An animal shelter spends $5.50 per day to care for each cat and $8.00 per day to care for each dog. Owen noticed that the shelter spent $191.50 caring for cats and dogs on wednesday. How many cats were at the shelter on wednesday?

13, if 28 cats & dogs

Step-by-step explanation:

let c be the no. of cats and d be the no. of dogs

5.50c + 8d = 191.50

Notice that the sum is in 0.5, which is only possible when c is odd.

Try different combinations of c being odd and check which one gives d as a whole number, using

d = (191.50-5.50c)/8

c = 1, d = [191.50-5.50(1)]/8

d = 23.25 (not possible)

c = 3, d = [191.50-5.50(3)]/8

d = 21.875 (not possible)

c = 5, d = [191.50-5.50(5)]/8

d = 20.5 (not possible)

c = 7, d = [191.50-5.50(7)]/8

d = 19.125 (not possible)

c = 9, d = [191.50-5.50(9)]/8

d = 17.75 (not possible)

c = 11, d = [191.50-5.50(11)]/8

d = 16.375 (not possible)

c = 13, d = [191.50-5.50(13)]/8

d = 15 (possible)

So c = 13 and d = 15

10a^3+277a^2-132a-792

step-by-step explanation:

(2a+11)(5a-12)(foil)

=10a^2-24a+55a-132 =10a^2+31a-132

(10a^2+31a-132)(a+6)

=10a^3+60a^2+31a^2+186a^2-132a-792 =10a^3+277a^2-132a-792

i hope this is what you are looking for : )

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: