Answer:
17/6 in
Step-by-step explanation:
Since we know that the formula of Volume of prism is L*W*H
And we know the area of the base as L*W, or in this case 24
We divide the volume or 68 by 24 the base to get height of 17/6
Step-by-step explanation:
For every month increase by 1, the amount of dollars increase by 7. (from 65 to 72, 72 to 79, 79 to 86 etc.)
Hence at Month 7, there will be 100 + 7 = 107 dollars.
Answer:
![\large\boxed{y-4=\dfrac{9}{2}(x+5)}\\\boxed{9x-2y=-53}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7By-4%3D%5Cdfrac%7B9%7D%7B2%7D%28x%2B5%29%7D%5C%5C%5Cboxed%7B9x-2y%3D-53%7D)
Step-by-step explanation:
The point-slope form of an equation of a line:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
m - slope
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (-7, -5) and (-5, 4).
Calculate the slope:
![m=\dfrac{4-(-5)}{-5-(-7)}=\dfrac{9}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B4-%28-5%29%7D%7B-5-%28-7%29%7D%3D%5Cdfrac%7B9%7D%7B2%7D)
Put it and coordinates of the point (-5, 4) to the equation:
![y-4=\dfrac{9}{2}(x-(-5))](https://tex.z-dn.net/?f=y-4%3D%5Cdfrac%7B9%7D%7B2%7D%28x-%28-5%29%29)
→ <em>the point-slope form</em>
Convert to the standard form <em>Ax + By = C :</em>
<em>multiply both sides by 2</em>
<em>use the distributive property</em>
<em>add 8 to both sides</em>
<em>subtract 9x from both sides</em>
<em>change the signs</em>
→ <em>the standard form</em>
Answer: ![f(n)= 2.5(3)^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3D%202.5%283%29%5E%7Bn-1%7D)
Step-by-step explanation:
The given sequence : 2.5,7.5,22.5,67.5,202.5
here first term (a)= 2.5
Second term = 7.5
Third term = 22.5 and so on
The difference between the two consecutive terms is increasing but have common ratio as:
Common ratio (r) = ![\dfrac{Second\ term}{First\ term}=\dfrac{7.5}{2.5}=3](https://tex.z-dn.net/?f=%5Cdfrac%7BSecond%5C%20term%7D%7BFirst%5C%20term%7D%3D%5Cdfrac%7B7.5%7D%7B2.5%7D%3D3)
So this sequence follows geometric progression.
nth term in GP = ![ar^{n-1}](https://tex.z-dn.net/?f=ar%5E%7Bn-1%7D)
Required function notation: ![f(n)=ar^{n-1}= 2.5(3)^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3Dar%5E%7Bn-1%7D%3D%202.5%283%29%5E%7Bn-1%7D)
i.e. the function notation of given sequence : ![f(n)= 2.5(3)^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3D%202.5%283%29%5E%7Bn-1%7D)
Answer:
VWU and FWT are vertical angles.
<u>Their measure is same and:</u>
- VWU = 1/2(mVU + mFT)
- x = 1/2(174° + 52°)
- x = 113°