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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

PLEASE HELP WITH THIS QUESTION

Burka [1]

One nice thing about this situation is that you’ve been given everything in the same base. To review a little on the laws of exponents, when you have two exponents with the same base being:

– Multiplied: Add their exponents
– Divided: Subtract their exponents

We can see that in both the numerator and denominator we have exponents *multiplied* together, and the product in the numerator is being *divided* by the product in the detonator, so that translates to *summing the exponents on the top and bottom and then finding their difference*. Let’s throw away the twos for a moment and just focus on the exponents. We have

[11/2 + (-7) + (-5)] - [3 + 1/2 + (-10)]

For convenience’s sake, I’m going to turn 11/2 into the mixed number 5 1/2. Summing the terms in the first brackets gives us

5 1/2 + (-7) + (-5) = - 1 1/2 + (-5) = -6 1/2

And summing the terms in the second:

3 + 1/2 + (-10) = 3 1/2 + (-10) = -6 1/2

Putting those both into our first question gives us -6 1/2 - (-6 1/2), which is 0, since any number minus itself gives us 0.

Now we can bring the 2 back into the mix. The 0 we found is the exponent the 2 is being raised to, so our answer is

2^0, which is just 1.

5 0

3 years ago

Plzzzzz help tomorrow is my maths test

maria [59]

16 ) GO...

a) 5487 × ( 65 + 35 ) = 5487 × 100 = 548700

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b) 647 × ( 112 - 12 ) = 647 × 100 = 64700

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c) 502 × 1,008 = ( 500 + 2 ) ( 1,000 + 8 ) = 500,000 + 4,000 + 2,000 + 16 = 506,016

____________________________

17 ) Go...

a) 585 × 16 × 625 = 585 × 4 × 4 × 25 × 25 = 585 × 4 × 25 × 4 × 25 = 585 × 100 × 100 = 5,850,000

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b) 147 × 50 × 2 = 147 × 100 = 14,700

____________________________

18) Go...

look : 1729 = ( 1400 + 329 ) = 7 × 200 + 7 × 47 = 7 ( 200 + 47 ) = 7 × 247 = 7 × 13 × 19

____________________________

19) Go...

look : 96 = 16 × 6 = 2⁴ × 2 × 3 = 2⁵ × 3

Thus ;

the factors are : ( 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 32 , 48 , 96 )

3 0

3 years ago

Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic

lidiya [134]

Answer: A

Step-by-step explanation:

The first thing we need to do is to make sure our equation is in standard form. The given equation is not in standard form.

3x²-2x=0

Now that the equation is in standard form, we can find our A, B, C to see which quadratic equation is correct.

A=3

B=-2

C=0

We can automatically eliminate D because the first value is -3 when it is supposed to be -(-2). Also, the denominator is supposed to be 2a. We know that A=3. The denominator should be 2(3), not 2(-2).

Next, we can eliminate B and C. For the 4ac, we know it has to be 4(3)(0) because A=3 and C=0. B and C have given 4(3)(2) and 4(3)(1), respectively. This does not match A=3 and C=0.

Therefore, A is the correct answer.

4 0

3 years ago

Work out an estimate for 456.2-51<br> _______<br><br> 0.0512

AnnZ [28]

It equals 7958.1. hope it helps

7 0

3 years ago