Could someone answer the question with the photo linked below? Then explain how to solve it?
1 answer:
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Answer:
<h2>1. x = 4</h2><h2>2. x = 20</h2>Step-by-step explanation:
1.
ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:
We have:
AC = 1 + 4 = 5
AJ = 1
AB = 1 + x
AK = 1
Substitute:
<em>subtract 1 from both sides</em>
2.
ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:
We hve:
VU = x + 8
VM = x
VT = 49
VN = 49 - 14 = 35
Substitute:
<em>cross multiply</em>
<em>use the distributive property a(c + b) = ab + ac</em>
<em>subtract 35x from both sides</em>
<em>divide both sides by 14</em>
To solve this we are going to use the future value of annuity due formula: ![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
is the future value
is the periodic deposit
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of deposits per year
We know for our problem that
and 
. To convert the interest rate to decimal form, we are going to divide the rate by 100%: 
. Since Ruben makes the deposits every 6 months, 
. The interest is compounded semiannually, so 2 times per year; therefore, .
Lets replace the values in our formula:
![FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%20%29%2A420%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%29%5E%7B%282%29%2815%29%7D-1%20%7D%7B%20%5Cfrac%7B01%7D%7B2%7D%20%7D%20%5D)
We can conclude that the correct answer is <span>$29,299.53</span>
where
We know for our problem that
Lets replace the values in our formula:
We can conclude that the correct answer is <span>$29,299.53</span>