Given klmn is a trapezoid, kl = mn, m<1 = m<2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs
Answers
Answer:
The length of legs lm, mn, and lk is 32 while that of kn is 36.
Step-by-step explanation:
The diagram is attached in the answer.
As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk
This leads the two set of legs such as
[tex]\dfrac{lm}{kn}=\dfrac{8}{9}[/tex]
Or this could be written as
[tex]lm=8x\\kn=9x[/tex]
Now the remaining two sides are given as
[tex]lk=lm[/tex] as this form an isosceles triangle so
[tex]lk=8x[/tex]
Similarly
[tex]mn=lm\\[/tex]
Or
[tex]mn=8x[/tex]
Now the perimeter is given as
[tex]\text{perimeter}=lm+mn+kn+lk\\[/tex]
Here perimeter is given as 132 so this gives:
[tex]\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4[/tex]
So the four legs are of length as given below:
[tex]lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36[/tex]
So the length of legs lm, mn, and lk is 32 while that of kn is 36.
Related Questions
Lauren is booking a band and a DJ for a dance, and wants to keep the cost of the
entertainment under $1,300. A band can play for part of the time at an hourly rate of $120,
and a DJ can play for the remaining time at an hourly rate of $92.
Select the inequality in standard form that describes this situation. Use the given
numbers
and the following variables.
x = the number of hours the band will play
y = the number of hours the DJ will play
Answers- A 120+x+92+y>1,300
B: 120x+92y>1,300
C: 120x+92y<1,300
D: 120+x+92+y<1,300
Answers
Answer:
C: 120x+92y<1,300
Step-by-step explanation:
Since the band plays at an hourly rate of $120 for x hours, the total cost of the band playing is 120x.
Also the DJ can play for the remaining time at an hourly rate of $92 for y hours, the total cost of the band playing is 92y
The total cost of the band is DJ playing is thus 120x + 92y.
Since we require this to be under $1,300, we us the less than sign '<' to show the relation.
So, 120x + 92y < 1300
So, the answer is C
The fuel mix for a small engine contains only 2 ingredients: gasoline and oil. If the mix requires 5 ounces of gasoline for every 6 ounces of oil, how many ounces of gasoline are needed to make 33 ounces of fuel mix?
Answers
Answer:
15
Step-by-step explanation:
(brainiest)
Find the surface area of the rectangular prism.
5 in.
7 in
4 in.
Answers
Answer:
A=166
that's all can calculate
The scores for all the sixth graders at Roberts School on a statewide test are normally distributed with the mean of 76 and a standard deviation of 10.
What percent of the scores were below 66?
What is the probability that a student earned a score between 66 and 86?
Answers
Answer:
a) 15.866%
b) 0.68268
Step-by-step explanation:
The scores for all the sixth graders at Roberts School on a statewide test are normally distributed with the mean of 76 and a standard deviation of 10.
We solve the above question using z score formula
= z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 76
σ is the population standard deviation = 10
a) What percent of the scores were below 66?
x < 66
Hence,
z = 66 - 76/10
z = -1
Probability value from Z-Table:
P(x<66) = 0.15866
Converting to Percentage =
0.15866 × 100
= 15.866%
b) What is the probability that a student earned a score between 66 and 86?
For x = 66
Hence,
z = 66 - 76/10
z = -1
Probability value from Z-Table:
P(x≤ 66) = 0.15866
x = 66 = 0.15866
For x = 86
Hence,
z = 86 - 76/10
z = 1
Probability value from Z-Table:
P(x≤ 86) = 0.15866
x = 66 = 0.15866
Probability value from Z-Table:
P(x = 86) = 0.84134
The probability that a student earned a score between 66 and 86 is calculated as:
P(x = 86) - P(x = 76)
= 0.84134 - 0.15866
= 0.68268
Which expression is equivalent to 34(4h - 6)?
) 3h -92
) 4h +92
) 3h - 6
) 4h + 6
Answers
Answer:
Step-by-step explanation:
136h-24 which is not listed in your choices
X - 2y = -3
2x + y = -1
Answers
Answer:
y = 1
x = -1
Step-by-step explanation:
x - 2y = -3, then x = 2y - 3
2x + y = -1
substitute for x:
2(2y - 3) + y = -1
4y - 6 + y = -1
5y = 5
y = 1
x = 2 - 3 = -1
Answer:
it can only be simp[lified
so it will be
(x+2x)+(y+2y)=-3-1
3x+3y=-4
cannot be solved further
Step-by-step explanation:
Which expression is equivalent to 7x + 4x2 – 5x?
Answers
Answer:
2x+8
Step-by-step explanation:
Answer:
[tex]4x^{2} +2x[/tex]
Step-by-step explanation:
I'm not sure what you want, because it says "which expression", but you didn't provide any answer choices.
So all you have to do for this is combine like terms, and the only ones were 7x and -5x, which equals 2x.
Girrls and boys plsss i need help like frl:)
Answers
D- Most babysit because it pays more per-hour.
