In the figure below, AMNO
APQR. Determine the length of QR.
M
2y + 3
4x-2
x+ y
R
21
9
O 14
O3
O 12

In The Figure Below, AMNOAPQR. Determine The Length Of QR.M2y + 34x-2x+ YR219O 14O3O 12

Answers

Answer 1

Given:

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

To find:

The length of QR.

Solution:

We have,

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

Then, [tex]MN=PQ[/tex]                 (CPCTC)

[tex]10=4x-2[/tex]

[tex]10+2=4x[/tex]

[tex]12=4x[/tex]

Divide both sides by 4.

[tex]\dfrac{12}{4}=x[/tex]

[tex]3=x[/tex]

Similarity,

[tex]MO=PR[/tex]            (CPCTC)

[tex]2y+3=21[/tex]

[tex]2y=21-3[/tex]

[tex]2y=18[/tex]

Divide both sides by 2.

[tex]y=9[/tex]

Now,

[tex]x+y=3+9[/tex]

[tex]x+y=12[/tex]

Therefore, the correct option is d.


Related Questions

What is the correct evaluation of x2 - x + y2 when x is equal to 5 and y is equal to -2?

Answers

the value for the expression x² - x + y² for x = 5 and y = - 2 will be 24.

We are given an expression:

x² - x + y²

We need to find the value of the expression for x = 5 and y = - 2.

Now, substituting the values of x and y in the expression that is given to us, we get that:

x² - x + y²

( 5 )² - ( 5 ) + ( - 2 )²

Solving the squares of the numbers, we get that:

25 - 5 + 4

Simplifying to get the value of the expression, we get that:

= 24

Therefore, the value for the expression x² - x + y² for x = 5 and y = - 2 will be 24.

Learn more about expression here:

https://brainly.com/question/723406

#SPJ9

The mass of a bag of potatoes is 860 kg round to the nearest 10kg. i) Give the upper and lower bounds for the mass.

Answers

Answer:

Lower bound ⇒ 855 kgUpper bound ⇒ 865 kg

Step-by-step explanation:

The upper bound is the highest number that a figure can be to be rounded off to the rounded figure.

The lower bound is the lowest number that a figure can be to be rounded odd to the rounded figure.

The lower bound of 860 to the nearest 10 is;

= 855 kg

855 is the lowest figure that can be rounded up to 860.

The Upper bound is;

= 865

865 is the highest figure because no figure above this can be rounded to 860.

855 kg ≤ 860 kg < 865 kg

I didn’t understand this question please help

Answers

Answer:

(a) y = 4x - 15

(b) y = (-1/4)x + 2

Step-by-step explanation:

The slope-intercept equation form for a line is
y = mx + b

Here m is the slope (rise/run) and b is the y-intercept ie the y-value at which the line crosses the y axis at x = 0. Drawing a picture helps

If two lines have the same slope, they are parallel
If another line has slope -(1/m) then  it is perpendicular to the line with slope m

First convert the line equation into slope-intercept form as follows
8x - 2y = 1

Subtract 8x from both sides ==> -2y = 1- 8x
Multiply both sides by -1 ==> 2y = 8x - 1

Divide both sides by 2:
y = 4x - 1/2

Parallel line

y = 4x - 1/2

A parallel line should also have slope = 4

So it's equation will be of the form
y = 4x + b

To determine b, the y intercept, plug in values for x = 4, y =1 ad solve for b
1 = 4(4) + b ==> 1 = 16 + b ==> b = -15

So the equation of a line parallel to 8x - 2y = 1 passing through (4,1) is
y = 4x - 15   (Answer a)

Perpendicular Line

A perpendicular line to y = 4x - 1/2  should have the negative of the reciprocal of the slope
So the slope of the perpendicular line is -(1/4)

Equation is

y =  -(1/4)x  + b

Plug in the point values for (4, 1) to get
1 = - (1/4)(4) + b

1 = -1 + b

b = 2

So the equation of a line perpendicular to 8x - 2y = 1 passing through (4,1) is y = -(1/4)x + 2

Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $21.90. The oil change for the other car required 7 quarts of oil and cost $25.40. How much is the labor fee and how much is each quart of oil?

Answers

Answer:

Step-by-step explanation:

Let x = the fee and let y = the cost per quart of oil

x + 5y = 22.45

x + 7y = 25.45     Multiply this equation by (-1) and add it to the 1st equation

 

-x -7y = -25.45

x + 5y = 22.45

     -2y = -3

        y = $1.50 /quart

 

x + 5(1.50) = 22.45

     x + 7.50 = 22.45

                 x = $14.95   is the basic fee

who made the song welcome to the party

bonus question: what is 1+1

if you answer both correctly i will give you brainlest

Answers

The answer is 2 okokok

Answer:

Diplo, Lil Pump, French Montana

2

Step-by-step explanation:

U
Question 9
10 pts
Solve this system of equations using substitution algebraically. Check your answer using
substitution.
3x + 4y = 36
y= x+8

Answers

Answer:

x = 4/7

y = 60/7

Step-by-step explanation:

3x + 4y = 36

y = x + 8

Substitute the second equation into the first since it already has the y isolated for you:

3x + 4(x + 8) = 36

3x + 4x + 32 = 36

7x = 4

x = 4/7

Take the answer you got from the equation above and plug that into the second equation:

y = 4/7 + 8

y = 60/7

To check just LS/RS both equations:

3(4/7) + 4(60/7) = 36

12/7 = 240/7 = 36

252/7 = 36

36 = 36

LS = RS

60/7 = 4/7 + 8

60/7 = 60/7

LS = RS

Graph the point that has the coordinates

Answers

Answer/Step-by-step explanation:

From the middle go left, stop between -4 and -5, then go up and stop between 2 and 3,

factorise xy-3x²+2x​

Answers

[tex]xy-3x^2+2x[/tex]

Factor by pulling out the x-term.

[tex]x(y-3x+2)[/tex]

Arrange as we get -

[tex]x(-3x+y+2)[/tex]       ----------> Answer

A frisbee-golf club recorded the ages of its members and used the results to construct this histogram.

Find the number of members 30 years of age or younger

Answers

26-30 : 10 members
21-24 : 2 members
16-20 : 6 members
10 + 2 + 6 = 18 members which are 30 or younger
- hope this helps ♡

A histogram is a representation of the frequency distribution of a given data point of one variable on a graph.

The number of members for different ages.

16 - 20 = 6 members

21 - 25 = 2 members

26 - 30 = 10 members

31 - 35 = 3 members

The number of members 30 years and younger is 18 members.

What is a histogram?

A histogram is a representation of the frequency distribution of a given data point of one variable on a graph.

We have,

From the graph, we see that,

Number of members for different ages.

16 - 20 = 6 members

21 - 25 = 2 members

26 - 30 = 10 members

31 - 35 = 3 members

Now,

The number of members 30 years and younger

= 6 + 2 + 10

=  18 members

Thus,

16 - 20 = 6 members

21 - 25 = 2 members

26 - 30 = 10 members

31 - 35 = 3 members

The number of members 30 years and younger is 18 members.

Learn more about histograms here:

https://brainly.com/question/16819077

#SPJ2

A box of cereal weighs 0.48 kilograms. What is the weight in pounds to the nearest hundredth of the cereal box

Answers

Answer:

1.06

I hope this helps :D

The shaded fiqure is a thombus,
The area of the shaded section is 60 square units, What
is the value of x?
4 units
6 units
8 units
9 units

Answers

Actually the answers 8

Carrie can weed a garden in 7 hours, and her mother can do it in 3 hours. How long will take the two of them working together to weed the garden?

Answers

Answer:

10 hours.

Step-by-step explanation:

7 + 3 = 10.

Dawn bought 3 video games and 9 DVDs for $75. Jerry bought
5 video games and 10 DVDs for $25 more than Dawn. How
much did each DVD cost?

Answers

Answer:

$5

Step-by-step explanation:

We can solve this using a system of linear equations. The equations are written like this:

3v + 9d = 75

5v + 10d = 100 (25 more than Dawn's total is 100)

V represents video games and d represents DVDs.

