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sergij07 [2.7K]

4 years ago

9

PLEASE HELP! Triangle A’B’C’ is a dilation of triangle ABC.

2 answers:

sergejj [24]4 years ago

6 0

The scale factor is (x2)!

9×2 = 18
4 1/2 × 2 = 9

hram777 [196]4 years ago

3 0

Answer: 0.5

Step-by-step explanation:

We know that the scale factor for dilation is the ratio of the side-length of the image to the side-length of the pre-image.

From the given figure, In Pre-image ΔABC , we have AC=18

In Pre-image ΔA'B'C', we have A'C'=9

Now, the scale factor will be :_

$k=\dfrac{A'C'}{AC}=\dfrac{9}{18}=\dfrac{1}{2}=0.5$

Now, the scale factor for this dilation = 0.5

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The sum of the digits of a 2-digit number is 10. If 18 is added to the number, the digits of the new number are those of the ori

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Answer:

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Step-by-step explanation:

Let $(ab)$ represent a number with $a$ in the ten's position and $b$ is the one's position.

This means $(ab)$ actually has value of $10a+b$ .

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It says if 18 is added to the number $(ab)$ , then the result is $(ba)$ .

So $(ab)$ has value $10a+b$ and

$(ba)$ has value $10b+a$ .

We are given then:

$(ab)+18=(ba)$

$10a+b+18=10b+a$

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Subtract $b$ on both sides:

$18=10b-b-9a$

$18=9b-9a$

Divide both sides by 9:

$2=b-a$

Rearrange by commutative property:

$2=-a+b$

So the system of equations we want to solve is:

$a+b=10$

$-a+b=2$

-------------------------Add equations together (this will eliminate the variable $a$ and allow you to go ahead and solve for $b$ :

$0+2b=12$

$2b=12$

Divide both sides by 2:

$b=\frac{12}{2}$

Simplify:

$b=6$

If $b=6$ and $a+b=10$ , then $a=4$ . $a=4$ since 4+6=10.

So the original number is (46).

18 more than 46 is 18+46=(64) which is what we wanted.

We also have the sum of 4 and 6 is 10 as well.

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