In the diagram, △NPQ ∼ △NLM and PL = 8.
a. Find the value of x
b. Find the lengths NP and NL, rounding to the nearest hundredth.
NP =
and NL =
Answers
Answer:
x = 14
NP = 3.66
NL = 8.01
Step-by-step explanation:
since △NPQ ∼ △NLM
<L = <P
3x + 18 = 60
3x = 60 - 18
3x = 42
x = 42/3
x = 14
Similarly;
PN/PL = QN/QM
y/8 = 3.2/7
Cross multiply
7y = 3.2* 8
7y = 25.6
y = 25.6/7
y = 3.66
Hence NP = 3.66
Also
NP/NQ = NL/NM
3.66/3.2 = NL/7
3.2NL = 7 * 3.66
3.2NL = 25.62
NL = 25.62/3.2
NL = 8.01
Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle. The value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).
Given information-The given tingle NPQ and triangle NLM are the similar triangle.
The length of the line PL is 8 cm.
Similar triangle-Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle.
Value of the x-
As the two triangle are similar triangle, thus the length of the angle P is equal to the angle L. Therefore,
[tex]\angle L =\angle P\\ [/tex]
Keep the value of the angle from the diagram,
[tex]\begin{algined}\\ 3x+18&=60\\ 3x&=60-18\\\\ 3x&=42\\ x&=\dfrac{42}{3} \\ x&=14\\ \end[/tex]
Thus the value of the x is 14.
The length of the NP.
In the similar triangle the following ratios are equal,
[tex]\dfrac{PN}{PL} =\dfrac{QN}{QM} [/tex]
Put the values from the diagram,
[tex]\begin{aligned} \dfrac{y}{8}&=\dfrac{3.2}{7} \\ y&=\dfrac{3.2}{7} \times 8\\ y&=3.66\\ \end[/tex]
Value of y is equal to the length NP. Hence the length of the NP is equal to the 3.66 cm.
The length of the NL-
In the similar triangle the following ratios are equal,
[tex]\dfrac{NP}{NQ} =\dfrac{NL}{NM} [/tex]
Put the values from the diagram,
[tex]\begin{aligned} \dfrac{3.66}{3.2}&=\dfrac{NL}{7} \\ NL&=\dfrac{3.66}{3.2} \times 7\\ y&=8.01\\ \end[/tex]
Thus the length of the NL is equal to the 8.01 cm.
Hence the value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).
Learn more about the similar triangle here;
https://brainly.com/question/25882965
Related Questions
The circle graph shows how Tremaine divided his time on the computer last week. Tremaine used the computer a total of 30 hours last week. How many more hours did Tremaine use the computer to play games than to do research?
A) 20 hours
B) 6 hours
C) 1.5 hours
D) 7.5 hours
Answers
Answer:
A) 20 hours
Step-by-step explanation:
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25-5=20
Find the 52nd term of the arithmetic sequence 5, 9, 13, ...
Answers
Answer I need it please
Answers
Answer:
the answer is A
Step-by-step explanation:
Multiply.
−3.9(−5.6)(3)
The product is
Answers
Answer:
65.52
Step-by-step explanation:
−3.9×−5.6×3
Multiply −3.9 and −5.6 to get 21.84.
21.84×3
Multiply 21.84 and 3 to get 65.52.
65.52
Mr. Dash recorded the odometer
readings in his car for a business trip.
Before the trip, the odometer read
23,125.6. At the end of the trip it read
23,219.1. If Mr. Dash is reimbursed
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hewp pwease ☺️thanks
Answers
The Answer Is 35 Inches Squared
The vertices of a quadrilateral are M(-1,1), N(1,-2),O(5,0), and P(3,3).
Which statement describes quadrilateral MNOP?
Quadrilateral MNOP is a rhombus, but not a square.
Quadrilateral MNOP is a rectangle.
Quadrilateral MNOP is a trapezoid.
Quadrilateral MNOP is a parallelogram, but not a rectangle
Answers
Answer:
Quadrilateral MNOP is a rectangle.
Step-by-step explanation:
Quadrilateral MNOP is a parallelogram, but not a rectangle.
What is a rhombus?
A rhombus is a quadrilateral with all equal sides but angles not right angles. Diagonals of a rhombus intersect at 90°.
M(-1,1), N(1,-2),O(5,0), and P(3,3)
MN=√13
NO=√20
OP=√13
PM=√20
This means opposite sides are equal.
Slope of MN = -2/3
Slope of NO=2
The Slope of MN * The Slope of NO =-4/3 ≠ -1
This means the angle between adjacent sides is not equal to 90°
This means MNOP is not a rectangle
The Slope of MO = -6
The Slope of NP = 2/5
The Slope of MO * The Slope of NP =-12/5 ≠ -1
This means diagonals do not intersect at right angles.
This means MNOP is not a rhombus.
