Answer:
The answer would be C.
Step-by-step explanation:
let's say that C is "x" units farther from B, that means that CB = x, and therefore AC = 1.5x.
![\bf \underset{\leftarrow ~~30~~\to}{\boxed{A}\stackrel{1.5x}{\rule[0.35em]{18em}{0.25pt}}C\stackrel{x}{\rule[0.35em]{10em}{0.25pt}}\boxed{B}} \\\\\\ AB=AC+CB\implies \stackrel{AB}{30}=\stackrel{AC}{1.5x}+\stackrel{CB}{x}\implies 30=2.5x \\\\\\ \cfrac{30}{2.5}=x\implies 12=x \\\\[-0.35em] ~\dotfill\\\\ AC=1.5(12)\implies AC=18~\hspace{8em} CB=x\implies CB=12](https://tex.z-dn.net/?f=%5Cbf%20%5Cunderset%7B%5Cleftarrow%20~~30~~%5Cto%7D%7B%5Cboxed%7BA%7D%5Cstackrel%7B1.5x%7D%7B%5Crule%5B0.35em%5D%7B18em%7D%7B0.25pt%7D%7DC%5Cstackrel%7Bx%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D%5Cboxed%7BB%7D%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3DAC%2BCB%5Cimplies%20%5Cstackrel%7BAB%7D%7B30%7D%3D%5Cstackrel%7BAC%7D%7B1.5x%7D%2B%5Cstackrel%7BCB%7D%7Bx%7D%5Cimplies%2030%3D2.5x%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B30%7D%7B2.5%7D%3Dx%5Cimplies%2012%3Dx%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0AAC%3D1.5%2812%29%5Cimplies%20AC%3D18~%5Chspace%7B8em%7D%20CB%3Dx%5Cimplies%20CB%3D12)
<span>1/4(x + 16) - x =
First, distribute the 1/4.
= 1/4x + 1/4 * 16 - x
= 1/4x + 4 - x
= 1/4x + 4 - 4/4x
= 1/4x - 4/4x + 4
= -3/4x + 4

</span>
1 ft = 12 inches
(1 ft)^3 = (12 inches)^3
1 cubic foot = 1728 cubic inches
You'll multiply by the conversion factor (1278 in^3)/(1 ft^3) to convert from cubic feet to cubic inches. Notice how the cubic feet ft^3 unit is at the bottom of the conversion fraction, so that the cubic feet units cancel.
Answer: A) multiply by 1728
Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4, 
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.