Answer:the cost of each CD for a member is $5.25
Step-by-step explanation:
The membership costs $22 per year, and then a member can buy CDs at a reduced price.
Let x represent the cost of each CD for a member.
Let n represent the number of CDs that each member buys. This means that the total cost of buying n CDs for a member for a year would be
22 + nx
If a member buys 17 CDs in one year, the cost is $111.25. This means that
17x + 22 = 111.25
17x = 111.25 - 22 = 89.25
x = 89.25/175 = 5.25
Answer:
Step-by-step explanation:
We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 5655
r = 1.4% = 1.4/100 = 0.14,
a) Therefore, the equation that estimates the population t years after 2010 is
A = 5655(1 + 0.14)^t
A = 5655(1.14)^t
b) in 2022, the number of years t = 2022 - 2010 = 12
Therefore,
A = 5655(1.14)^12
A = 27245
Answer 5
Step-by-step explanation:
6/12=.5
.5*10=5
Your answer is false. hope that helped
Answer:
<h2>x = 9, y = -72/5</h2>
Step-by-step explanation:
Given the 2 by 2 matrix ![A = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
, we are to find the value of x and y for the expression A² = A to be true.
First we need to find A² by multiplying the same matrix together
![A^2 = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right] \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\\\ \ we \ normally \ multiply \ the \ rows \ of \ the \ first \ matrix \ with \ the \ column \ of \ the \ second \\\\A^2 = \left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right]\\\\Since \ A^2 = A,\ hence;\\\\\left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right] = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\](https://tex.z-dn.net/?f=A%5E2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%20%5C%20we%20%5C%20normally%20%5C%20multiply%20%5C%20the%20%5C%20rows%20%5C%20of%20%5C%20the%20%5C%20first%20%5C%20matrix%20%5C%20with%20%5C%20the%20%5C%20column%20%5C%20of%20%5C%20the%20%5C%20second%20%5C%5C%5C%5CA%5E2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%5E2%2B5y%265x-40%5C%5Cxy-8y%265y%2B64%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CSince%20%5C%20A%5E2%20%3D%20A%2C%5C%20hence%3B%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%5E2%2B5y%265x-40%5C%5Cxy-8y%265y%2B64%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C)
Equating the first row and second column of both matrices together, we will have;
5x-40 = 5
add 40 to both sides of the equation
5x-40+40 = 5+40
5x = 45
x = 45/5
x = 9
Similarly, we will equate the second row and second column of both matrices to have;
5y+64 = -8
Subtract 64 from both sdies
5y+64-64 = -8-64
5y = -72
y = -72/5
<em>Hence the value of x is 9 and y is -72/5</em>
