Help? Show work!
Triangle PQR ≅ Triangle XYZ
PQ = 3a + 4 and XY = 5a – 12. Find a and PQ.

Answers

Answer 1

Given:

[tex]\Delta PQR\cong \Delta XYZ[/tex]

[tex]PQ=3a+4[/tex]

[tex]XY=5a-12[/tex]

To find:

The value of a and PQ.

Solution:

We have,

[tex]\Delta PQR\cong \Delta XYZ[/tex]

[tex]PQ\cong XY[/tex]                            (CPCTC)

So,

[tex]PQ=XY[/tex]

[tex]3a+4=5a-12[/tex]

Isolating variable terms, we get

[tex]3a-5a=-4-12[/tex]

[tex]-2a=-16[/tex]

Divide both sides by -2.

[tex]a=\dfrac{-16}{-2}[/tex]

[tex]a=8[/tex]

Now,

[tex]PQ=3a+4[/tex]

[tex]PQ=3(8)+4[/tex]

[tex]PQ=24+4[/tex]

[tex]PQ=28[/tex]

Therefore, the value of a is 8 and the value of PQ is 28.


Related Questions


Not every straight line will pass the vertical line test. What is the only type of straight line that would fail the vertical line test?

Answers

Answer:

Gfdyuihgff hibhhiuuuuyyygfxf. Hugfti. Hffty9

Answer:

vertical line

Step-by-step explanation:

Mike recorded the number of hours he slept each night for a period of 5 days as shown in the table below.

Based on the information in the table, what was the total number of hours that Mike slept from Monday through Friday?

Answers

Step-by-step explanation:

8+9= 17

7 3/4 + 7 1/4= 15

15 + 5 1/2= 20 1/2

17 + 20 1/2 = 37 1/2

HELP GIVING BRAINLIEST NUMBER 5!!!!!!

Answers

Answer:

1 solution

Step-by-step explanation:

4x + 5 = 6(x+3) - 20 - 2x

4x + 5 = 6x + 18 - 20 - 2x

4x + 5 = 4x -2

X = 3 therefore, there is only one solution

what is the ordered pair to y=7x-2

Answers

It would be (0,-2) I believe

Can someone tell just the answer

Answers

Answer:

Option D is correct .

Step by step explanation:

A function is given to us and we need to find its inverse . The function is g(x) = -2x⁵ - 2.

So for finding its inverse , exachange x with y .

⇒ g(x) = -2x⁵ - 2 .

Let g(x) = y ,

⇒ y = -2x⁵ - 2 .

Replace x with y ,

⇒ x = -2y⁵ - 2

⇒ x + 2 = -2y⁵

⇒ y⁵ = x+2 / -2

⇒ y⁵ = (-1) ( x + 2) / (-1)(-2)

⇒ y⁵ = -x - 2/ 2

y = [ ( -x -2)/2 ]

Hence the inverse of the function is ,

[tex]\boxed{\red{\bf f^{-1}(x)=\sqrt[5]{\dfrac{-x-2}{2}}}}[/tex]

Hence the correct option is (D) .

Write as a power of 10. How did you do it? a) 100 b) 10 000 c) 100 000 d) 10 e) 1000 f) 1 000 000

Answers

Answer: ↓↓↓

Step-by-step explanation:

a.) 100 - 10^2

b.) 10,000 - 10^4

c.) 100,000 - 10^5

d.) 10 - 10^1

e.) 1000 - 10^3

f.) 1,000,000 - 10^6

What I do personally is that I count the number of zeros in the number and that is how many powers the ten powers to. Like a, there are two zeros in 100 so its 10 to the power of 2.

tom goes on hoilday south africa

Answers

Answer:

Yes, good for him. lol

Step-by-step explanation:

Answer:

what he do there?

solve by the method of elimination 2xy=3;3x+y_7






please answer me




meeeeeee​

Answers

Answer:

x = 2 and y = 1

Step-by-step explanation:

Given equations are :

2x-y=3 ...(1)

3x+y=7 ...(2)

Add equation (1) and (2) as follows :

2x-y + 3x+y = 3 + 7

2x + 3x = 10

5x = 10

x = 2

Put the value of x in equation (1)

2(2)-y=3

4-y = 3

y = 4-3

y = 1

Hence, the solution of the given equations are (2,1).

John has a jar of between 500 and 600 coins that are all nickels, dimes and quarters. The ration of the number of quarters to dimes is 8 : 5 and the ratio of the number of dimes to the number of nickels is 6 : 11. What is the total value of the Money in john’s jar of coins?

