The figure below shows three quadrilaterals on a coordinate grid:
2 answers:
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Answer:
A) y^3+27
Step-by-step explanation:
There are two ways of solving this problem:
1. Recognizing this as the factored form of the sum of perfect cubes
2. Distribute and add the like terms.
1. In order to distribute we must multiply y by y^2-3y+9, and then 3 by y^2-3y+9:
After we add the positive and negative 3y^2 and 9y, they will cancel out and be gone entirely:
2. You know how you can factor the difference of perfect squares?
As an example:
Well, not many people know this but you can actually factor both the sum and difference of perfect cubes:
Because we have these identities, we can easily establish here that we have the sum of perfect cubes, and that (y+3)(y^2-3y+9)= y^3+3^3 = y^3+27
Answer:
see the procedure
Step-by-step explanation:
Let
x ----> the number of dogs
y ---> the number of cats
we know that
The ratio of the number of dogs to the number of cats is 4:5
so
----> equation A
That means ---> The number of dogs is 4/5 the number of cats
There are 270 animals on the rescue farm
so
----> equation B
Substitute equation A in equation B
solve for y
Find the value of x
<u><em>Verify each statement</em></u>
a) The number of dogs is 4/5 the number of cats
The statement is true (see the explanation)
b) 4/5 of the pets at the farm are dogs
The statement is false
Because
(4/5)(270)=216 dogs
The number of dogs is 120 not 216 (see the explanation)
c) There are exactly 30 more cats than dogs
The statement is true
Because, there are 150 cats and 120 dogs (see the explanation)
d) There are exactly 30 dogs at the farm
The statement is false
Because, there are 120 dogs in the farm (see the explanation)
e) 5/9 of the pets at the farm are cats
The statement is true
Because
(5/9)270=150 cats
The number of cats is 150 (see the explanation)