The answer is the slope m=1
x = 6
Step-by-step explanation:
It's based on similarity of triangles
DEF ~ △XYZ
![\implies \mathsf{ \frac{DE }{ XY } = \frac{EF}{YZ} = \frac{ FD}{ZX}}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%20%5Cfrac%7BDE%20%7D%7B%20XY%20%7D%20%3D%20%20%5Cfrac%7BEF%7D%7BYZ%7D%20%3D%20%20%5Cfrac%7B%20FD%7D%7BZX%7D%7D)
The sides should be taken in order, like the triangles start with DE and XY so, we'll proportionate DE and XY and then the next two sides and so on.
I'm using
to get the value of x.
[You can use any two fractions out of the three given above. ]
![\implies \mathsf{ \frac{10}{x - 1} = \frac{8}{4} }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%20%5Cfrac%7B10%7D%7Bx%20-%201%7D%20%3D%20%20%5Cfrac%7B8%7D%7B4%7D%20%20%7D)
![\implies \mathsf{ \frac{10}{x - 1} = 2 }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%20%5Cfrac%7B10%7D%7Bx%20-%201%7D%20%3D%20%202%20%20%7D)
![\implies \mathsf{ 10 = 2 (x - 1) }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%2010%20%3D%20%202%20%28x%20-%201%29%20%7D)
![\implies \mathsf{ 10 = 2 x - 2 }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%2010%20%3D%20%202%20x%20-%202%20%7D)
![\implies \mathsf{ 10 + 2= 2 x }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%2010%20%20%2B%202%3D%20%202%20x%20%20%7D)
![\implies \mathsf{ 1 2= 2 x }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%201%202%3D%20%202%20x%20%20%7D)
![\implies \mathsf{ x = 6 }](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Cmathsf%7B%20x%20%3D%206%20%7D)
Hence, the value of x is 6.
It would be 70r if you are using distributive property
we know that
The simple interest formula is equal to
![I=Prt](https://tex.z-dn.net/?f=I%3DPrt)
where
P is the Principal amount of money to be invested
I is the amount of money in interest
r is the rate of interest
t is Number of Time Periods
in this problem we have
![t=2\ years\\ I=\$14.65\\r=0.025](https://tex.z-dn.net/?f=t%3D2%5C%20years%5C%5C%20I%3D%5C%2414.65%5C%5Cr%3D0.025)
substitute in the formula above and solve for P
![14.65=P(0.025)(2)](https://tex.z-dn.net/?f=14.65%3DP%280.025%29%282%29)
![P=14.65/[(0.025)(2)]](https://tex.z-dn.net/?f=P%3D14.65%2F%5B%280.025%29%282%29%5D)
![P=\$293](https://tex.z-dn.net/?f=P%3D%5C%24293)
therefore
<u>the answer is</u>
![\$293](https://tex.z-dn.net/?f=%5C%24293)