Let's isolate a variable, I'm going to isolate v in the first equation:

3v = -9d + 75

v = -3d + 25

Now that we isolated v we can plug it in to the second equation:

5(-3d + 25) + 10d = 100

-15d + 125 + 10d = 100

-5d + 125 = 100

-5d = -25

d = 5

Therefore, each DVD cost $5.

Check:

3v + 9(5) = 75

3v + 45 = 75

3v = 30

v = 10

5(10) + 10(5) = 100

50 + 50 = 100

100 = 100

I hope this helps!!

- Kay :)

Juan rented a paddleboard for $5.75 per hour plus a $17.50 fee. Write an expression that shows how much it will cost Juan to rent the paddleboard for x hours. Then evaluate the expression for 3 hours

Answers

Answer:

17.50 + 5.75x

$34.75

Step-by-step explanation:

17.50 + 5.75x

17.50 + 5.75(3)

17.50 + 17.25

34.75

The required algebraic expression is $5.75x + $17.50 which it will cost Juan to rent the paddleboard for x hours.

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given that Juan rented a paddleboard for $5.75 per hour plus a $17.50 fee.

Let x represents the number of hours

According to the given question,

The algebraic expression would be as:

⇒ $5.75 × x + $17.50

⇒ $5.75x + $17.50  ....(i)

Now we have to evaluate the expression for 3 hours.

Substitute the value of x = 3 in the above expression model (i), and we get

⇒ $5.75 × 3 + $17.50

⇒ $17.25 + $17.50

⇒ $34.75

Thus, the required algebraic expression is $5.75x + $17.50

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ2

a color printer prints 26 pages in 12 minutes. how many minutes does it take per page​

Answers

Answer:

0.46 ( i didn’t want to calculate the whole thing because it repeats) or 6/13

Step-by-step explanation:

12 over 26 = 6 over 13

6 over 13 is 0.46

NEED HELP ASAP!
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(7x-8)
59°
73°

Answers

Answer: 8

Step-by-step explanation: Add up the angles that do not include x.

Subtract 180 by 132, which equals 48.

7x-8=48
Remove -8 by adding 8 to 48.
7x=56
Divivde 7x by 7 on both sides
x=8

PLEASE HELP THIS IS DUE AT 11:00

Answers

Your answer is 3 feet
The answer is 3 feet long


If the graph of y=-x^2 is translated horizontally 10 units to the right and translated vertically 3 units upwards, what is its new
equation?

Answers

Answer:

y=[tex](x-10)^{2}[/tex]+3

Step-by-step explanation

in order to shift the equation to the right you must subtract a positive number from x (ex: -10)

to shift the equation upwards just add the positive number to the end of the equation (ex: +3)

-12 divided by (-2/3)

Answers

the answers is 18 or 18/1

please help. I dont understand it ​

Answers

Answer:

D. 32

Step-by-step explanation:

[tex] {4}^{ - 1} \times ( {2}^{3} \div {4}^{ - 2} )[/tex]

[tex] {2}^{ - 2} \times ( {2}^{3} \div {2}^{ - 4} )[/tex]

[tex] {2}^{ - 2} \times {2}^{7} [/tex]

[tex] = {2}^{5} = 32[/tex]

Round 4.645 to the
nearest whole number.

Answers

5. since .6 is greater than 5, we round up.

Answer:

the answer is 5

Step-by-step explanation:

Number Rounded to Nearest Whole Number

4.645 5

5.645 6

6.645 7

7.645 8

8.645 9

9.645 10

10.645 11

11.645 12

12.645 13

13.645 14

Who's excited for Christmas?!?! :D
if not why?

Answers

I’m very excited, I get to see my brothers so that’s fun

Answer:

me

Step-by-step explanation:

Sketch the graph of each line 2x+y=2

Answers

Answer:

Step-by-step explanation:

mark at y2 and 2x

A well know Statistical Institution claims that the average College tuition for a law degree costs at least thirty five thousand dollars. Analyzing a sample of fifty law schools in the vicinity of the study we found the sample had a mean tuition of $33,450 with a population standard deviation of $5,978 per year. At 2% level of significance test the Institution's claim.

