The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively.

Which best explains why this triangle is or is not a right triangle?

erastovalidia [21]

Answer:

<h2>This triangle is a right triangle:</h2><h2>36² + 15² = 39².</h2>

Step-by-step explanation:

If a ≤ b <c is the length of the sides of a right triangle, then:

$a^2+b^2=c^2$

We have

$a=15\ in,\ b=36\ in,\ c=39\ in$

Check the equality:

$L_s=15^2+36^2=225+1296=1521$

$R_s=39^2=1521$

$L_s=R_s$

It's a right triangle.

6 0

2 years ago

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Triangle QRS is dilated according to the rule DO,2 (x,y).

Gemiola [76]

The correct options about the dilation are; Options A, B and E

<h3>How to interpret Dilated Objects?</h3>

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

Read more about Dilated Objects at; brainly.com/question/10253650

#SPJ1

8 0

2 years ago

Select the correct answer.What is 2/5 divided by 4/7 by equal to?A.7/5 B.7/10 C.10/7 D.7/5

qwelly [4]

The answer would be A . 7/5

7 0

2 years ago

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Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

Makovka662 [10]

Given:

The geometric sequence is:

$n$ $a_n$

1 -4

2 20

3 -100

To find:

The explicit formula and list any restrictions to the domain.

Solution:

The explicit formula of a geometric sequence is:

$a_n=ar^{n-1}$ ...(i)

Where, a is the first term, r is the common ratio and $n\geq 1$ .

In the given sequence the first term is -4 and the second term is 20, so the common ratio is:

$r=\dfrac{a_2}{a_1}$

$r=\dfrac{20}{-4}$

$r=-5$

Putting $a=-4,r=-5$ in (i), we get

$a_n=-4(-5)^{n-1}$ where $n\geq 1$

Therefore, the correct option is B.

5 0

2 years ago

6) A standard deck has 52 cards, and contains 13 cards of each of the four suits: diamonds, spades, hearts, and clubs. What is t

Crazy boy [7]

Answer:

$\dfrac{12}{51}\cong\dfrac{4}{17}$

Step-by-step explanation:

You have 52 cards in a deck and 13 cards of each suit.

The probability of picking a diamond in a complete deck of cards is:

$\dfrac {13}{52}$

Or the probability is 13 put of 52.

Since you took out 1 diamond card already there would be only 51 cards left and 12 diamond cards left. So you would have a probability of:

$\dfrac{12}{51}$

If we simplify it you will have a probability of:

$\dfrac{4}{17}$

6 0

2 years ago