If Triangle PQR ~ Triangle SQT, Find the value of x.

If Triangle PQR ~ Triangle SQT, Find The Value Of X.

Answers

Answer 1

Answer:

x = 15

Step-by-step explanation:

Given that ∆PQR ~ ∆SQT, therefore their side lengths are proportional to each other.

Thus:

[tex] \frac{PQ}{SQ} = \frac{PR}{ST} [/tex]

PQ = (x + 5) + 8 = x + 13

SQ = 8

PR = 21

ST = x - 9

Plug in the values

[tex] \frac{x + 13}{8} = \frac{21}{x - 9} [/tex]

Cross multiply

[tex] (x + 13)(x - 9) = 8*21 [/tex]

[tex] x(x - 9) +13(x - 9) = 168 [/tex]

[tex] x^2 - 9x + 13x - 117 = 168 [/tex]

[tex] x^2 + 4x - 117 = 168 [/tex]

Subtract 168 from both sides

[tex] x^2 + 4x - 117 - 168 = 0 [/tex]

[tex] x^2 + 4x - 285 = 0 [/tex]

Factorize

[tex] x^2 + 19x - 15x - 285 = 0 [/tex]

[tex] x(x + 19) - 15(x + 19) = 0 [/tex]

(x + 19)(x - 15) = 0

x = -19 or x = 15

Answer 2

Answer:

x = 15

Step-by-step explanation:

x+13/9 = 21/x-9

x^2+4x−117=168

x^2+4x−285=0

(x−15)(x+19)=0

x=15

it cannot be a negative number so x cannot be -19


Related Questions


Help!!! Worth 50 points!

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Answer:

Step-by-step explanation:

Hey I can't read what's in the picture it's blurry

Answer:

According to the words used by the poet, they made the reader visualize a little village with a group of hardworking men. I know this because of the little details the poet used, like ‘washing their red hands’, or ‘easing their stiff limbs’, meaning that they are tired for an exhausting day of work. To sum it up, the poet gave the effect of a hard working, nostalgic effect.

Step-by-step explanation:

Enter a formula using k to connect the two variables. t is proportional to x .

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Answer:

x:y I think this answer is correct

Step-by-step explanation:

find the value of p in the figure​

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Answer:

Im pretty sure the answer is maybe 90 degrees

what is the volume of this rectangular prism 7/5cm 5cm 7/2cm? plz help asap ​

Answers

Answer:

24.5 cm³

Step-by-step explanation:

Volume of rectangular prism is:

V = lwhV = 7/5 × 5 × 7/2 = 49/2 =24.5 cm³

Answer:

The volume of this rectangular prism with dimensions 7/5cm, 5cm and 7/2cm.

Volume=length× breadth× height

V=7/5cm×5cm×7/2cm= 49/2cm³= 24.5cm³

24.5cm³ is the right answer.

Determine the x- and y- intercepts for the graph defined by the given equation.
y = x + 8
a. x-intercept is (0,8)
c. x-intercept is (-8, 0)
y-intercept is (-8, 0)
y-intercept is (0,8)
b. x-intercept is (0, -8)
d. x-intercept is (8,0)
y-intercept is (8,0)
y-intercept is (0, -8)

Answers

Answer:

Y-intercept is (0,8)

Step-by-step explanation:

The line of an equation is y=mx+b. M in this case is 1 and "b" is the y intercept. since in the place of b is positive 8 the y-intercept is 8

X-intercepts (-8,0) Y-intercepts (0,8)

Round 48.078 to the nearest tenth

Answers

Answer:

50

Step-by-step explanation:

48 rounds to 50

ANSWER: 50

Answer:

48.1

Step-by-step explanation:

5 and up, add 1

4 and down, don't change and the numbers after are gone.

3) Which expression is equivalent to: 6(7-2) *
O 67-62
O42-12
O 7-2
O 13 - 8

Answers

Answer:

42-12

Step-by-step explanation:

Here you go mate

Step 1

6(7-2)  Equation

Step 2

6(7-2)  simplify

6x5

answer

42-12=30  check

What is the constant of proportionality for the following situation?

A student reads 65 pages per hour.

