Width = w
Length = 3w - 6
Area = 360
Equation Area = wl
w (3w-6) = 360
3w^2- 6w = 360
3w^2 - 6w - 360 = 0
3 (w^2 - 2w - 120)=0
3(w + 10)(w - 12) = 0
w = -10 & 12
l = 3w-6 = 3 (-10)-6= -30 - 6= -36
l = 3w-6 = 3(12) - 6 = 36-6 = 30
Answer: -10 and 12. Yet, since this is a measurement, it must be positive so 12 ft
Answer:
i got u
Step-by-step explanation:
i got u
ANSWER
![\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28z%20%2B%20%208%20%20%29)
EXPLANATION
We want to factor
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
out of
![\frac{3}{4} z + 6](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206)
The first term is already having a factor of
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
The constant term which is the second term is not having a factor of
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
so we need to use a trick of multiplying and dividing by the same factor to obtain,
![\frac{3}{4} z + 6 = \frac{3}{4} z + \frac{3}{4} \times \frac{6}{ \frac{3}{4} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%5Ctimes%20%20%5Cfrac%7B6%7D%7B%20%5Cfrac%7B3%7D%7B4%7D%20%7D%20)
We can now factor
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
out of the right hand side to obtain,
![\frac{3}{4} z + 6 = \frac{3}{4} (z + \frac{6}{ \frac{3}{4} } )](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28z%20%2B%20%20%5Cfrac%7B6%7D%7B%20%5Cfrac%7B3%7D%7B4%7D%20%7D%20%29)
Let us rewrite the right most fraction using the normal division symbol.
![\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \div \frac{3}{4} )](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28z%20%2B%20%206%20%5Cdiv%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%29)
We simplify to obtain,
![\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \times \frac{4}{3} )](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28z%20%2B%20%206%20%20%5Ctimes%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%29)
This further gives us,
![\frac{3}{4} z + 6 = \frac{3}{4} (z + 2 \times 4 )](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20z%20%2B%206%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28z%20%2B%20%202%20%5Ctimes%20%204%20%20%29)
Answer: V = (12in - 2*x)*(8 in - 2*x)*x
Step-by-step explanation:
So we have a rectangular cardboard sheet, and we cut four squares of side length x in each corner so we can make a box.
Remember that for a box of length L, width W and height H, the volume is:
V = L*W*H
In this case, the length initially is 12 inches, but we remove (from each end) x inches of the length, then the length of the box will be:
L = 12 in - 2*x
For the width we have a similar case:
W = 8in - 2*x
And te height of the box will be equal to x, then:
H = x
This means that the volume is:
V = (12in - 2*x)*(8 in - 2*x)*x
Here we can see the connection between the cutout and the volume of the box
Answer:
<em>y = x ÷ 2</em>
Step-by-step explanation:
We are given a table of values, which will be represented as ordered pairs (x,y) below:
(2,1) (4,2) (8,4) (10,5) (16,8)
We are required to select one of the functions that match the numeric relationship between x and y.
We could test them one by one, but at simple observation, we can note the values of y are half of the values of x:
2/2=1
4/2=2
And so on. Thus the only function that divides the value of x by 2 to find the value of y is:
y = x ÷ 2