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valentinak56 [21]
3 years ago
15

Calculate x you must include the steps in your solution and the definitions and/or conjecture that u use

Mathematics
1 answer:
Andreas93 [3]3 years ago
4 0

Answer:

x = 40

Step-by-step explanation:

(3x - 10) \degree = (2x + 30) \degree \\ (vertical \:  \angle s) \\  \\  \\ 3x - 10 = 2x + 30 \\  \\ 3x - 2x = 30 + 10 \\  \\ x = 40

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Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

so

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

so

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

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we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

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therefore

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so

<u><em>A) If the length of a rectangle was tripled, but the  width did not change?</em></u>

Perimeter

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The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

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The new area  would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

<u><em>B) If the length was tripled and the width was decreased by a factor of 1/4?</em></u>

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The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

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