MATHEMATICS MIDDLE SCHOOL

20 POINTS!A circle is cut out of a piece of plywood that is 10 in. square. The scrap is thrown away
What is the area of the circle.
How many square inches are thrown away?

Answers

Answer 1
Answer:
The piece of plywood is a square, 10 inches on each side.
Its area is (10 x 10) = 100 square inches.

You can cut a circle out of it with any size you want, as long as
the diameter of the circle is not more than 10 inches.  You didn't
tell us what size circle, so I'll assume that you cut out the biggest
possible circle.

Diameter = 10 inches
Radius = 5 inches

Area of any circle is (pi) x (radius)²

           Area = (pi) x (5)²

           Area = (pi) x (25) = 78.5 square inches .

The rest of the plywood is scrap.

You discard  (100 - 78.5) = 21.5 square inches.

(By the way ... you cut out a disk, not a circle.)

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Emilia bought 9/12 pound of sliced salami at the deli counter.Which of the following decimals did the scale show?0.25
0.34
0.7
0.75

Answers

To start this problem, what we need to do is try to simplify the fraction into one we might know already. The best way to go about doing this is to see if we can divide the top and bottom by any of the same numbers. 

We can divide 9 by 1, 3, and 9
We can divide 12 by 1, 3, 4, and 12

Looking back over the  numbers, we can see that both 9 and 12 are divisible by 3, so if we divide both of them by 3, we will get a new fraction! This fraction will be 3/4.

Our next step is to see if we know what 3/4 is. I know 1/4 is .25 because the coin called a quarter is 25 cents, so if I had 3 quarters, I would have 75 cents, so I know know that 9/12 = 3/4 = .75!

Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8 3x + 3y = 0 7x − y = 8 3x + 3y = 0 −7x − y = 8 3x + 3y = 0 −7x + 7y = 8 3x + 3y = 0 −4x + 7y = 8

Answers

Answer:

A.

3x + 3y = 0

7x − y = 8

Step-by-step explanation:

Given

3x + 3y = 0

-4x + 4y = -8

Required

Find the equivalent

To solve for the equivalent we simply solve for x and y in the given equation.

Subtract 3x from both sides in 3x + 3y = 0

3x - 3x + 3y = 0 - 3x

3y = -3x

Multiply both sides by ⅓

⅓ * 3y = -3x * ⅓

y = -x

Substitute -x for y in -4x + 4y = -8

-4x + 4(-x) = -8

-4x -4x = -8

-8x = -8

Multiply both sides by -⅛

-⅛ * -8x = -⅛ * -8

x = 1

Recall that y = -x

y = -1

So, we have that x = 1 and y = -1

We'll substitute these values in the list of options;

A.

3x + 3y = 0

7x − y = 8

7(1) - -(1) = 8

7 + 1 = 8 ----- This is equivalent

B.

3x + 3y = 0

−7x − y = 8

-7(1) - (-1) = 8

-7 + 1 = 8

-6 ≠ 8 .... This is not an equivalent expression

C.

3x + 3y = 0

−7x + 7y = 8

-7(1) + 7(-1) = 8

-7 -7 = 8

-14 ≠ 8 .... This is also not an equivalent expression

D.

3x + 3y = 0

-4x + 7y = 8

-4(1) + 7(-1) = 8

-4 -7 = 8

-11 ≠ 8 -_- This is also not an equivalent expression

Answer:

A is the correct one

Step-by-step explanation:

What is the unit rate for a 13 ounce box of cereal that costs $3.99

Answers

Answer:

.31

Step-by-step explanation:

You do 3.99 divided by 13 to get the price of one

Which is the unit price.

How to solve 5/6k=1/6

Answers

5/6k=1/6
We multiply it by 6 to remove the fraction part
5k=1
Divide both sides by 5
k=1/5

Answer:

k= 1/5

Step-by-step explanation:

Take reciprical on both sides.

6/5 * 5/6k = 1/6 * 6/5

k = 6/30

(reduced) k = 1/5

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Answers

$25.50-$12.00=$13.50 

Lisa spent $13.50
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Suppose you are decorating 2 frames with yarn. You want the 2 pieces of yarn to be the exact same size. Which 2 pieces of yarn should you use? Draw a number line to show how you found your answer?

Answers

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