Answer:
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Step-by-step explanation:
Initially, Charlotte owes $7680. She finishes her payments after a total of 6 + 36 = 42 months. Using a simple compounding formula, the amount she owes is worth P at the end of 42 months, where P is:
P = 7680 * (1 + .2045/12)^42 = 15616.67379
Now, the first installment she pays (at the end of six months) is paid 35 months in advance of the end, so it is worth x * (1 + .2375/12)^35 at the end of her loan period.
Similarly, the second installment is worth x * (1 + .2375/12)^34 at the end of the loan period.
Continuing, this way, the last installment is worth exactly x at the end of the loan period.
So, the total amount she paid equals:
x [(1 + .2375/12)^35 + (1 + .2375/12)^34 + ... + (1 + .2375/12)^0]
To calculate this, assume that 1+.2045/12 = a. Then the amount Charlotte pays is:
x (a^35 + a^34 + ... + a^0) = x (a^36 - 1)/(a - 1)
Clearly, this value must equal P, so we have:
x (a^36 - 1)/(a - 1) = P = 15616.67379
Substituting, a = 1 + .2045/12 and solving, we get
x = 317.82
Answer: D
Step-by-step explanation:
Given:
m∠2 is 19° more than m∠1.
To find:
The value of m∠1.
Solution:
Let the measure of ∠1 be x.
Then, 
, it means the sum of m∠1 and m∠2 is 109°.
Divide both sides by 2.
Therefore, the value of m∠1 is 45°.
Answer:
Step-by-step explanation:
Given:
A translation upward or downward affects the 
value of a coordinate while a translation left or right affects the 
value of a coordinate.
We are translating the whole triangle down three units, so we subtract all the values by 3.
We are also translating the whole triangle to left left five units, so we will subtract all the values by 5.
New Coordinates:
