What equation can be written for 29 is 6 more then k? what is K?

After triangle ACE is dilated by a factor of 6, it has an area of 180 square inches. What was its area before dilation?

Agata [3.3K]

Answer:

The area of triangle ACE before dilation is: 30 square inches

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

If the scale factor > 1, the image is enlarged

If the scale factor is between 0 and 1, it gets shrunk

If the scale factor = 1, the object and the image are congruent

The length of the image can be determined by multiplying the length of the original point by a certain scale factor.

Given that after triangle ACE is dilated by a factor of 6, it has an area of 180 square inches.

Thus, it means the dilated area is 6 times the area before dilation.

Let x be the pre-dilation area

As the dilated area is 6 times the area before dilation, so

6x = 180

divide both sides by 6

6x/6 = 180/6

x = 30 square inches.

Therefore, the area of triangle ACE before dilation is: 30 square inches

4 0

3 years ago

At a local grocery store, hamburger meat is normally $3.50 per pound, but this week hamburger meat is on sale for $2.10 per poun

AysviL [449]

Answer:

I think it would be a 1.40 decrease

Step-by-step explanation:

8 0

3 years ago

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Carl bought 19 apples of 2 different varieties to make a pie.The total cost of the apple was $5.10.Granny Smith apples cost $0.2

disa [49]

For this case we propose a system of equations:

x: Let the variable representing the quantity of Granny Smith apples

y: Let the variable representing the number of Gala apples

According to the statement we have:

$x + y = 19\\0.25x + 0.30y = 5.10$

From the first equation we have to:

$x = 19-y$

replacing in the second equation:

$0.25 (19-y) + 0.30y = 5.10\\4.75-0.25y + 0.30y = 5.10\\4.75 + 0.05y = 5.10\\0.05y = 5.10-4.75\\0.05y = 0.35\\y = \frac {0.35} {0.05}\\y = 7$

So, Carl bought 7 Gala apples

On the other hand:

$x = 19-7 = 12$

So, Carl bought 12 Granny Smith apples

Answer:

Carl bought 7 Gala apples and 12 Granny Smith apples

8 0

3 years ago

What is (9p - 2) - (6p - 8)

Bezzdna [24]

The answer is 3p+6 gggghhnbhjjn

3 0

3 years ago

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Sanjay and Felipe are putting together a 500-piece puzzle. Sanjay could do the entire puzzle by himself in 6 hours, while it wou

Nata [24]

What is the time it takes Sanjay to complete the puzzle? 6 hours

What is the time it takes Felipe to complete the puzzle? 8 hours

We can use the general formula of rate and time to solve this problem. Generally we have,

Rate * Time = Work/Job

** where Work/Job for this problem is 1 since they are doing 1 work, which is solving a puzzle

Finding rate of Sanjay:

$R(6)=1\\R=\frac{1}{6}$

Finding rate of Felipe:

$R(8)=1\\R=\frac{1}{8}$

Working together, their rate is the sum,

Total Rate = $\frac{1}{6} + \frac{1}{8} = \frac{7}{24}$ .

Using the general formula again, we can find the time it will take to solve the puzzle when both works together.

$(\frac{7}{24})T=1\\ T=\frac{1}{\frac{7}{24}}= \frac{24}{7} = 3.43$ hours

Rounding the answer, we have 3.4 hours.

ANSWER: 3.4 hours

6 0

3 years ago

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