Answer:
D) 1/4
Step-by-step explanation:
To solve this, first lets figure out what this variable is. We know we must multiply by t. Well, looking at it, we know that t is one. So lets plug that in.
2*1/2^3(1)
Now we need to figure out what the exponent is that 2 will be raised to. To find that, find out what 3 times one is.
2*1/2^3
Now we need to solve the exponent.
2*1/8
Remember, 2 cubed is eight.
Now we need to find out what 2*1/8 is. To solve this more easily, I am going to turn two into a fraction. This will give us 2/1*1/8. Now we cross multiply, multiplying the numerators by the numerators, and the denominators by the denominators. Remember, the numerator is the top number, and the denominator is the bottom number.
If we do that, we get:
2/8
If we simplify it, we get 1/4. So the asnwer is D) 1/4
Step 1
<u>Find the slope of the line PQ</u>
we know that
the formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
we have
![P(-3,-3)\\Q(3,-1)](https://tex.z-dn.net/?f=P%28-3%2C-3%29%5C%5CQ%283%2C-1%29)
substitute the values
![m=\frac{-1+3}{3+3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%2B3%7D%7B3%2B3%7D)
![m=\frac{2}{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B6%7D)
![m=\frac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D)
Step 2
Find the equation of the line that passes through point R ans is parallel to line PQ
we know that
If two lines are parallel, then their slopes are the same
The equation of the line into point-slope form is equal to
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=\frac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D)
![(x1,y1)=R(1,1)](https://tex.z-dn.net/?f=%28x1%2Cy1%29%3DR%281%2C1%29)
substitute the values
![y-1=\frac{1}{3}(x-1)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B1%7D%7B3%7D%28x-1%29)
Step 3
we know that
The point on the y-axis that is on the line
is equal to the y-intercept of the line
The y-intercept is the value of y when the value of x is equal to zero
so
For
find the value of y in the linear equation
![y-1=\frac{1}{3}(0-1)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B1%7D%7B3%7D%280-1%29)
![y-1=-\frac{1}{3}](https://tex.z-dn.net/?f=y-1%3D-%5Cfrac%7B1%7D%7B3%7D)
![y=1-\frac{1}{3}](https://tex.z-dn.net/?f=y%3D1-%5Cfrac%7B1%7D%7B3%7D)
![y=\frac{2}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B3%7D)
The point that is on the y-axis is ![(0,\frac{2}{3})](https://tex.z-dn.net/?f=%280%2C%5Cfrac%7B2%7D%7B3%7D%29)
therefore
<u>the answer is the option A</u>
![(0,\frac{2}{3})](https://tex.z-dn.net/?f=%280%2C%5Cfrac%7B2%7D%7B3%7D%29)
see the attached figure to better understand the problem
Take Ms.Barton plus her three neighbors which makes 4 and divide it by the $439.20 each person would pay $190.80 equally