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[tex]\boxed{\boxed{\pink{\bf \dag Value \ of \ x \ is \ 6\ and\ y \ is\ (-21) .}}}[/tex]

In the Question , its given that ∆ART [tex]\cong[/tex] ∆ DFI . And we need to find the values of x and y . So we know that ,

Hence here in ∆ ART & ∆ DFI :-

[tex]\bf\implies AT = DI \\\\\bf\implies 6x + 31 = 67 \\\\\bf\implies 6x = 67 - 31 \\\\\bf\implies 6x = 36 \\\\\bf\implies x =\dfrac{36}{6}\\\\\bf\implies \boxed{\red{\bf x = 6}}[/tex]

Hence the value of x is 6 .

[tex]\rule{200}2[/tex]

[tex]\bf\implies AR = DF \\\\\bf\implies -4y+19 = 103\\\\\bf\implies -4y = 103-19 \\\\\bf\implies -4y = 84 \\\\\bf\implies y =\dfrac{84}{-4}\\\\\bf\implies \boxed{\red{\bf y = -21}}[/tex]

Answer:

x=-20

Step-by-step explanation:

3x=-56-4

3x=-60

x=-20

Answer:

library-6

auditoriam-54

Answer:

3p - 19

Step-by-step explanation:

8 + 3(p - 9)

Distribute;

8 + 3p - 27

Collect like terms;

-19 + 3p

3p-19 by using addition and the distributive property

Answer:

9:50

Step-by-step explanation:

270/1500

divided by 10

27/150

divided by 3

9:50

Answer:56.36

Step-by-step explanation:

The percentage of observations lying above z = 0.16 will be 56.36%. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The percentage of observations lie above z = 0.16 will be given as,

⇒ P(z < 0.16) x 100

⇒ 0.5636 x 100

⇒ 56.36%

The percentage of observations lying above z = 0.16 will be 56.36%. Then the correct option is C.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ2

Answer:

Step-by-step explanation:

it switches the x and y coordinates and places a negative on the new x

P=(x,y)

90° CCW rotation P'(-y,x)

Answer:

it switches the x and y coordinates and places a negative on the new x

P=(x,y)

90° CCW rotation P'(-y,x)

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

....................

Answer:

3

Step-by-step explanation:

1/5 / 1/15 = 3

Answer:

7

Step-by-step explanation:

42 divided by 6

Answer:

Step-by-step explanation:

Answer:

12.8in

Step-by-step explanation:

Pythagorean theorem

8^2 + 10^2 = c^2

64 + 100 = 164 = c^2

C= 12.8in

Answer:

from fithagorh the line =

[tex] \sqrt{10 ^{2} + 8 ^{2} } = \sqrt{164} = 12.961 \: inch[/tex]

Answer:

14 cups

Step-by-step explanation:

Amount of juice had = 7/5 gallons

Cup to fill = 1/10 gallons

We can therefore write;

1cup = 1/10 gallons

x cups =7/5 gallons

ross multiply

1/10 x = 7/5

x/10 = 7/5

70 = 5x

x = 70/5

x = 14

Hence 14 cups cam be filled

Answer:

im here for the points

Step-by-step explanation:

Answer:

y = 49

x = 15

Step-by-step explanation:

The angle is 90 degrees and on one side of the bisector is 41 so to find y all you have to do is 90 - 41 = 49

(7x + 13) + (2x - 9) + 41 = 180

add like terms -     9x + 45 = 180

subtract -               9x = 135

Divide -                    x = 15

Answer:

200mph

Step-by-step explanation:

Speed is expressed using the expression

Speed = Distance/Time

For Mattie

Distance = 200miles

Speed = x

Time taken by mattie = Distance/speed

Time taken by mattie = 200/x ... 1

For the propeller plane:

Distance = 800miles

Speed = x+150 (The speed of the plane was 150 mph faster than the speed of the car)

time taken by the plane = 800/x+150

Since Mattie took the same amount of time that it took a turbo propeller plane to travel, then we will equate both expressions as shown:

200/x = 800/150+x

Cross multiply

800x = 200(150+x)

