Answer: 5, because if x=5 then the denominator would be equal to 0 which is not possible.
Let's look at the picture, let's imagine that the gray line is the perimeter fence and that the red OR the blue is the one dividing it. We can see that the blue line is longer than the red one, so it will be advantageous, to have a bigger area, to have the dividing fence the smallest possible.
Let's say then that the width (W) is bigger (or equal) to the length (L), so we have:
![W \geq L W+W+L+L+L=240 2W+3L=240 W=\frac{240-3L}{2}](https://tex.z-dn.net/?f=W%20%5Cgeq%20L%0A%0AW%2BW%2BL%2BL%2BL%3D240%0A%0A2W%2B3L%3D240%0A%0AW%3D%5Cfrac%7B240-3L%7D%7B2%7D)
The area is W*L, so we have
![A=W*L=L*\frac{240-3L}{2}=\frac{-3}{2}(L^2-80L)=\frac{-3}{2}L(L-80)](https://tex.z-dn.net/?f=A%3DW%2AL%3DL%2A%5Cfrac%7B240-3L%7D%7B2%7D%3D%5Cfrac%7B-3%7D%7B2%7D%28L%5E2-80L%29%3D%5Cfrac%7B-3%7D%7B2%7DL%28L-80%29)
this function is a parabola facing down, its zeros are 0 and 80, therefore its maximum is when L=40
hence, L=40 and W=(240-120)/2=60
It will be a rectangle, measuring 60x40 and the divinding fence will be 40
Here you would want to use the sine function, since it’s making a triangle with the ground, and length of the string, the height to the kite. This can be found by 65sin(70°) which is ≈ 61.08 meters
Answer: He ran 8 miles on week 5, which was an improvement of 6.4 miles compared to the 1.6 miles he ran on the first week,
Step-by-step explanation:
In the fifth week, the ratio of the number of miles he ran to the number of miles he walked improved to 8:5
Nash ran 8 miles in 5 weeks.
In 1 week he ran 1.6 miles
8 - 1.6 = 6.4
Given:
Figure of similar triangles.
To find:
The value of x and the measure of NR.
Solution:
In triangle RST and RMN,
(Vertically opposite angles)
(Alternate interior angles)
(By AA property of similarity)
We know that, corresponding sides of similar triangles are proportional.
![\dfrac{RS}{RM}=\dfrac{RT}{RN}](https://tex.z-dn.net/?f=%5Cdfrac%7BRS%7D%7BRM%7D%3D%5Cdfrac%7BRT%7D%7BRN%7D)
![\dfrac{40}{8}=\dfrac{60}{2x-2}](https://tex.z-dn.net/?f=%5Cdfrac%7B40%7D%7B8%7D%3D%5Cdfrac%7B60%7D%7B2x-2%7D)
![5=\dfrac{60}{2x-2}](https://tex.z-dn.net/?f=5%3D%5Cdfrac%7B60%7D%7B2x-2%7D)
![2x-2=\dfrac{60}{5}](https://tex.z-dn.net/?f=2x-2%3D%5Cdfrac%7B60%7D%7B5%7D)
On further simplification, we get
![2x=12+2](https://tex.z-dn.net/?f=2x%3D12%2B2)
![x=\dfrac{14}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B14%7D%7B2%7D)
![x=7](https://tex.z-dn.net/?f=x%3D7)
The value of x is 7.
Now,
![NR=2x-2](https://tex.z-dn.net/?f=NR%3D2x-2)
![NR=2(7)-2](https://tex.z-dn.net/?f=NR%3D2%287%29-2)
![NR=14-2](https://tex.z-dn.net/?f=NR%3D14-2)
![NR=12](https://tex.z-dn.net/?f=NR%3D12)
Therefore, the value of x is 7 and the measure of NR is 12 units.