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
Answers
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
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
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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
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,
If K is the midpoint of JL, JK = 9x - 1 and KL = 2x + 27, find JL
Answers
Answer:
JL = 70
Step-by-step explanation:
Who's excited for Christmas?!?! :D
if not why?
Answers
Answer:
me
Step-by-step explanation:
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
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.
Sketch the graph of each line 2x+y=2
Answers
Answer:
Step-by-step explanation:
mark at y2 and 2x
kenson and shelly are each saving money
Answers
Answer:
for what reason? lol
Step-by-step explanation:
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.
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g(n) = -n²-3
evaluate g(-2)
?
Answers
g(-2) = 1
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
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
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
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.
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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
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
52 POINTS KIND OF EASY QUESTION
Answers
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
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
Round 4.645 to the
nearest whole number.
Answers
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
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
PLEASE HELP THIS IS DUE AT 11:00
Answers
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
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
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
Answer:
Diplo, Lil Pump, French Montana
2
Step-by-step explanation:
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 :)
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]
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 kgStep-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