Question

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....

Answer 1

Answer:

Width: 5x-2

Height: 6x+1

Step-by-step explanation:

Answer 2

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.