Sharon is paving a rectangular concrete driveway on the side of her house. The area of the driveway is 5x^2 + 43x - 18, and the length of the driveway is x + 9.

Additionally, Sharon plans to install a carport over a small portion of the driveway. The volume that the carport can enclose is 48x^3 + 68x^2 - 8x - 3, and the area of driveway beneath the carport is 8x^2 + 10x - 3.

Determine the width of the entire driveway and height of the carport in terms of x. Replace the values of m and b to complete the expression that represents the width of the entire driveway on the first line, and then replace the values of m and b to complete the expression that represents the height of the carport on the second line.

You have to type the answer in mx+b

im just trying to graduate ...

Question

Krystal Hickman

Mathematics

30 April, 17:29

Sharon is paving a rectangular concrete driveway on the side of her house. The area of the driveway is 5x^2 + 43x - 18, and the length of the driveway is x + 9.

Additionally, Sharon plans to install a carport over a small portion of the driveway. The volume that the carport can enclose is 48x^3 + 68x^2 - 8x - 3, and the area of driveway beneath the carport is 8x^2 + 10x - 3.

Determine the width of the entire driveway and height of the carport in terms of x. Replace the values of m and b to complete the expression that represents the width of the entire driveway on the first line, and then replace the values of m and b to complete the expression that represents the height of the carport on the second line.

You have to type the answer in mx+b

im just trying to graduate ...

+5

Answers (1)

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Russell · Answer 1

The width of the driveway is 5x-2.

The height of the carport is 6x+1.

We complete polynomial long division for both of these.

For the driveway:

Dividing 5x²+43x-18 by x+9, we first see how many times x will go into 5x². It goes in 5x times; we write this in the division problem above 43x. Multiplying back through,

5x (x+9) = 5x²+45x. This goes below 5x²+43x. We now subtract:

5x²+43x - (5x²+45x) = - 2x; this goes below the 45x we wrote earlier. Bring down the - 18.

Now we see how many times x goes into - 2x; it goes - 2 times. This goes beside our 5x in our answer at the top. Multiplying back through,

-2 (x+9) = - 2x-18. This goes below our - 2x-18 we had, and gives us an answer of 5x-2 with a remainder of 0.

For the carport:

To divide 48x³+68x²-8x-3 by 8x²+10x-3, we see how many times 8x² will go into 48x³. It will go 6x times; write this above - 8x. Multiplying back through,

6x (8x²+10x-3) = 48x³+60x²-18; write this below 48x³+68x²-8x. Now subtract:

48x³+68x²-8x - (48x³+60x²-18) = 8x²+10x; this goes below our 48x³+60x²-18. Bring down the - 3.

Now we want to see how many times 8x² will go into 8x². It goes 1 time; write this beside our 6x at the top. Multiplying back through,

1 (8x²+10x-3) = 8x²+10x-3; write this below the 8x²+10x-3 we have already down. When we subtract these, we get a remainder of 0, with our answer up top as 6x+1.