Answer:
D
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:
x = 5
Step-by-step explanation:
The interior angles of a triangle <em>always</em> have to add up to 180 degrees.
This means you can form an equation with the three angles you have:
(10x - 4) + (8x + 3) + 91 = 180
Then, solve:
combine like terms
subtract 90 from both sides
divide both sides by 18
What equation describes this variation?
z = kxy
What is the constant of variation?
k = 5
When x = 1 and y = –2, z =
-10
Step by Step Explanation:
With the equation z = kxy and the values for z, x, and y, we can find k.
z = kxy
-75 = (k) (3) (-5)
-75 = (k) (-15)
5 = k
k = 5 (final answer).
To check our work, we just enter all of the values and make sure it adds up.
z = kxy
-75 = (5)(3)(-5)
-75 = 15(-5)
-75 = -75
correct!
Do the same to find the answer for the next part to get -10.
Further proof in the file attached.