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andrezito [222]
3 years ago
14

(Constructed Response) Determine whether the binomial, 9x² - 49, is a difference of

Mathematics
1 answer:
vovikov84 [41]3 years ago
8 0

Answer: It is a difference of two squares, and it factors to (3x-7)(3x+7)

=============================================================

Explanation:

We can write the 9x^2 as (3x)^2 since

(3x)^2 = (3x)*(3x) = (3*3)*(x*x) = 9x^2

The 49 can be written as 7^2 because 7^2 = 7*7 = 49.

This means 9x^2 - 49 is the same as (3x)^2 - 7^2. We have a difference of two squares.

The difference of squares factoring rule is

a^2 - b^2 = (a-b)(a+b)

which we have a = 3x and b = 7 in this case

So,

a^2 - b^2 = (a-b)(a+b)

(3x)^2 - 7^2 = (3x-7)(3x+7)

9x^2 - 49 = (3x-7)(3x+7)

Side note: This is the same as (3x+7)(3x-7). We can multiply two numbers in any order.

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Step-by-step explanation:

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3 years ago
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When a number is tripled and 8 is subtracted from the result, the answer is 16. What is the number?
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6 0
2 years ago
At an animal shelter, there are 15 dogs and 12 cats.
Bond [772]

Answer:

Dogs: 44.44 Cats: 55.556

Step-by-step explanation:

*this is <em>only </em>if you are allowed to use a calculator*

1. You have to add the total of the cats and dogs

Why? Here, let me put it this way. You have a test with two sections: math and science. If there are 2 Maths Questions and 2 Science questions, what percent of the test are math questions? You would not say 2/2 and say 100. You would say 2/4 because it is obvious. You do the same in this case but it is not as noticeable because you are dealing with bigger numbers.

15 + 12 = <u>27</u>.

2. Solve

<u>a. </u>There are 15 dogs and 12 cats that makes up 27 pets total.

So you have to do 12/27 for cats,

15/27 for dogs. The fractions equal one and It shows you how much of one is there compared to the total.

<u>b. </u><u><em>Simplify</em></u>

You can simplify these fractions:

for 12/27, divide the numerator and the denominator by 3.

You get 4/9

Divide 15/27 for dogs by 3 as well to get 5/9.

5+4 is 9, which means that I am doing the math correctly.

According to the calculator, 5/9 is 55.556, and 4/9 is 44.444

They should be accurate because there are more dogs than cats and the percentage for dogs are higher. Hence, this is correct.

Cats = 4/9 = 44.444%

Dogs = 5/9 = 55.556%

Hope this helps :)

-jp524

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2 years ago
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Between the time Iko woke up and lunchtime, the temperature rose by 11°. Then by the time he went to bed, the temperature droppe
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Step-by-step explanation:

Lets say that the original temperature was "x."

The temperature rose by 11 degrees so it is now at 11+x.

Then the temperature fell by 14 degrees so you subtract. 11+x-14

11-14= -3 so you subtract 3 degrees from the original temperature and there fore the relative temperature is -3

I hope this helps!!!

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