Answers

Poooooooooooooooooooop

-20 > -2x + 4 inequality

Answers

Step-by-step explanation:

-20 > -2x + 4

2x > 4 + 20

2x > 24

x > 12

or

x ∈ 《12 , + ∞》

-20 > -2x + 4

-20 -4 > -2x

-24 > -2x

-24/-2 < x  <inequality changes when you divide by a -ve no. >

12 < x

Pls answer both I really need help...

Answers

Step-by-step explanation:

the correct answer is in there

Answer:

A. Jim did not simplify the (4-2)^2 which is the first step.

B.

5-3(4-2)^2 = 5-3(4)

5-12=-7

Step-by-step explanation:

Hopefully this helps. Got some help from math-way lol

NEED HELP FAST PLEASE.
Please answer all these.
AND BECAUSE YOUR GONNA ANSWER ALL OF THEN IMA GIVE YOU 50 POINT

Answers

Answer:

60

Step-by-step explanation:

which graph could represent a function ? ?

Answers

Answer:

The third Graph

Step-by-step explanation:

Using the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Answer:

The third Graph

Step-by-step explanation:

4 +14 x 17 x 4 + 3
Orders of operations

Answers

959
You do 14 times 17 then times that by 4 that add 4 and 3

1. If you randomly select a piece of fruit from this jar, what is the P(orange)? Write answer as a simplified fraction.
2 oranges and 6 apples are in the jar​

Answers

2/8 = 1/4

1/4 is the simplest form of the fraction.

There are 2 oranges out of 8 fruits

Find the value of x in the triangle shown below choose 1 answer

Answers

Answer:

x=10

Step-by-step explanation:

X^2=6^+8^

x^2=36=64

x^2=100, square root of 100 =10

x=10

its 10 ! hope this helps !

Which of the following is not a function?
a. (1,1),(2,2), (3,3), (4,4)
b. (2,3), (2,4), (3,3), (3,4)
c (2,4),(4,8).(10,12). (4,10)
d. (2,4), (3,4), (5,4), (6,4)​

Answers

Answer: B

Number on the left: x-value
Number on the right: y-value

If there are 2 y-values for one x-value it is NOT considered a function.

For instance in the answer:

(2,3), (2,4), (3,3), (3,4)

You can clearly see that the x-values (2 & 3) repeat more than once; therefore, it is NOT a function.

On the other hand if you have 2 DIFFERENT x-values for the same y-value it IS A FUNCTION.

For ex D: (2,4), (3,4), (5,4), (6,4)

As you can see there are 4 DIFFERENT x-values with same y-value; therefore it is A FUNCTION

To make it easier:

If x-values appear more than once = NOT A FUNCTION

If x-values appear only ONCE = FUNCTION

Remember: y-values are ALLOWED to repeat

I hope this helps. If you have any questions please let me know in the comments.

A copy machine makes 36 copies per minute. How long does it take to make 126 copies?

Answers

Answer:

It will take 3.5 minutes to make 126 copies

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can do 126/36 to get our answer since 126 is the total copies and 36 is the copies we can do in a minute. 126/36 = 3.5 so it will take 3.5 minutes.

Conner had 354$ and spent 243 cents. How much did conner have left and how many dollars? please help. If you do, then I will tell you a secret.

Answers

Conner: $354 - 243 cents

243 cents = $2.43 because 100 cents = 1 dollar

Conner: $354 - $2.43 = $351.57

$351.57

He has 351 dollars left.

Answer:

354 - 243 = 111

Step-by-step explanation:

300 - 200 = 100

 50 -    40 =   10

   4  -      3  =   1

100  +  10 + 1 = 111

Can someone answer these two problems??

Answers

9514 1404 393

Answer:

  B

Step-by-step explanation:

The given equation is in slope-intercept form:

  y = mx + b

where the slope is m = -3 and the y-intercept is b = +2.

So, the graph will have a slope of ...

  "rise"/"run" = -3 = -3/1

and will cross the y-axis at y=2.

Graphs A and B cross the y-axis in the right place, but only Graph B has a negative "rise" a x increases.

Please help me answer this question thank you.

