Ask question

Ask question

All categories

2 years ago

10

The figure shows two right triangles, each with its longest side on the same line. R 4 How long is XY? Type the answer in the bo

x.

1 answer:

Leokris [45]2 years ago

8 0

Answer: 6

Step-by-step explanation:

Because corresponding sides of similar triangles are proportional,

$\frac{XY}{3}=\frac{4}{2}\\ \\ \frac{XY}{3}=2\\ \\ XY=\boxed{6}$

You might be interested in

A conservative estimate of the number of stars in the universe is 6 x 10^22. The average human can see about 3,000 stars at nigh

Ilia_Sergeevich [38]

$2 \times 10^{19}$ times more stars are there in universe compared to human eye can see

<h3><u>Solution:</u></h3>

Given that, conservative estimate of the number of stars in the universe is $6 \times 10^{22}$

The average human can see about 3,000 stars at night with only their eyes

To find: Number of times more stars are there in the universe, compared to the stars a human can see

Let "x" be the number of times more stars are there in the universe, compared to the stars a human can see

Then from given statement,

$\text{Stars in universe} = x \times \text{ number of stars human can see}$

<em><u>Substituting given values we get,</u></em>

$6 \times 10^{22} = x \times 3000\\\\x = \frac{6 \times 10^{22}}{3000}\\\\x = \frac{6 \times 10^{22}}{3 \times 10^3}\\\\x = 2 \times 10^{22-3}\\\\x = 2 \times 10^{19}$

Thus $2 \times 10^{19}$ times more stars are there in universe compared to human eye can see

5 0

4 years ago

Explain why the two figures below are similar. Use complete sentences and provide evidence to support your explanation. (10 poin

alekssr [168]

Answer:

<em>The two figures are similar as the ratio of corresponding distances and slope of corresponding lines are EQUAL.</em>

Step-by-step explanation:

Noting the coordinates of points,

C(-1,6), D(3,4) , E(2,3) , F(3,0), G(1,-2) , A(0,1) , B(-2,2)

J(4.5,3.5), K(6.5,2.5), L(6,2), M(6.5,0.5) , N(5.5,-0.5) , H(5,1) , I(4,1.5)

using the distance formula = $\sqrt{(x-x1)^{2} + (y-y1)^{2} }$

we find that,

CD= $\sqrt{20}$ and JK= $\sqrt{5}$

thus, ratio of CD to JK is 2.

Similarly find ratio of DE to KL and so on, the ratio remains same.

Further one can even comment on the slopes of corresponding lines been equal.

Thus the figures turn out to be similiar to each other

7 0

3 years ago

A radioactive substance has a continuous decay rate of 0.056 per minute. How many grams of a 120 gram sample will remain radioac

sammy [17]

Answer:

The mass of the radioactive sample after 40 minutes is 12.8 g.

Step-by-step explanation:

The mass of the sample can be found by using the exponential decay equation:

$N_{t} = N_{0}e^{-\lambda t}$

Where:

N(t): is the amount of the sample at time t =?

N₀: is the initial quantity of the sample = 120 g

t = 40 min

λ: is the decay constant = 0.056 min⁻¹

Hence, the mass of the sample after 40 min is:

$N_{t} = N_{0}e^{-\lambda t} = 120g*e^{-0.056min^{-1}*40 min} = 12.8 g$

Therefore, the mass of the radioactive sample after 40 minutes is 12.8 g.

I hope it helps you!

5 0

3 years ago

Suppose that 12 inches of wire cost 48 cents at the same rate how many inches of wire can be bought for 28 cents

goldenfox [79]

Answer:

7 in

Step-by-step explanation:

If 12 inches of wire can be bought for $0.48, we can set up the following ratio:

$\frac{12\text{ in}}{\$0.48}$

Then, to determine how many inches of wire can be bought for $0.28, set up equivalent fractions, as such:

$\frac{12\text{ in}}{\$0.48}=\frac{x}{\$0.28}$

Then, cross-multiply and solve for $x$ :

$\$0.48x=(\$0.28)(12)$

$\$0.48x=\$3.36$

$x=\frac{\$3.36}{\$0.48}$

$x=7$

3 0

1 year ago

6.Angle 30degrees + x is equal to 180 degrees. Find x

Harrizon [31]

The answer is 150 because 30+150=180

6 0

3 years ago