Answer:
1/9
Step-by-step explanation:
x^-2
We know that a^-2 = 1/ a^2
1/x^2
Let x = -3
1/ (-3)^2
1/9
Answer:
<h2>x = 9, y = -72/5</h2>
Step-by-step explanation:
Given the 2 by 2 matrix
, 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>
Answer:
Option D) 47.25 in
Step-by-step explanation:
we know that
The equation of a exponential decay function is equal to

where
y is the total length
x is the number of pieces of ribbon
a is the initial value
r is the rate of change
we have

substitute


we have that
For x=0 ----->
For x=1 ----> 
For x=2 ----> 
For x=3 ---->
For x=4 ----> 
For x=5 ----> 
Adds the length of the first 6 pieces of ribbon

1) since its pairs your working with what you do is y2-y1 and x2-x1 so to start its 9-(-2) which equals 11 then -4-(-3) which equals -1, 11/-1 is -11 I hope this is helpful . . .
2) to start its y=mx+b so since your slope is 2 and your pair is (0,-3) the equation would be -3=2(0)+b since 2(0) equals 0 your left with -3=0+b subtract 0 over answers b=-3
There are 198.628 centimeters in 78.2 inches. Hope I helped love! <3