3/8=9/24 and 1/6=4/24
9/24+4/24=13/24
Paula spent 13/24 of her allowance on other items.
Answer:
x = 57/28
y = -95/84
z = 97/168
Step-by-step explanation:
Use the application in the next link: https://www.zweigmedia.com/RealWorld/tutorialsf1/scriptpivotold.html
Start with the expanded array:
![\left[\begin{array}{cccc}1&5&8&1\\3&2&2&5\\-2&-7&2&5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C3%262%262%265%5C%5C-2%26-7%262%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
then using the tool provided, make row operations until you find the solution:
r2 = r2-3r1
![\left[\begin{array}{cccc}1&5&8&1\\0&-13&-22&2\\-2&-7&2&5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C0%26-13%26-22%262%5C%5C-2%26-7%262%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r3 = r3+2r1
![\left[\begin{array}{cccc}1&5&8&1\\0&-13&-22&2\\0&3&18&7\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C0%26-13%26-22%262%5C%5C0%263%2618%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r2 = r2*(-1/13)
![\left[\begin{array}{cccc}1&5&8&1\\0&1&22/13&-2/13\\0&3&18&7\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%263%2618%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r1 = r1- r2*5
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&22/13&-2/13\\0&3&18&7\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%263%2618%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r3 = r3+ r2*-3
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&22/13&-2/13\\0&0&168/13&97/13\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%260%26168%2F13%2697%2F13%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r3 = r3*13/168
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&22/13&-2/13\\0&0&1&97/168\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%260%261%2697%2F168%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r2 = r2- r3*22/13
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&0&-95/84\\0&0&1&97/168\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%260%26-95%2F84%5C%5C0%260%261%2697%2F168%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r2 = r2+ r3*6/13
![\left[\begin{array}{cccc}1&0&0&57/28\\0&1&0&-95/84\\0&0&1&97/168\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%2657%2F28%5C%5C0%261%260%26-95%2F84%5C%5C0%260%261%2697%2F168%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Here you have a reduced array an therefore the answers to each variable are on each row:
![\left[\begin{array}{c}x\\y\\z\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D)
Answer:
(7, - 7 )
Step-by-step explanation:
- 4x + y = - 35 → (1)
- 2x - y = - 7 → (2)
adding the 2 equations term by term will eliminate the y- term
(- 4x - 2x) + (y - y) = - 35 - 7
- 6x + 0 = - 42
- 6x = - 42 ( divide both sides by - 6 )
x = 7
substitute x = 7 into either of the 2 equations and solve for y
substituting into (1)
- 4(7) + y = - 35
- 28 + y = - 35 ( add 28 to both sides )
y = - 7
solution is (7, - 7 )
Answer:
the measure of the angle is 72
x=36
Step-by-step explanation:
we can make an algebraic equation using the info given
2x+80=152
2x=72
x=36
the measure of the angle is 72