The reason this is the correct answer is because the question said which is NOT a valid response. This one is not because it didnt tell you how much they get paid per-hour so its incorrect.
Hope this helps!
Have a great day!
- Hailey
The net below is used to form a rectangular prism. Using the net, determine the surface area of the figure.
7 cm
7 cm
7 cm
7 cm
26 cm
Answers
Step-by-step explanation:
54 because you add 7+7+7+7+26=54
Marianne's ring has a radius of 8mm. She needs to get it resized so that the circumference is 52 mm. How much larger will the new circumference be? Round your answer to the nearest tenth
Answers
Answer:
0.28mm larger
Step-by-step explanation:
Given data
Radius of ring= 8mm
Circumference
C= 2πr
C= 2*3.14*8
C=50.24mm
The resized ring has a circumference of =52 mm
Hence the radius will be
52= 2*3.14*r
52= 6.28r
r= 52/6.28
r= 8.28mm
Hence the resized ring is
8.28-8
=0.28mm larger
The diameter of a circle is 14 ft.
What is the area of the circle in terms of π?
Answers
Answer:
49π ft²
Step-by-step explanation:
[tex]A=\pi r^2[/tex] where r is the radius of the circle
To find the radius, divide the diameter by 2:
14 ft ÷ 2 = 7 ft
Plug the radius 7 ft into the equation
[tex]A=\pi (7)^2\\A=49\pi[/tex]
Therefore, the area of the circle in terms of pi is 49π ft².
I hope this helps!
Answer:
49π
Step-by-step explanation:
Diameter=14
Radius=14/2=7
Area=πr squared
Area=7 squared π
Area=49π
Whoever gives an answer first gets Brainliest
Answers
Answer:
answer to what?
Step-by-step explanation:
Answer:
Thanks mate n.n
Have a good one !
how do i include a screenshot
Answers
There will be a nail clip tool when you press the + button. Then you will be able to access your file you need to enter.
The building on Daughtery road are even numbered from 12-136. How many buildings have an address with at least one 4?
Answers
Answer:
Total 22 buildings have at least one 4 in their address
Step-by-step explanation:
Number between 12 to 136 are as given below -
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
Total numbers having at least 1 four are
14
24
34
40
41
42
43
44
45
46
47
48
49
54
64
74
84
94
104
114
124
134
Total 22 buildings have at least one 4 in their address
the greatest common factor of 9w2 and 10w4.
Answers
Answer:
9 and 2: 1
10 and 4: 2
Step-by-step explanation:
9: 1, 3, 9
2: 1, 2
Answer: 1
10: 1, 2, 5, 10
4: 1, 2, 4
Answer: 2
what is the correct form of the partial fraction decomposition for: start fraction 35-27x over 4xsquared+28x endfraction
Answers
Answer: The answer is A
Step-by-step explanation:
A/4x+B/x+7
The correct form of the partial fraction decomposition for the given expression is Option A
What is Partial Fraction Decomposition ?Partial Fraction Decomposition is the method of simplifying rational expressions.
The expression given is
[tex]\rm \dfrac{ 35-27x} { 4x^2+28x}[/tex]
Applying Partial Decomposition
[tex]\rm \rm \dfrac{ 35-27x} { 4x(x+7)}\\\\\\\dfrac{35}{4x(x+7)} - \dfrac{27x}{4x(x+7)}\\\\\\Taking \;A = 35/ x+7\\\\Taking \; B = -27/4\\\\[/tex]
It can be written as
[tex]\rm \dfrac{A}{4x} + \dfrac{B}{x+7}[/tex]
Therefore Option A is the answer.
To know more about Partial Factor Decomposition
https://brainly.com/question/2516522
#SPJ2
You deposit $100 in your bank account. The account earns 2% simple interest in 5 years. How much interest did you earn?
Answers
A triangle has sides with lengths of 48 meters, 51 meters, and 31 meters. Is it a right triangle?
Answers
Answer:
Step-by-step explanation:
Formula = a^2 + b^2 = c^2
Putting values
= (31)^2 + (48)^2 = (51)^2
= 961 + 2304 = 2601
= 3265 = 2601
Both sides are not equal so it is not a right triangle
A group of children bought 3 presents that cost $W each and a card that cost $200. The children shared the total cost equally. Express the amount of money each student paid in terms of W
Answers
Answer:
Amount of money paid by each student is equal to [tex]\$3W+\$200[/tex]
Step-by-step explanation:
Given: A group of children bought [tex]3[/tex] presents that cost [tex]\$W[/tex] each and a card that cost [tex]\$200[/tex].
