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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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linda,rumi,liz,amy,adam,and sam ran a 800-meter race.Adam BEAT liz by 7meter Sam beat linda by 12 meters. Adam finished 5 meters
Stels [109]
The distance between Adam and Liz is 7 meters. Sam ang Linda are 12 meters apart. Adam and Sam are 3 meters apart while Adam is 5 meters ahead of anyone. So, Sam finished first, then Adam, next is Liz, next is Rumi, last is Linda. 
5 0
2 years ago
Kayleigh babysat for 11 hours this week. That was 5 fewer than 2/3 as many hours as she babysat last week, h. Write an equation
lukranit [14]

Answer: The answer is \textup{x}=\dfrac{2}{3}\textup{h}-5.


Step-by-step explanation: Given that Kayleigh babysat for 11 hours the present week. Also, this was 5 less than two-third of the number of hours she babysat last week, which is represented by 'h'.

We are to write an equation to represent the number of hours she babysat each week.

So, for that, let 'x' be the number of hours she babysat this week. Then, according to the question, we can write

\textup{x}=\dfrac{2}{3}\textup{h}-5.

Also, it is given that

\textup{x}=11.

Therefore,

11=\dfrac{2}{3}\textup{h}-5\\\\\Rightarrow \dfrac{2}{3}\textup{h}=16\\\\\Rightarrow \textup{h}=24.

Hence, using the above relation, we can find the number oh hours Keyleigh babysat each week.

Thus, the required equation is

\textup{x}=\dfrac{2}{3}\textup{h}-5,

where, 'x' and 'h' are the number of hours she sat this week and last week respectively.

 


4 0
2 years ago
The width of a triangle is six more than twice the height. The area of the triangle is 88in2. Find the height and base of the tr
malfutka [58]

For this case we have that by definition, the area of a triangle is given by:

A = \frac {b * h} {2}

Where:

b: It is the base of the triangle

h: It is the height of the triangle

According to the statement data we have:

b = 6 + 2h

Substituting we have:

88 = \frac {(6 + 2h) * h} {2}\\176 = 6h + 2h ^ 2\\2h ^ 2 + 6h-176 = 0

We divide between 2 on both sides:

h ^ 2 + 3h-88 = 0

We factor by looking for two numbers that, when multiplied, are obtained -88 and when added together, +3 is obtained.

These numbers are +11 and -8.

(h + 11) (h-8) = 0

We have two roots:

h = -11\\h = 8

We choose the positive value.

Thus, the base of the triangle is:b = 6 + 2 (8) = 22

Answer:

The base of the triangle is 22 units.

5 0
2 years ago
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If the value of Y is between 0.0078 and 0.01 which of the following could be Y?
yuradex [85]

Answer: 0.0099

Step-by-step explanation:

3 0
2 years ago
A house on the land measures 45 feet by 38 feet,a wooded area covers 118 feet by 60 feet,and the front yard is 78 feet by 40 fee
den301095 [7]
Rectanglearea=legnth timees width
triagnlearea=1/2base times height

ok so we find volume of entier land first

we can cut into triangle an rectangle

triangle=height=650-200=450
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area=1/2*600*450=135000 ft^2

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add
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find other areas and subtract
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areawooded=118*60=7080
frontyard=78*40=3120
add
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minus

255000-11910=243090

how many acres are farmed

43560ft^2=1acre
divide both sides by 43560
1ft^2=1/43560 acre

multiply both sides by 243090
243090ft^2=243090/43560acre=5.5805acre=5.6acre rounded

answer is 5.6 acer


6 0
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