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3 years ago

PLEASE HELP ME ITS DUE TODAY! PLEASE ANSWER CORRECTLY AND EXPLAIN.

Mathematics

1 answer:

GenaCL600 [577]3 years ago

7 0

Answer:

1. figure b' is similar but not congruent to figure b

2. m<k'=-m<k

3. reflect across the x-axis, rotate 90 degrees counterclockwise about the origin, and then dilate by a scale factor of 4 centered at the origin

4. on reflection, parallel lines are taken to parallel lines, so a'b' will be parallel to c'd'.

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Step-by-step explanation:

1. it is similar because it has the same number of sides, shape, etc. it is not congruent because the two figures are not the same size

2. because it is rotated and reflected instead of dilated, it will be equal to the original image. but, the original will be negative because it is on the negative half of the plane.

3. the second image becomes positive, so we know it reflects over the x-axis. we can also see that the '-1' turns into a '4', which means that it was dilated by a factor of 4.

4. basically, when you reflect the image, it it just a few points below the original one. because of this, lines a'b' and c'd' will never touch, as they are parallel

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Answer:

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Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let $x$ represent the width.

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Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

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And multiply our area by 3.

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Then multiply $3(x^{2} +7x)$

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$21x+98=2x^{2} +21x$

Subtract $21x$ from both sides.

$98=2x^{2}$

Divide by 2.

$49=x^{2}$

And finally take the sqaure root of both sides.

$\sqrt{x^{2} }=\sqrt{49}\\x=7$

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.

Now that we have the value of $x$ , we can plug it into our original values.

For width we simply get 7.

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To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

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