Respuesta :
The width of the driveway is 5x-2 and the height of the carport is 6x+1.
The area of a rectangle is given by length * width. Since the area is 5x²+43x-18 and the length is x+9, to find the width, we divide:
The first term of the quotient will be the number of times x goes into 5x². It goes 5x times; multiply this by the divisor, and we have 5x²+45x to write under the first two terms of the dividend.
Subtracting these, we have -2x left over; bring down the -18. The second term of the quotient will be the number of times x+9 goes into -2x-18; it goes -2 times. Multiply this by the divisor, and we have -2x-18 with no remainder. This gives the quotient 5x-2.
The volume of the carport is given by the area of the base * the height; since the volume is 48x³+68x²-8x-3 and the area of the base is 8x²+10x-3, we divide to get the height.
The first term of the quotient will be the number of times 8x² goes into 48x³. It goes 6x times; multiply this by the divisor and we have 48x³+60x² to write under the first two terms of the dividend.
Subtract these and we have 8x²+10x left over; bring down the -3. The second term of the quotient will be the number of times 8x² goes into 8x²; it goes 1 time. Multiply this by the divisor and we have 8x²+10x-3 with no remainder. This makes the height 6x-3.
The area of a rectangle is given by length * width. Since the area is 5x²+43x-18 and the length is x+9, to find the width, we divide:
The first term of the quotient will be the number of times x goes into 5x². It goes 5x times; multiply this by the divisor, and we have 5x²+45x to write under the first two terms of the dividend.
Subtracting these, we have -2x left over; bring down the -18. The second term of the quotient will be the number of times x+9 goes into -2x-18; it goes -2 times. Multiply this by the divisor, and we have -2x-18 with no remainder. This gives the quotient 5x-2.
The volume of the carport is given by the area of the base * the height; since the volume is 48x³+68x²-8x-3 and the area of the base is 8x²+10x-3, we divide to get the height.
The first term of the quotient will be the number of times 8x² goes into 48x³. It goes 6x times; multiply this by the divisor and we have 48x³+60x² to write under the first two terms of the dividend.
Subtract these and we have 8x²+10x left over; bring down the -3. The second term of the quotient will be the number of times 8x² goes into 8x²; it goes 1 time. Multiply this by the divisor and we have 8x²+10x-3 with no remainder. This makes the height 6x-3.