800x = 30,000 + 200x

800x-200x = 30,000

600x = 30,000

x = 30,000/600

x = 50

Get the speed of the plane

Since the speed of the plane is 150+x

Speed of the plane = 150+50

Speed of the plane = 200mph

Answer:

yes

Step-by-step explanation:

Answer:

3/5, 4/5, 3/4

Step-by-step explanation:

First BC is 12 because of the Pythagorean Theorem. I use sohcahtoa to remember. sine is the side opposite of the angle divided by the hypotenuse of the triangle so 12/20 which is 3/5. cosine is adjacent / hypotenuse so 16/20 which is 4/5, and lastly tangent is opposite / adjacent which is 12/16 which is 3/4

The sine, cosine and the tangent of angle should be [tex]3\div 5, 4\div 5, 3\div 4[/tex].

Here first we determine the BC by applying the Pythagorean Theorem.

[tex]= 20^2 - 16^2\\\\= 400 - 256\\\\= 144[/tex]

So the BC should be 12

hence, based on this, we can say that The sine, cosine and the tangent of angle should be [tex]3\div 5, 4\div 5, 3\div 4[/tex].

Learn more about an angle here: https://brainly.com/question/3401487

Answer: Correct option: B. ΔQRS ≈ ΔUTV, SAS

Step-by-step explanation:

IN the given triangles (ΔQRS and ΔUTV),

m∠R = 29° and m∠T = 29°  (given)

[tex]\dfrac{QR}{UT}=\dfrac{16}{8}=2\\\\\dfrac{SR}{VT}=\dfrac{64}{32}=2\\\\\therefore\dfrac{QR}{UT}=\dfrac{SR}{VT}[/tex]

By SAS similarity rule , ΔQRS ≈ ΔUTV .

Correct option: B. ΔQRS ≈ ΔUTV, SAS

Answer:

3

Step-by-step explanation:

You said x=3

Answer:

if the answer isn't 3 then its 1

Answer:

x ≥ 98

[tex]\frac{x}{7}\ge \:14[/tex]

[tex]\frac{7x}{7}\ge \:14\cdot \:7[/tex]

[tex]x\ge \:98\\[/tex]

I hope this helps:

Answer:

the answer is A x>_98

Step-by-step explanation:

just trust me. hoped I helped:)

Answer:

Yes

Step-by-step explanation:

Substitute the x and y values in for x and y to check.

-1 = 7 - 8

-1 = -1

In this instance, (7, -1) is a solution of y = x - 8.

Answer:

[tex] \frac{11}{2} k + \frac{1}{2} (18 + 16k) \\ = \frac{11k + 18 + 16k}{2}=\frac{1}{2} (27k + 18) \\ = (13.5k + 9)[/tex]

Step-by-step explanation:

5 days = 750 miles

=> 1 day = 750 / 5 = 150 miles.

Theo's family will drive 150 miles per day.

Answer:

We reject H₀

Step-by-step explanation:

Normal Distribution with  n  = 22   ( sample size)

n<30 we need to use a t-student distribution

Sample mean  μ =   396        

Population mean  ( required mean )  μ₀  = 405

Sample variance is  441 then sample standard deviation s = √441

s  =  21

Hypothesis Test

Null Hypothesis                                          H₀         μ   =   μ₀

Alternative Hypothesis                               Hₐ       μ   <   μ₀

Significance level   α = 0,1    

The test is a one-tail test to the left

From t-student table we find for  t(c)

degree of fredom     df  = 22 -1       df  =  21

and  α = 0,1           t(c)  =  - 1,3232

To compute t(s)

t(s)  =  ( μ  -  μ₀ ) / s /√n

t(s)  =  ( 396  - 405 )*√n / 21

t(s)  =  - 9 *4,69 /21

t(s)  =  -  2,01

Comparing

t(s) and  t(c)          - 2,01     and   - 1,3232

|t(s)| > |t(c)|   then   t(s) is in the rejection region we must reject H₀

9514 1404 393

Answer:

  36°

Step-by-step explanation:

BY bisects angle B, which has a measure of 72°. That means angles 3 and 4 are each half of 72°, or 36°.

  m∠4 = 36°