Answers

Answer:

122°

Step-by-step explanation:

10a + 2° + 5a - 2° = 180° [ being linear pair ]

15a = 180°

a = 180° / 15

a =12°

Now

<XYQ = 10a + 2° = 10 * 12° + 2° = 120° + 2° = 122°

Hope it will help :)

pls help i’ll give you brainliest

Answers

Step-by-step explanation:

5x and -7x are like terms

5x-7x+9=-2x+9 and there's your equivalent expression

Answer:

i want to say 7x is the answer

Step-by-step explanation:

because if you add 5x to 9 = to 14 the -7 = to 7x

Hey ! I’m trying to find the slope. If you could help me that’ll be great thank you !!

Answers that might be:

A. 2/3
B. 1
C. 0
D. -1

Answers

Answer:

The answer is B. 1

Step-by-step explanation:

rise over run

1/1=1

Answer:

I'm pretty sure it's B. 1

Step-by-step explanation:

Because I got 2 points where the line crosses and I made a triangle joining the points

Then I did the change in y/change in x

and so I did 2/2 and got 1

hopefully that's right :)

A piece of timber is x cm long. 9 cm is cut off how much is left

Answers

Answer:

x-9cm

Step-by-step explanation:

compute

Amy and Ben share £21 between them in the ratio 5 : 2. How much does Amy get?

(Im really sorry I just don't understand ratio.)

Answers

Answer:

✑ [tex] \underline{ \underline{ \sf{First ,\: Let's \: learn \: about \: the \: ratio}}} : [/tex]

Let us consider , there are 30 boys and 40 girls in a school. So, the ratio of number of boys to number of girls = [tex] \sf{ \frac{30}{40} = \frac{3}{4} = 3:4}[/tex] and read as 3 is to 4. We can say , the ratio compares two of more quantities of same unit. Until two quantities have same units , it is meaningless to compare by ratio. So, to find the ratio of two quantities , it is necessary to express them in same unit or of same kind. Since , they are in division form. So ,ratio is unit less quantity. Thus , the ratio is a comparison of two quantities of the same kind in division which doesn't have any units. For example : [tex] \sf{ \frac{a}{b}} [/tex] is a ratio and is read as ' a is to b ' in which ' a : is antecedent and ' b ' is called consequent.

✎ [tex] \underline{ \underline{ \sf{Now \: let's \: solve : }}}[/tex]

☪ [tex] \underline{ \sf{Solution}} : [/tex]

£ 21 is to be divided between Amy and Ben in the ratio 5 : 2. So, let Amy get £ 5x and Ben get £ 2x.

Then , According to the question , [tex] \text{5x +2x = 21}[/tex]

Solve for x :

⇝ [tex] \sf{7x = 21}[/tex]

⇝ [tex] \sf{ \frac{7x}{7} = \frac{21}{7} }[/tex]

⇝ [tex] \sf{x = 3}[/tex]

The value of x is 3. Now , substitute the value of x in 5x :

Amy received £ 5x = 5 × 3 = £ 15 .

☥ [tex] \boxed{ \boxed{ \tt{Our \: final \: answer \: is \bold{£ \: 15}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day / night ♡

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Find the total amount given the original price and tax rate. Round to the nearest cent if necessary.
$15.25,7%

Answers

Given:

Original price = $15.25

Tax rate = 7%

To find:

The total amount.

Solution:

We know that,

Total amount = Original price + Tax

According to the question,

Total amount = 15.25 + 7% of 15.25

[tex]\text{Total amount}=15.25+\dfrac{7}{100}\times 15.25[/tex]

[tex]\text{Total amount}=15.25+1.0675[/tex]

[tex]\text{Total amount}=16.3175[/tex]

Round to the nearest cent (two decimal places).

[tex]\text{Total amount}\approx 16.32[/tex]

Therefore, the total value is $16.32.

5 12 14 will form a acute?
True or false

Answers

No it won't. it's false

cuz proofs here.

(5²)+(12²)= (169)

√(169) = 13

.. so if 13 was the number at 14

it would have been true.

currently the answer is false

A delivery truck drove 52 miles per hour. It took 4 hours to travel between two towns. What is the distance between the two towns? Use the equation dert, where d is distance, r is rate, and t is time. The distance between the two towns is miles. ​

Answers

Answer:

104?

Step-by-step explanation:

52*4 = 208 ÷ 2 = 104

What is the sum of all prime numbers beetween 70 to 80?

What is the product of prime numbers immediately before and after 50?

Answer both plz thx....​

Answers

Answer:

Prime numbers between 70 and 80 are 71,73,79

71+73+79=223

50 =2x5x5=2x5^2

PLEASE HELP!!
Graph the line with the equation

Answers

Answer:

Step-by-step explanation:

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