Answers

Answer:

for every 1 hour he reads 65 pages

Step-by-step explanation:

make a graph

65,1

and you got up from there

rise over run

ok

simplify 0.12×0.04÷ 0.0024 giving the answer in standard forrm​

Answers

Answer:

2

Step-by-step explanation:

(0.12)(0.04)

0.0024

=2

kazito sold an item for sh 4950 and made a 12 ¹/2profit.what was the cost price of the item?​

Answers

Answer:

[tex]Cost\ Price = 4331.25[/tex]

Step-by-step explanation:

Given

Selling Price = Sh. 4950

Profit = 12.5%

Required

Determine the cost price

Profit is calculated as:

[tex]Profit = \frac{Selling\ Price - Cost\ Price}{Selling\ Price} * 100\%[/tex]

Substitute values for Selling Price and Profit

[tex]12.5\% = \frac{4950 - Cost\ Price}{4950} * 100\%[/tex]

Cross Multiply:

[tex]4950 * 12.5\% = (4950 - Cost\ Price) 100\%[/tex]

[tex]\frac{4950 * 12.5\%}{100\%} = (4950 - Cost\ Price)[/tex]

[tex]618.75 = (4950 - Cost\ Price)[/tex]

Collect Like Terms

[tex]Cost\ Price = 4950 - 618.75[/tex]

[tex]Cost\ Price = 4331.25[/tex]

Hence, the cost price of the item is: Sh. 4331.25

You’re taking an exam in math, and you spend 5 minutes for every 2 questions you answer on the test.(Plz answer! I’m failing and I need to get this correct!)

Answers

Given:

Time spend on every 2 questions = 5 minutes.

To find:

The missing values for the given table.

Solution:

Let x be the number of questions and y be the number of minutes.

We have,

Time spend on every 2 questions = 5 minutes

Time spend on 1 question = [tex]\dfrac{5}{2}=2.5[/tex] minutes

Time spend on x questions = [tex]2.5x[/tex] minutes

Now,

[tex]y=2.5x[/tex]

For x=0,

[tex]y=2.5(0)=0[/tex]

For x=1,

[tex]y=2.5(1)=2.5[/tex]

For x=2,

[tex]y=2.5(2)=5[/tex]

For x=3,

[tex]y=2.5(3)=7.5[/tex]

For x=4,

[tex]y=2.5(4)=10[/tex]

Therefore, the required table is

Questions        :           0                1                2               3                 4

Time (minutes) :           0             2.5              5              7.5              10

The Picture has the question

Answers

Answer:

Pythagorean Theorem:

a² + b² = c²

x² + 5x² = 78²

6x² = 6084

6x²/6 = 6084/6

x²=1014

√x² = √1014

x = 31.84

Mark Brainliest Please

Answer:

x ≈ 15.3

Step-by-step explanation:

Based on the pythagoras theorem

[tex]a^{2} + b^{2} = c^{2}[/tex]

Since the legs are "5x" and "x" we know the following....

[tex](5x)^{2} + x^{2} = 78^{2} \\25x^{2} + x^{2} = 6084\\26x^{2} = 6084\\x^{2} = 234\\x = \sqrt{234} \\x = 15.3[/tex]

(This is round did to the nearest tenth)

Find the value of g (x) = 7/8 x - 1/2 where x is 7

Answers

Answer:

5.625

Step-by-step explanation:

Dogs or cats which one is better???

Answers

Answer:

dogs

Step-by-step explanation:

they are more freindly

Answer:

dogs

Step-by-step explanation:

i just had to take a test and one of the questions was to write an essay about dogs or cats being better so i searched it up and it said  dogs

The equation y=39/4x describes the number of miles y that an airplane travels in x minutes. What is the constant speed of the airplane in miles per​ minute? How many miles does the airplane travel in ​hours?

Answers

Answer:

The plane goes 9.75 Miles/Minute

The plane goes 585 Miles/Hour

What is the multiplicative rate of the change of the function?

Answers

Since X increases by 1,

Divide the 2nd Y value by the first Y value:

4/6 = 2/3

The answer is 2/3

Solve this problem

........... ​

Answers

Answer:

40.5

Step-by-step explanation:

[tex]\frac{2^3*3^4*4}{2*32} \\\\Firstly\ we\ have\ to \ expand\ the\ terms\ as\ factors:\\\\=\frac{(2*2*2)*(3*3*3*3)*(2*2)}{(2)*(2*2*2*2*2)`}\\\\We\ cancel \ terms\ that \ are\ common\ to \ both \ numerator\ and\ denominator\ to\ get:\\\\=\frac{3*3*3*3}{2}\\\\ =\frac{81}{2} \\\\We\ simplify\ the\ terms\ to \ its\ lowest\ form:\\\\=40.5[/tex]

