Divide 5/8 in 1 5/8 first. and get 0.625 now take the one and get 1.625.
now take the 8 1/4 and do the same to get 8.25
now divide 8.25 by 1.625.
and get 5.07692308
so the answer is 5
we are given
first term is
![a_1=42](https://tex.z-dn.net/?f=%20a_1%3D42%20)
common ratio is
![r=\frac{3}{4}](https://tex.z-dn.net/?f=%20r%3D%5Cfrac%7B3%7D%7B4%7D%20%20)
now, we can find nth term
![a_i=a_1(r)^{i-1}](https://tex.z-dn.net/?f=%20a_i%3Da_1%28r%29%5E%7Bi-1%7D%20)
now, we can plug values
![a_i=42(\frac{3}{4})^{i-1}](https://tex.z-dn.net/?f=%20a_i%3D42%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bi-1%7D%20)
now, we can write in sigma form
![sum=\sum _{i=1}^{\infty }\:42(\frac{3}{4})^{i-1}](https://tex.z-dn.net/?f=%20sum%3D%5Csum%20_%7Bi%3D1%7D%5E%7B%5Cinfty%20%7D%5C%3A42%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bi-1%7D%20)
now, we can find sum
we can use formula
![sum=\frac{a}{1-r}](https://tex.z-dn.net/?f=%20sum%3D%5Cfrac%7Ba%7D%7B1-r%7D%20%20)
now, we can plug values
we get
![sum=\frac{42}{1-\frac{3}{4}}](https://tex.z-dn.net/?f=%20sum%3D%5Cfrac%7B42%7D%7B1-%5Cfrac%7B3%7D%7B4%7D%7D%20%20)
![sum=168](https://tex.z-dn.net/?f=%20sum%3D168%20%20)
so, option-D.................Answer
Answer: A
Step-by-step explanation: The student gathers an extra 5,174.11 with the interest.
The sides of the triangle are 5√2 , 5√2 and 10.
<h3>What is a Triangle ?</h3>
A triangle is a polygon with three sides , three vertices and three angles , When one angle is equal to 90 degree , it is called a Right Angled Triangle.
It is given that two angles given is 45 and 45 degree each so by using trigonometric ratios the sides can be calculated.
From the data given in the image
sin 45 ° = 5√2 / x
x = 5√2 / sin 45°
x = 10
The hypotenuse = 10
From The Pythagoras theorem
10² = (5√2)² + y²
y = (5√2) unit
Therefore the sides are 5√2 , 5√2 and 10.
To know more about Triangle
brainly.com/question/2773823
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