Answer:
B
Step-by-step explanation:
It is complementary because adding DEQ and REQ together adds up to 90 degrees
Answer:
Step-by-step explanation:
The word problem describes two relationships between the numbers of cookies baked. When b and f represent the numbers of cookies baked by Bill and Felicia, respectively, those relationships are ...
- Bill bakes 3 times as many cookies as Felicia. (b = 3f)
- Felicia bakes 24 fewer cookies than Bill. (f = b-24)
Take the augmented matrix,
![\left[\begin{array}{ccc|c}2&1&-3&-20\\1&2&1&-3\\1&-1&5&19\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D2%261%26-3%26-20%5C%5C1%262%261%26-3%5C%5C1%26-1%265%2619%5Cend%7Barray%7D%5Cright%5D)
Swap the row 1 and row 2:
![\left[\begin{array}{ccc|c}1&2&1&-3\\2&1&-3&-20\\1&-1&5&19\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%262%261%26-3%5C%5C2%261%26-3%26-20%5C%5C1%26-1%265%2619%5Cend%7Barray%7D%5Cright%5D)
Add -2(row 1) to row 2, and -1(row 1) to row 3:
![\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&-3&4&22\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%262%261%26-3%5C%5C0%26-3%26-5%26-14%5C%5C0%26-3%264%2622%5Cend%7Barray%7D%5Cright%5D)
Add -1(row 2) to row 3:
![\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&9&36\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%262%261%26-3%5C%5C0%26-3%26-5%26-14%5C%5C0%260%269%2636%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 3 by 1/9:
![\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%262%261%26-3%5C%5C0%26-3%26-5%26-14%5C%5C0%260%261%264%5Cend%7Barray%7D%5Cright%5D)
Add 5(row 3) to row 2:
![\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&0&6\\0&0&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%262%261%26-3%5C%5C0%26-3%260%266%5C%5C0%260%261%264%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 2 by -1/3:
![\left[\begin{array}{ccc|c}1&2&1&-3\\0&1&0&-2\\0&0&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%262%261%26-3%5C%5C0%261%260%26-2%5C%5C0%260%261%264%5Cend%7Barray%7D%5Cright%5D)
Add -2(row 2) and -1(row 3) to row 1:
![\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%260%260%26-3%5C%5C0%261%260%26-2%5C%5C0%260%261%264%5Cend%7Barray%7D%5Cright%5D)
So we have 
.
201 minutes because 6 multiplied by 33.5 = 201 minutes
Hmmm, I think it’s 17. Three quarters of 128 is 96. 96 minus 37 is 59. And then 1/3 of 96 is 32, so 59 minus 32 is 17. Then there remains 17 students! So 17 students have horses. I hope this helped!
