Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40 square meters.

Answers

Answer 1

Answer: The rectangle is 8 metres by 5 metres.

You find the two numbers which can multiply to make 40 and see which of those also would result in a perimeter of 26. To make 40 you can have 4 and 10, 2 and 20, 1 and 40, or 8 and 5. 8 and 5 are the only lengths which give a perimeter of 26.

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What is 2 1/4 inches + 5 3/4 inches + 8 1/2 inches equals

Answers

2 1/4 inches + 5 3/4 inches + 8 1/2 inches:

First, to start solving this problem, we will have to add the whole numbers first. The whole numbers are the...whole numbers in front of the fraction. In this case, the whole numbers would be 2, 5, and 8. So, we have to add those three numbers up (2 + 5 + 8) to get the answer which is 15.
$15 + (1)/(4) + (3)/(4) + (1)/(2)$

Second, now we have to find the least common denominator (LCD) of the three denominators. The denominators are the bottom number of the fraction. This case the denominators would be 4, 4, and 2.To find the LCD, we will have to list the multiples of each denominator and find the first common one.

Multiples of 4: 4
Multiples of 4: 4
Multiples of 2: 2, 4

Since 4 appears in the multiples of each denominator, 4 is our LCD.

Third, since only one fraction needs their denominator changed (the other two fractions already carry the denominator of 4), we have to multiple each number by whatever gets us 4. Remember, whatever you do to the bottom, do to the top.
$15 + (1)/(4) + (3)/(4) + (1*2)/(2*2) = 15 + (1)/(4) + (3)/(4) + (2)/(4)$

Fourth, since all of our denominators are the same, we can now combine our numerators (join the denominators) and add them all up.
$15 + (1+3+2)/(4) = 15 + (6)/(4)$

Fifth, we now need to convert 6/4 into a mixed fraction. To find the mixed fraction form of 6/4, we will need to divide the denominator (4) by the numerator (6) and then write any remainder above the denominator.

Mixed fraction: $15 + 1 (2)/(4) = 16 (2)/(4)$

Sixth, we can simplify 2/4 down some more. To do so, we need to find the greatest common factor of the numerator and denominator, then divide the GCF by them. To find the GCF, we list all of the factors of them and find the first common one.

Factors of 2: 1, 2
Factors of 4: 1, 2, 4

The GCF is 4.

Seventh, we can now divide both our numerator and denominator by our recently found GCF which was 2.
$2 / 2 = 1 \n 4 / 2 = 2$

Answer in fraction form: $\fbox {16 1/2 inches}$
Answer in decimal form: $\fbox {16.5 inches}$

2.25 + 5.75 + 8.5 = 16.5 inches or 1.375 feet.

Anne buys her store's art supplies from a wholesaler. She purchases 8 canvases that are 16 by 20 inches for $7.16each. How much profit does Anne make on the sale of these 8 canvases?
OA. $35.92
OB. $45.63
OC.
$57.28
OD. $86.04

Answers

Anne makes a profit of $57.28 on the sale of these 8 canvases. which is the correct answer would be option (C).

What is the profit?

The profit is equal to the difference between the selling price and the original cost price.

Anne purchases art supplies for her business from a wholesaler. She spends $7.16 on eight 16 by 20-inch canvases.

To calculate the profit that Anne makes on the sale of these 8 canvases, you need to know the price at which she sells them and the cost of buying them from the wholesaler. If the cost of each canvas is $7.16 and she buys 8 of them, the total cost of the canvases is :

⇒ 8 × $7.16

Apply the multiplication operation and we get

⇒ $57.28.

Therefore, she makes a profit of $57.28 on the sale of these 8 canvases.

Hence, the correct answer would be an option (C).

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Answer:

OC. $57.28

Step-by-step explanation:

It depends on how much she sells them for.

Let's say Anne sells them for $x.

Then her profit is:

8x-(8*7.16)

=8x-57.28

To make a minimum to at least make even is $57.28 and sell for $7.16 a piece.

Nina wants to download games for her video game console. Older games cost 100 points and new releases cost 200 points to use. The equation 100a+200b=4000, where a is the number of der games and b is the number of new releases, models the situation. How many older games can she download if she downloads 4 new games? 5 new games?

Answers

Replace b with 4: 100a+200(4)=4000. 100a+800=4000. Combine like terms: 100a=3,200. Get the unknown by itself: A=32. She can download 32 old games if she downloads 4 new ones. Same steps: 100a+200(5)=4000. 100a+1000=4000. 100a=3000. A=30. She can download 30 old games if she downloads 5 new ones. :)

Final answer:

If Nina downloads 4 new games, she can additionally download 16 older games. If she downloads 5 new games, she can download 15 older games.

Explanation:

The problem can be solved by substituting the number of new games into the equation and solving for 'a' which represents the number of older games.

For 4 new games, the equation becomes 100a+200*4=4000. Solving this, we get 'a' as 16. Hence, Nina can download 16 older games.

For 5 new games, the equation becomes 100a+200*5=4000. Solving this, we get 'a' as 15. Hence, Nina can download 15 older games when she downloads 5 new games.

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The temperature of liters of a ideal gas was increased from 600 to 800 kelvins. If the volume remained constant and the final pressure was 30 atmospheres, what was the initial pressure?