If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore
ΔABC is similar to ΔADE.
The sides of smaller triangle are in proportion with sides of bigger triangle.
Therefore we have the equation:

We have AC = x, AE = x + 15, AB = 8, AD = 8 + 10 = 18.
Substitute:
<em>cross multiply</em>
<em>use distributive property a(b + c) = ab + ac</em>
<em>subtract 8x from both sides</em>
<em>divide both sides by 10</em>

<h2>Answer: AC = 12</h2>
Answer:
(-infinity to infinity)
Step-by-step explanation:
Answer:
$
After 3 years
Step-by-step explanation:
Use I P R T it's a method for simple interest
I = Interest
P = Amount of money
R = Percent in decimal
T = Time in years
Answer:
I =
(we dont know yet)
P = $
R =
% 
T =

Steps:
1. Set up your numbers with the method I P R T.
2. $65 will be your amount of money.
3. 7.5% needs to be converted because you will need to multiply later on in the problem. Simply move 2 places to the left to convert your percent into a decimal.
4. They want to know the total amount of money in his account at the end of 3 years. So 3 years will be your time in years.
5. After setting up your problem you need to multiply your Amount of money x percent as decimal x time in years.

6. After you find your interest you need to add your amount of money + interest.
Money after 3 years
hope this helped
Answer:
5
Step-by-step explanation:
We are given the geometric series:
-1, - 2, - 4, - 8.......
In the geometric series above, the common ratio = second term/first term = -2/-1
= 2
Where common ratio is greater than 1(r >1)
The sum of a geometric progression =
Sn = a(rⁿ -1)/r - 1
In the question we are asked to find the number of term = n
Sn = -31
a = -1
r = 2
Hence,
-31 = -1(2ⁿ - 1)/2 - 1
-31 = -1(2ⁿ - 1)
-31 = -2ⁿ + 1
2ⁿ = 1 + 31
2ⁿ = 32
2ⁿ = 2^5
n = 5
Therefore, the number of terms(n) = 5
The answer to the question is a=3