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3 years ago

5

The graph shows the dilation of quadrilateral MNOP with the origin as its center. Which rule describes this transformation?

1 answer:

lana66690 [7]3 years ago

8 0

Answer:

D) (x, y) → (1/3x , 1/3 y)

Step-by-step explanation:

A dilation is a change of size, if the dilation factor is greater than 1, then the figure is enlarged. If the dilation factor is smaller than 1, the figure is shrinked. In both cases, the coordinates are MULTIPLIED by the dilation factor.

Among the 4 choices, only 2 are dilations. One is with a dilation factor of 3 (A), which means the shape was enlarged. And the other is with dilation factor of 1/3, meaning the shape was shrinked.

Since we went from MNOP (LARGE one) to M'N'O'P' (small one), the dilation factor was < 1... so 1/3 is the answer.

Answers B and C show a translation/movement of the shape, not a dilation.

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Each figure shows a triangle with one of its angle bisectors.<br> 12) 22 - 38°. Find mZTRS.

jarptica [38.1K]

Answer:

76 degrees

Step-by-step explanation:

this special line is an angle bisected.

that means it splits the angle at its starting point in 2 halves. as these names indicate, both parts are of equal size (half of the general angle).

we know one part (2) of this split angle : 38 degrees.

the other part (1) had to be equally sized : 38 degrees.

so, the total angle at point R is the sum of both split angles:

TRS = 38+38 = 76 degrees.

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3 years ago

The sum of an infinite geometric series is three times the first term. Find the common ratio of this series.

adelina 88 [10]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

The sum of an infinite geometric series is expressed according to the formula;

$S_\infty = \dfrac{a}{1-r}$ where;

a is the first term of the series

r is the common ratio

If the sum of an infinite geometric series is three times the first term, this is expressed as $S_\infty = 3a$

Substitute $S_\infty = 3a$ into the formula above to get the common ratio r;

$3a = \dfrac{a}{1-r} \\\\$

$cross \ multiply\\\\3a(1-r) = a\\\\3(1-r) = 1\\$

open the parenthesis

$3 - 3r = 1\\\\$

subtract 3 from both sides

$3 - 3r -3= 1-3\\\\-3r = -2\\\\r = \frac{2}{3}$

<em>Hence the common ratio of this series is </em> $\frac{2}{3}$ <em></em>

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Answer:

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3 years ago

Identify the index in the radical below.<br> A. 1<br> B. 2<br> C. 3<br> D. 4

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Answer:

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Step-by-step explanation:

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3 years ago

What is the sum of 4.9 × 102 and 6.8 × 103?

dusya [7]

Answer:

The sum is

$7.92\times 10^3$

Step-by-step explanation:

We want to add

$4.9\times 10^2 and 6.8\times 10^3$

The sum of these two numbers is:

$4.9\times 10^2 +6.8\times 10^3$

This is the same as:

$4.9\times 100 +6.8\times 1000$

$490 +6800=7290$

We rewrite 7290 in standard form to get;

$7.92\times 10^3$

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3 years ago