Answers

Step-by-step explanation:

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 35000

Alternative Hypothesis, Ha: μ < 35000

Test statistic,

z = (xbar - mu)/(sigma/sqrt(n))

z = (33450 - 35000)/(5978/sqrt(50))

z = -1.83

P-value Approach

P-value = 0.0336

As P-value >= 0.02, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the average College tuition for a law degree costs at least thirty five thousand dollars.

kenson and shelly are each saving money

Answers

Answer:

for what reason? lol

Step-by-step explanation:

Subtract:

(6 + 3x) - (-4 - 7x

Answers

Answer:

10+10x

Step-by-step explanation:

(6+3x)-(-4-7x)=

6+3y+4+7x=

10+10x

Answer:

10x+10

brainlest

Step-by-step explanation:

(6 + 3x) - (-4 - 7x

If K is the midpoint of JL, JK = 9x - 1 and KL = 2x + 27, find JL

Answers

Answer:

JL = 70

Step-by-step explanation:


g(n) = -n²-3
evaluate g(-2)

?

Answers

g(-2) = -2² = 4 - 3 = 1

g(-2) = 1

52 POINTS KIND OF EASY QUESTION

Answers

9b . Simplify the first and second term above the division. Then simplify the bottom part. Then divide the final terms.

6. If a refrigerator has a mass of 750 kg and a volume of 600 mL, what is it's density?

Answers

Answer:

[tex] \sf \rho \: = 1.25[/tex]

Step-by-step explanation:

Density, is the substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

[tex]{\displaystyle \rho ={\frac {m}{V}}} [/tex]

where ρ is the density, m is the mass, and V is the volume.

[tex] \sf \rho = \frac{750}{600} [/tex]

[tex] \sf \rho \: = 1.25[/tex]

Therefore, density is equal to 1.25

Other Questions
Xavier goes to the gym several days a week and does random exercises without a workout plan. After a month, he realizes that he is not making any progress. What should Xavier do? A. Increase the intensity. B. Set clear goals. C. Break for one week. D. Find a workout partner. Write the reciprocal of (-6/7)^57^0 If a driver uses 1/ 10 of gas every day what fraction of a tank will he use in 1 week ]I need help with just B and c I got AYear number Western Beach width (in feet) Dunes Beach width (in feet)0 100 205 90 4510 80 7011 78 7512 76 8015 70 95A. Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.B. Between which years will the beaches have approximately the same width?C. Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width? Solve for x. 4(1 - x) + 2 x = -3(x + 1) this general term describes the wavelike pattern of rising and falling economic activity, consisting of expansions, peaks, contractions, and troughs. how long did it take for a car to travel 20 meters with a speed of 10m/s Describe two ways civillians were killed during World War II According to the author, research on autonomous vehicles -A. addresses their concern for safety.B. shows that they will cut back on human error.C. does not yet prove their safety.D. indicates a positive outcome. Which sentence best describes how matter moves through an ecosystem? A. Matter is made by producers and is destroyed when eaten. B. Matter only moves from consumers to producers. C. Matter only moves from producers to decomposers. D. Matter is continually cycled through an ecosystem.Reset FAST PLEASSSEEEEEE 1. All points along the same contour line are at the same, elevation2. All contour lines eventually connect with themselves.-3. Contour lines never cross each other.4. Contour lines never split or branch.Each drawing below violates a rule of contour lines. Match each rule with thedrawing that violates the rule.A1400B.C.250D500 Factor each expression into its simplest form5x-30 Place the numbers in order from smallest to largest. 22, -14, -35, 6 What is the value of x with 2x + 57 degree angle and 4x - 3 degree angle in a Alternate exterior Use the diagram to fill in the angle that makes the statement true. Can some one help me wit this please Which style of decision making will consumers who develop brand loyalty use?A.extensive decision makingB.limited decision makingC.routine decision making D.opportunity based decision making A nurse assesses a client with dry, rough, scaly skin without lesions on the legs. the client reports itching in the affected area. what skin assessment would the nurse document? question 5: 6 people go to a movie and sit next to each other in 6 adjacent seats in the front row of the theatre. if a cannot sit to the right of f, how many different arrangements are possible? Mendel crossing plants problem :which one is the answer and why?