Therefore the answer to the problem = 40.5

lololljhfhjfgdfhfghghjf

yo

Answers

You loloohngygvfthbfryhgd

17÷338
what is the remainder

Answers

Answer:

Step-by-step explanation:

= 19 R 15

= 19 15/17

338 divided by 17 equals

19 with a remainder of 15

Solution:

   0 1 9

1 7 {3 3 8

 − {0    

   3 3  

 − 1 7  

   1 6 8

 − 1 5 3

     1 5

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   < ⌒ヽ A

  /   へ\ B

  /  / \\ U

  レ ノ   ヽ_つ L

 / / O

 / /| U

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19 with a remainder of 15

What is the final price of a $50 pair of headphones with sales tax of 5%.

Answers

Answer:

$52.50

Step-by-step explanation:

$50+5%= $52.50

Hope this helps

9/7 simplified is?
a) 21/14
b) 21/7
c) 22/7
d) 21/3​

Answers

Answer:

None of those answers is true.

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

Ignore the one I filled in
Please help tho!

Answers

Answer:

it's the last one

Step-by-step explanation:

The answer is the last option listed: 9 1/5

Craig earns extra money as a lifeguard he earns $37 for 4 hours and $64.75 for 7 hours. write and equation for the following proportional relationship

Answers

Answer: m = 9.25h

Step-by-step explanation:

The money he earns per hour is $9.25

m = total money  h = hours he worked

m = 9.25h

Given that points A, B, and C are the midpoints of their respective sides, which of the following is true about the figure?
Question 2 options:

A)



B)

ΔBCZ ≅ ΔYAB

C)



D)

ΔZYX ≅ ΔABC

Answers

Answer:

zx ≅ ab

Step-by-step explanation:

took the test

A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore.
x 0 1 2 3 4 or more
% 43% 35% 15% 6% 1%
(a) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.
(b) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)
(c) Compute μ, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)
μ = fish
(d) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)
σ = fish

Answers

Answer:

a. 0.57

b. 0.22

c. 0.87

d. 0.9450

Step-by-step explanation:

A.

P(X>=1)

= 0.35 + 0.15 + 0.06 + 0.01

= 0.57

This is the probability of catching one or more fishes.

b.

P(X>=2)

0.15 + 0.06 + 0.01

= 0.22

This is the probability of catching 2 or more fishes.

C.

Compute μ

μ = E(X)

= (0x0.43) + (1x0.35) + (2x0.15) + (3x0.06) + (4x0.01)

= 0+0.35+0.3+0.18+0.04

= 0.87

D.

The standard deviation

Sd = √V(X)

V(X) = E(X²) - (E(X))²

E(X²) = (0²x0.43)+(1²x0.35)+(2²*0.15)+(3²*0.06)+(4²*0.01)

E(X²) = 0.35+0.6+0.54+0.16

= 1.65

V(X) = 1.65 - (0.87)²

= 1.65 - 0.7569

= 0.8931

Sd = √0.8931

= 0.9450

-[tex]-8\9 + 1/5+ -8/15

Answers

Answer:

[tex]-\frac{11}{9}[/tex] , OR [tex]-1\frac{2}{9}[/tex], OR -1.2

Step-by-step explanation:

[tex]-\frac{8}{9}+\frac{1}{5}+(-\frac{8}{15})[/tex]      When there is a (+) in front of an expression in parentheses, the expression remains the same

[tex]-\frac{8}{9}+\frac{1}{5}-\frac{8}{15}[/tex]  Calculate the sum or difference

[tex]-\frac{11}{9}[/tex]

0.03is 10 times as much as

Answers

Answer:

0.03 is 10 times as much as 0.003

Step-by-step explanation:

its the answer

Who can help me out with this question

Answers

Answer:

i think it is d) neither

Step-by-step explanation:

......

Round 4213 to 3.sf, 2,sf and 1.sf​

Answers

Answer:

3sf-0.421, 2sf- 42, 1sf-0004

Answer:

4210 4200 4000

Step-by-step explanation:

your welcome :)

In ASTU, mZS = (6x – 15)°, mZT = (2x − 2)°, and
mZU = (4x – 7)º. What is the value of x?

Answers

Answer:

x = 17

Step-by-step explanation:

all three expressions should be added together and set equal to 180 degrees

6x - 15 + 2x - 2 + 4x - 7 = 180

now combine like terms

12x - 24 = 180

add 24

12x = 204

x = 204/12

x = 17

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