A rug is to fit in a room so that a border of even width is left on all four sides.
If the room is 16 feet by 25 feet and the area of the rug is 220 square feet, how wide will the border
:
Let x = the width of the border around the rug
then
(25-2x) by (16-2x) the dimensions of the rug
:
The area equation
(25-2x)*(16-2x) = 220 sq/ft
FOIL
400 - 50x - 32x + 4x^2 = 220
:
Arrange as a quadratic equation
4x^2 - 82x + 400 - 220 = 0
:
4x^2 - 82x + 180 = 0
Simplify, divide by 2
2x^2 - 41x + 90 = 0
Factor
(2x - 5)(x - 18) = 0
Two solutions
2x = 5
x = 2.5 ft
and
x = 18 ft, obviously this not the solution
;
Border will be 2.5 ft
:
:
Check this by finding the dimension of the rug, and then the area
(25 - 2(2.5))*(16 - 2(2.5)) =
(25 - 5) * (16 - 5) =
20 * 11 = 220
Answer:
CMB=50 ACM=75 ABC=125
Step-by-step explanation:
I know it’s too late for your principal test but i need my points.
Answer:
x=59
Step-by-step explanation:
3x+3=180
3x=177
x=59
Answer:
27.92 units
Step-by-step explanation:
Radius (qr) = r = 16 units
<QŘS = θ = 82°
Length of an arc = (Θ / 360) * 2πr
L = (θ / 360) *2πr
L = (82 / 360) * 2π * 16
L = 0.2777 * 100.53
L = 27.917 units
L = 27.92 unit
Answer:
![x= 6](https://tex.z-dn.net/?f=x%3D%206)
Step-by-step explanation:
RT = RS + ST
![48=5x+3x](https://tex.z-dn.net/?f=48%3D5x%2B3x)
![48=8x](https://tex.z-dn.net/?f=48%3D8x)
Swap sides:
![8x=48](https://tex.z-dn.net/?f=8x%3D48)
Divide both sides by 8:
![\frac{8x}{8} =\frac{48}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B8x%7D%7B8%7D%20%3D%5Cfrac%7B48%7D%7B8%7D)
![x=6](https://tex.z-dn.net/?f=x%3D6)