You can reduce the expression by cancelling out common factor
:
Part (a)
The picture alone, without the frame, is 16 by 20
When accounting for the frame, the larger rectangle is 16+2x by 20+2x
We add up all four sides to get the perimeter
(16+2x)+(20+2x)+(16+2x)+(20+2x)
8x+72
or you can use this perimeter of a rectangle formula
P = 2(L+W)
P = 2(20+2x+16+2x)
P = 2(4x+36)
P = 8x+72
Answer: 8x+72
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Part (b)
Multiply the length and width to find the area of the rectangle.
area = length*width
A = L*W
A = (20+2x)*(16+2x)
A = 20(16+2x) + 2x(16+2x)
A = 320+40x + 32x + 4x^2
A = 4x^2 + 72x + 320
Answer: 4x^2 + 72x + 320
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Part (c)
Plug x = 2 into the perimeter equation found in part (a)
P = 8x+72
P = 8*2+72
P = 16+72
P = 88
Now plug x = 2 into the area equation found in part (b)
A = 4x^2 + 72x + 320
A = 4(2)^2 + 72(2) + 320
A = 4(4) + 72(2) + 320
A = 16 + 144 + 320
A = 160+320
A = 480
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Answers:
Perimeter = 88 inches
Area = 480 square inches
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Answer: 1) b = 2
2) c = 20
Explanation:
I hope this helped!
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Let the constant of variation be c.
We are given that y varies inversely with 2.5x, this means that:
y = (c) / (2.5x)
This can be written as:
2.5xy = c
Now, we a re given that y = 5.6 at x = 30.
Substitute with these values in the equation to get the value of c as follows:
2.5xy = c
2.5(30)(5.6) = c
c = 420
Therefore, the equation that describes the relation is:
2.5xy = 420
