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Snezhnost [94]
3 years ago
7

If a^2=b^2, does a=b? Explain and justify your answer.

Mathematics
1 answer:
anygoal [31]3 years ago
4 0

Answer:

  not necessarily

Step-by-step explanation:

Taking the square root of both sides, you have ...

  ±a = ±b

Those four cases resolve to two unique cases:

  a = ±b

The given equation will be true if a = b or if a = -b. If a and b are constrained to have the same sign, then a=b is the only solution.

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3 0
3 years ago
Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply. The le
vazorg [7]
<h2>Answer </h2>

You should check the following:

The length of AB is 2

The length of A'B' is 3

The scale factor is \frac{3}{2}

<h2>Explanation</h2>

- To find the length of AB, we will use the distance formula:

d(A,B)=|x_{1}-x_{2}|

From the picture we can infer that x_{1}=2 and x_{2}=4, so let's replace the values.

d(A,B)=|2-4|

d(A,B)=|-2|

d(A,B)=2

The length of AB is 2, so you should check the first answer

- To find the length of A'B', we will use the distance formula one more time:

From the picture we can infer that x_{1}=3 and x_{2}=6, so let's replace the values.

d(A',B')=|3-6|

d(A',B')=|-3|

d(A',B')=3

Since the length of A'B' is 3, you should also check the second answer as well.

- In a transformation (in this case a dilation) the pre-image is the original shape and the image is the shape after the transformation.

Since the image is bigger than the pre-image, the third answer is false.

- Let k be the scale factor

We know that the length of AB is 2 and we need to multiply that length by the scale factor to get length of A'B' i.e 3, so:

2k=3

k=\frac{3}{2}

Since the scale factor is \frac{3}{2}, you should check the fourth answer as well.

- We already prove that the scale factor is \frac{3}{2}, so the fifth answer is false.

5 0
4 years ago
Read 2 more answers
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