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Lemur [1.5K]
2 years ago
14

Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length o

f Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15. Given △QRS ~ △XYZ, what is the value of tan(Q)? Three-fifths Three-fourths Four-fifths Four-thirds

Mathematics
2 answers:
kumpel [21]2 years ago
7 0

Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

<em>In the right triangle XYZ</em>

Find the tangent of angle X

tan(X)=\frac{YZ}{XZ} ---> opposite side angle X divided by adjacent side angle X

substitute the given values

tan(X)=\frac{9}{12}

Simplify

tan(X)=\frac{3}{4}

Remember that

∠Q≅∠X

so

tan(Q)=tan(X)

therefore

tan(Q)=\frac{3}{4} ---->Three-fourths

tekilochka [14]2 years ago
6 0

Answer:

B

Step-by-step explanation:

I took the test on E2020.

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There are many toys in a kindergarten. The ratio of the number of dolls to the number of balls to the number of cars is 7:8:5. I
Nina [5.8K]

Answer:

There are 28 dolls, 32 balls,  20 cars   for 80 total toys

Step-by-step explanation:

dolls : balls: cars: total

7           8          5    (7+8+5)

7           8           5        20

We have a total of  80  

80/20 = 4

We need to multiply each number by 4

dolls : balls: cars: total

7*4     8*4     5*4      20*4

28       32      20       80


There are 28 dolls, 32 balls,  20 cars   for 80 total toys

4 0
3 years ago
Multiply this expression :: -2/7 • (-3 5/8)​
Helen [10]

Answer: 29/28

Step-by-step explanation:

-2/7 x (-3 5/8)

= -2/7 x -29/8

= 2/7 x 29/8 = 1/7 x 29/4

= 29/28

7 0
2 years ago
Slope intercept form? A line passes through the point (10,4) and has a slope of -1 over 2 .
Law Incorporation [45]

The slope-intercept form:

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m - slope

b - y-intercept

We have the slope m=-\dfrac{1}{2} and the point (10, 4).

Substitute the value of slope and the coordinates to the equation of line:

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Answer: y=-\dfrac{1}{2}x+9

3 0
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Answer:

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Gre4nikov [31]

Answer:

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Step-by-step explanation:

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8 0
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