft^{3}
2.683 ft^{3}
1.056 ft^{3}
0.4140 ft^{3}
Find the area of the triangle with height (x+8) and base (2x+4). ( $A=\frac{1}{2}bh$ )
2x^{2}+20x+32
x^{2}+10x+16
4x^{2}+40x+64
x^{2}+32x+16
Find the volume of a rectangular prism with length (x+2), width (x-4), and height (2x+1).
$2x^3-3x^2-18x-8$
$x^2-2x-8$
$2x^3+5x^2+18x-8y$
$2x^2+4x+6$
A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner and the sides are turned up to form an open rectangular box. What is the maximum volume of the box?
59.259 cm^{3}
23.361 cm^{3}
37.483 cm^{3}
43.961 cm^{3}
You want to create a garden in your backyard. Given are the dimensions of the garden and a border. Determine the area of the gray border surrounding the garden bed.
8x + 24
6x + 32
2x^{2} - 8x + 4
x^{2} + 16x + 16
BONUS QUESTION: The length of your storage crate is 2 meters greater than its width, and its height is 1 meter greater than its width. If the volume if 24 cubic meters, find the width, length, and height.
width = 2m
length = 4m
height = 3m
width = 1m
length = 6m
height = 4m
width = 2m
length = 6m
height = 2m
width = 3m
length = 4m
height = 2m
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