MATHEMATICS MIDDLE SCHOOL

A state lottery commission analyzes the ticket purchasing patterns of its citizens. The following expression is developed to help officials calculate the likely number of people who will buy tickets for a certain size jackpot. 81a^2-36b^2
Factor the expression completely.

Answers

Answer 1
Answer: So,

We first factor out the GCF.

9(9a^2-4b^2)

Now, we notice that the expression is a difference of two perfect squares.
9(3a+2b)(3a-2b)

The expression is now factored completely.
Answer 2
Answer:

9(9a^2-4)

9(3a+2)(3a-2)

I hope this helps!

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can someone explain to me how to use "squared"? I do 2+2 and its four. but when I do 3+3 and I get 6, my brother tells me that's not squared. can you help me out?

Answers

Yes. You've come to the right place. I can help. To "square" a number means to MULTIPLY it by itself . . . NOT add it to itself. '2' is the ONLY number that gives the same result both ways. The square of 3 is 3 times 3 = 9 . The square of 6 is (6 times 6) = 36.

Do natural numbers have multiplicative inverse

Answers

no,because a multiplcative inverse is when your changing a division or multiplcation sign!

Explain how you would create opposite terms for the x-variable in this system.
3x - 6y = -8

-1/3x+ 4y = 6​

Answers

Answer:

Sample Response: To create opposite terms for the x-variable, you need to multiply the second equation by a number that will result in the x term becoming –3x. That number would need to be a multiple of the denominator, which is 3. Multiplying the second equation by 9 would create opposite terms for the x-variable.

Step-by-step explanation:

Answer:

Your answer would be, You can use the Elimination Method, by Multiplying, One or Both Equations by a Constant.

Solve System of Linear Equation:

3x - 6y = -8, -1/4x + 4y = 6 ====> y = 32 /21; x = 8 / 21

Steps:

[ 3x - 6y = -8, -1 / 4x + 4y = 6 ]

Isolate x for 3x - 6y = -8: x = -8 + 6y / 3

3x - 6y = -8

Add 6y both sides:

3x - 6y + 6y = -8 + 6y

Simplify:

3x = - 8 + 6y

Divide Both sides by 3:

3x / x = -8 / 3 + 6y / 3

Simplify:

x = -8 + 6y / 3

Substitute:

x = -8 + 6y / 3

[ 1 / 4 * -8 + 6y / 3 + 4y = 6 ]

Isolate:

-1 / 4 -8 + 6y / 3 + 4y = 6

y = 32 / 21

For x = -8 + 6y / 3

Substitute:

y = 32 / 21

x = -8 + 6 / 3 * 32 / 21

-8 + 6 / 3 * 32 / 21

x = 8 / 21

The Solution to the Systems of Equations are: y = 32 / 21; x = 8 / 21

Hope that helps!!! : )

Carl takes a random sample of 100 students in his school and finds that 72% of the sample prefers pizza over burgers there are 1,500 students in the school based on the sample proportion how many students in the school would be expected to prefer pizza over burgers \\\\ either 72,100,1080,1500

Answers

Out of the 100 people in the sample, 72% said they preferred pizza. That 72% should be the same for the whole school.

1500 × .72 = 1080

about 1080 students in the school prefer pizza

Answer:

it would be 1080

Do 2(x, y) → (3,5).
The point (x,y) is

Answers

Answer:

(1.5, 2.5)

Step-by-step explanation:

(x,y) is being multiplied by 2 to get (3,5). We need to divide it by 2 to find x and y.

3/2= 1.5

5/2=2.5

Thus, the answer is (1.5, 2.5). Hope this helped!

The sales tax rate is 8%. If Jim bought a new Buick and paid a sales tax of $1,930, what was the cost of the Buick before the tax?

Answers

Let the price of the car = x.

8% of the price of the car is $1930.

We now translate the sentence into an equation using x as the unknown amount. Then we solve the equation to find x, the price of the car before tax.

8% * x = 1930

0.08x = 1930

x = 1930/0.08

x = 24,125

Answer: The price of the car before tax is $24,125.
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