Slope of MN = -2/3
Slope of OP = -2/3
Slope of MN =Slope of OP
Similarly, Slope of MP =Slope of NO
So, quadrilateral MNOP is a parallelogram, but not a rectangle.
Thus, quadrilateral MNOP is a parallelogram, but not a rectangle.
To get more about rhombus visit:
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A composite figure is shown. What is the volume of the composite figure? 4 cm 6 cm 4 cm 9 cm 5 cm
Answers
Answer:
No figure shown.
Step-by-step explanation:
Answanswer:
the answer is 4,320.
Step by-step explanation:
The reason the volume is this is becuase you first need to know the volume.
V= L x W x H. (Length and width are also called base.)
Now what you do is just multiply 4*6= 24*4= 96*9= 944*5= 3,420
Complete the input-output table for log4X. How would I solve this?
Answers
Answer:
[tex]x \to f(x)[/tex]
[tex]0.25 \to -1[/tex]
[tex]0.5 \to -0.5[/tex]
[tex]1 \to 0[/tex]
[tex]2 \to 0.5[/tex]
[tex]4 \to 1[/tex]
[tex]8 \to 1.5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = log_4(x)[/tex]
[tex]x = 0.5[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(0.5) = log_4(0.5)[/tex]
Apply law of logarithm
[tex]f(0.5) = \frac{log(0.5)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(0.5) = -0.5[/tex]
[tex]x = 1[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(1) = log_4(1)[/tex]
Express 1 as 4^0
[tex]f(1) = log_4(4^0)[/tex]
Apply law of logarithm
[tex]f(1) = 0*log_4(4)[/tex]
[tex]f(1) = 0[/tex]
[tex]x = 2[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(2) = log_4(2)[/tex]
Apply law of logarithm
[tex]f(2) = \frac{log(2)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(2) = 0.5[/tex]
[tex]x = 4[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(4) = log_4(4)[/tex]
[tex]log_a(a) = 1[/tex]
So:
[tex]f(4) = 1[/tex]
[tex]x = 8[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(8) = log_4(8)[/tex]
Apply law of logarithm
[tex]f(8) = \frac{log(8)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(8) = 1.5[/tex]
So, the complete table is:
[tex]x \to f(x)[/tex]
[tex]0.25 \to -1[/tex]
[tex]0.5 \to -0.5[/tex]
[tex]1 \to 0[/tex]
[tex]2 \to 0.5[/tex]
[tex]4 \to 1[/tex]
[tex]8 \to 1.5[/tex]
Which fraction is the product of 5/4 x 6?
Answers
Answer:
15 x /2
Step-by-step explanation:
An example of a rectangular Prism can be: A globe or ball O Fish tank o Bowl Can
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Answer:
Fish Tank
Step-by-step explanation:
This of a rectangular prism as a cardboard box. It has rectangles on the top and the bottom. The fish tank is somewhat similar to this so it will be a rectangular prism.
what should be added to -7/3 to get 3/7
A.21/58
B.58/21
C.47/21
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Answers
Answer:
b
Step-by-step explanation:
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Answers
Answer:
4
Step-by-step explanation:
we have hypotenuse and opposite so we can use sin
sin(45) =O/4√2
rearrange
sin(45)x4√2 =O
=4
HELPPP 50 points. FASTTTT THANK YOU
Answers
Hope this helped. The answer is in the picture.
○( ＾皿＾)っ
Answer: I can think of is c but tell me if I'm wrong
Step-by-step explanation:
Come and get your love
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Hail (Hail), what's the matter with you feel right
Don't you feel right, baby
Hail, oh yeah, get it from the main vine, all right
Come and get your love
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Answer:
boom boom boom
Step-by-step explanation:
Answer:
ok?
Step-by-step explanation:
Dobie works as a window washer, and finds lots of time to think while working. He notices when windows are cracked, and fells that the number of cracked windows has been increasing. He wants to determine if this increase is statistically significant by applying a control chart. He collected data for the past 10 days measuring the number of cracked windows he observed per shift.
What is the UCL?
a. 5.90
b. 59.00
c. 13.19
d. 2.42
The LCL?
a. 0
b. 20.14
c. 5.90
d. 2014
Is the number of observed cracked windows within control limits?
a. No
b. Yes
Day Day Day Day Day Day Day Day Day Day
# of cracks 1 2 3 4 5 6 7 8 9 10
3 4 2 4 6 5 8 8 7 12
Dobie noted that the windows he washes may have multiple panes per window. So, rather than counting cracked windows, Dobie instead converts the prior data into cracked window panes. Based on the data below:
Day Day Day Day Day Day Day Day Day Day
# of cracks 1 2 3 4 5 6 7 8 9 10
6 11 4 12 13 12 11 13 7 19
What is the UCL?
a. 13.19
b. 23.66
c. 20.66
d. 10.80
The LCL?
a. 0
b. 10.8
c. 0.94
d. 3.29
Is the number of observed cracked window panes within control limits?
a. Yes
b. No
Is Dobie’s theory that the number of cracked window panes is increasing valid?
a. No
b. Yes
Answers
A.34
B.268
C.2,145
D.17,157
Answers
And um I’ll answer any time bzbehejrjr
Djejeje
Mariana's recipe calls for 2 cups of sugar to make 12 cupcakes. Which ratio of cups of sugar to cupcakes is equivalent to Mariana's recipe?
Answers
Answer:
2:12
Step-by-step explanation:
The ratio of cups of sugar to cupcakes is equivalent to 1:6.
Given that Mariana's recipe calls for 2 cups of sugar to make 12 cupcakes.
What is the ratio?The ratio is the comparison of two quantities. It is generally represented by a fraction.
2 cups of sugar: 12 cupcakes = 2:12
2:12 = 2/12 =1/6 =1:6
So, the ratio of cups of sugar to cupcakes is equivalent to 1:6.
Therefore, the ratio of cups of sugar to cupcakes is equivalent to 1:6.
To get more about ratios visit:
https://brainly.com/question/2328454
If a = 2 and b= -3, find the value of 2ab + 3b
Answers
Answer:
-21
Step-by-step explanation:
-12+(-9)= -21
Answer:
-21 is the answer to this question
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan's father and paternal grandfather were allergic to penicillin, Nathan has a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. If the test predicts that Nathan is not allergic to penicillin, what is the probability after the test that Nathan is not allergic to the drug?
A) 0.1135
B) 0.2450
C) 0.9423
D) 0.9932
Answers
25% x 98%
0.25 x 0.95 (changed to decimals)
= B) 0.2450
Answer:
this is the answer!!
Step-by-step explanation:
Henry plans to buy Pepsee for people to drink at his birthday party. The grocery store has a sale
in which the first liter of Pepsee costs $3, and every liter that is bought after that costs $1.50.
Henry has $9 to spend.
What is the maximum number of liters Henry can buy? 4 liters
4.67 liters
5 liters
6 liters
Answers
Answer:4,67
Step-by-step explanation:
Martina and Cameron each want to run for president of their school's student body council . In order to do so, they must collect a certain number of signatures and get a nomination So far Martina has 10 signatures , and Cameron has 15. Martina is collecting signatures at an average rate of 2 per day, whereas Cameron is averaging 1 signature every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures . many signatures will they both have? Write a system of equationsgraph them, and type the solution
Answers
Answer:
20
Step-by-step explanation:
I hope the answer satisfies you and hope that you understand my handwriting as I have explained. Thanks for the problem, it also helps me.
Plzzzz help I give 100points
Answers
Answer:
The second 1: Beaver dams can make water safer and cleaner
Step-by-step explanation:
Since Beaver dams create wetland = new plants and animals to area = clean water, so beaver dams = clean water.
Answer:
I WANT POINTS
Step-by-step explanation:
NOTHING TO SAY ABOUT I-Ready.
Which of the following inequalities matches the
graph?
Answers
The line is solid (which is why the sign has a line which represents equal to)
And u only have the x value which is 5 so yeah
PLEASE HELP ILL MARK BRAINLIEST
Answers
Answer:
convert it to improper fractions first
Step-by-step explanation:
4 x 7 + 3 = 31
So, 7 3/4 = 31/4
Similarly, 5 x 2 + 2 = 12
So, 2 2/5 = 12/5
Now we have,
31/4 - 12/5
Make the denominators same....
Multiply both the denominators by each other...
4 x 5 and 5 x 4 = 20 both the denominators equal to 20.
Now multiply the numerators like that
so, 31 x 5 and 12 x 4
equals to 151/20 and 48/20
Now subtract both ...
151-48 = 103
So the answer is 103/20
Hope it helps!!!
Write an equation, and solve. Round your answer to the nearest cent.
If 3 oz of granola costs $3.03, find the cost of 16 oz of granola.
The cost of 16 oz of granola should be $
Answers
Answer:
The cost of 16 oz of granola should be $16.16
Step-by-step explanation:
Given that,
The cost of 3 oz of granola is $3.03
We need to find the cost of 16 oz of granola..
As 3 oz = $3.03
1 oz = (3.03/3) = $1.01
The cost of 16 oz will be :
16 oz = 16×1.01
= $16.16
Hence, the cost of 16 oz of granola should be $16.16.
what is the measure of angle p enter your answer as a decimal in the box round only your answer to the nearest hundredth
Answers
Explanation: We know that Angle Q is 90 degrees, so if given sides and one angle, you can use the law of sines to find the angle measurements.
Law of Sines: Sin A/a=Sin B/b=SinC/c
in a box of 63 marbles, 4 out of 7 marbles are red. How many red marbles are in the box?
Answers
Answer:36
Step-by-step explanation:
Please answer if you are SURE.
Answers
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Which polynomial contains the powers in descending order?
Answers
Answer:
B.
Step-by-step explanation: