Answer:
114.
Step-by-step explanation:
- remove parenthesis
- multiply the numbers 6 x 3 + 18
18 + 4 + 2 x 3 x 15 + 2
multiply the numbers 2 x 3 x 15 + 90
18 + 4 + 2 + 90 + 2
add the numbers : 18 + 4 + 2 + 90 + 2
= 114!
Answer:
The expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Step-by-step explanation:
The formula to compute the future value is:
![FV=PV[1+\frac{r}{100}]^{n}](https://tex.z-dn.net/?f=FV%3DPV%5B1%2B%5Cfrac%7Br%7D%7B100%7D%5D%5E%7Bn%7D)
PV = Present value
r = interest rate
n = number of periods.
It is provided that $5,000 were deposited now and $3,000 deposited after 6 years at 10% compound interest. The amount of time the money is invested for is 14 years.
The expression to compute the amount in the investment account after 14 years is,
![FV=5000[1+\frac{10}{100}]^{14}+3000[1+\frac{10}{100}]^{14-6}\\FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14%7D%2B3000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14-6%7D%5C%5CFV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D)
The future value is:
![FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D%5C%5C%3D18987.50%2B6430.77%5C%5C%3D25418.27)
Thus, the expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
The plan that cannot be used to prove that the two triangles are congruent based in the given information is: b. ASA.
<h3>How to Prove Two Triangles are Congruent?</h3>
The following theorems can be used to prove that two triangles are congruent to each other:
- SSS: This theorem proves that two triangles are congruent when there's enough information showing that they have three pairs of sides that are congruent to each other.
- ASA: This theorem shows that of two corresponding angles of two triangles and a pair of included congruent sides are congruent to each other.
- SAS: This theorem shows that if two triangles have two pairs of sides and a pair of included angle that are congruent, then both triangles are congruent to each other.
The two triangles only have a pair of corresponding congruent angles, while all three corresponding sides are shown to be congruent to each other.
This means that ASA which requires two pairs of congruent angles, cannot be used to prove that both triangles are congruent.
The answer is: b. ASA.
Learn more about congruent triangles on:
brainly.com/question/1675117
#SPJ1
Answer:
193
Step-by-step explanation:
Merry Christmas
First we calculate the tax on the item:
11.4%($160) = 11.4(160)/100 = 18.24
hence the tax for the item is $18.24
The total price for the item would be:
160 + 18.24 = 178.24
hence the total price for the item including tax is:
$<span>178.24</span>
