An animal shelter has a total of 140 animals comprised of cats, dogs, and rabbits. if the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter?

What we know:

Total of 140 animals

Rabbits are 5 less than one-half of cats

20 more cats than dogs

Work:

We know that there are 20 more cats than dogs. So we subtract that from 140, making it 120.

- Why: If we subtract 20 from 140, 120, cats and dogs have the same number.

c = cats

The equation is: 140 = (1/2c - 5) + (c - 20) + c

I don't know how to solve it, but this is my way:

Cats: 70 66

Dogs: 40 46

Rabbits: 30 28

I tried sort of guessing. I got near the first time, so I tried reducing it. Second time, it was the answer!

There are 28 rabbits, 66 cat, and 46 dogs.

I'm sorry for not being able to use real work, but I hope this helps a little.

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240