To find: amount of money each student paid in terms of [tex]W[/tex]
Solution:
Cost of each present [tex]=\$W[/tex]
Cost of [tex]3[/tex] presents [tex]=\$3W[/tex]
Cost of a card [tex]=\$200[/tex]
Therefore,
Amount of money paid by each student in terms of [tex]W[/tex] = Cost of [tex]3[/tex] presents + Cost of a card
[tex]=\$3W+\$200[/tex]
Solve for n. 11(n – 1) + 35 = 3n n = –6 n = –3 n = 3 n = 6
Answers
Answer:
n = -3
Step-by-step explanation:
11(n – 1) + 35 = 3n
11n - 11 + 35 = 3n
24 = -8n
n = -3
what is the mean of the data? 24,31,12,38,12,15
Answers
Answer:
Hello Love! Answer: 22
Step-by-step explanation:
The mean is just an average of all the numbers added up then divided by how many numbers there are so I add up those numbers and I get 132 now I will just divide that by 6 sense there are 6 numbers and I get 22!
Thank you to anyone who answers .
Answers
Answer:
B: 33 3/4
Step-by-step explanation:
PLEASE HELP !!!!!!!!!!! WILL MARK BRIANLIEST !!!!!!!!!!!!!
Answers
Answer:
77-55=22, i don't know if this is the answer if i'm wrong sorry im just trying to help you.For every 22 followers tyler has, Naomi has 22 leser followers
Step-by-step explanation:
IF i am right pls subscribe to Amiredagoat Yt
Claim shape a is a rectangle please help
Answers
Answer:
ummkmmmm
Step-by-step explanation:
Answer:
No, the shape is not a rectangle.
Step-by-step explanation:
A rectangle is a 2-dimensional shape with two sets of parallel sides and four right angles. Shape a has both sets of parallel sides, but the corners of the figure are not right angles. It is a rhombus. So, the answer is no, the shape is not a rectangle.
Good luck ^^
HELP I WILL GIVE BRAINIEST
Answers
Answer:
For the first one the answer is:
<K = 31°
Sorry I don't know the second one.
I. Daska is situated at a distance of 15 miles from both Gujranwala and Sialkot. A bus travels from Gujranwala to Daska at an average speed of 25 miles per hour, from Daska to Sialkot at an average speed of 40 miles per hour and returns to Daska at an average speed of 30 miles per hour. Find the average speed for the entire trip.
Answers
Answer:
The average speed of the entire trip is 8.5 miles per hour.
Step-by-step explanation:
Speed = Total Distance / Total Time
So we have to find the total distance and the total time taken .
1) From Gujranwala to Daska
speed= 25miles/hour distance = 15miles
Time taken = distance / speed
= 15/25= 0.6 hours
2) From Daska to Sialkot
speed= 40miles/hour distance = 15miles
Time taken = distance / speed
= 40/15= 2.67 hours
3 ) From Sialkot to Daska
speed= 30miles/hour distance = 15miles
Time taken = distance / speed
= 30/15= 2 hours
The total distance traveled to three places is = 15+ 15+15= 45miles
The Total time taken is = 0.6+ 2.67+ 2= 5.267=5.3 hours
Speed = Total Distance / Total Time
Speed= 45/ 5.3
= 8.49=8.5 miles per hour
The average speed of the entire trip is 8.5 miles per hour.
Help me with this, will give brainlist to best explained asnwer
Answers
Answer:
I'd say the mode, 21, is the best response. It appears the most frequently and it's also the median.
Explanation:
Mean: 115 / 5 = 23
Median: 19, 21, 21, 26, 28
Mode: 19, 21, 21, 26, 28
Please look at the screenshot
Answers
Given:
The figure of circle E. [tex]m\angle ABD=(11x-3)^\circ,m\angle ACD=(8x+15)^\circ[/tex].
To find:
The measure of arc AD.
Solution:
We know that the inscribed angles on the same arc are congruent and their measures are equal.
[tex]\angle ABD[/tex] and [tex]\angle ACD[/tex] are inscribed angles on the same arc AD. So,
[tex]m\angle ABD=m\angle ACD[/tex]
[tex]11x-3=8x+15[/tex]
[tex]11x-8x=3+15[/tex]
[tex]3x=18[/tex]
[tex]x=6[/tex]
Now,
[tex]m\angle ABD=(11x-3)^\circ[/tex]
[tex]m\angle ABD=(11(6)-3)^\circ[/tex]
[tex]m\angle ABD=(66-3)^\circ[/tex]
[tex]m\angle ABD=63^\circ[/tex]
We know that the intercepted arc is always twice of the inscribed angle.
[tex]m(Arc(AD))=2\times m\angle ABD[/tex]
[tex]m(Arc(AD))=2\times 63^\circ[/tex]
[tex]m(Arc(AD))=126^\circ[/tex]
Therefore, the measure of arc AD is 126 degrees.
A sphere has a volume of 1,436 in3. What is its radius?
Answers
Answer:
do the reverse of pie r squared
Step-by-step explanation:
ANSWER FOR BRAINLIEST:
Mark all of the following that are measures of Central Tendency.
Mean
Range
Mode
Median
Mean Absolute Deviation
Outlier
Answers
Step-by-step explanation:
I think mode,range and median dpo ako sure