LMN is a right-angle triangle. Angle NLM=90. PQ is parallel to LM. The area of triangle PNQ is 8cm^2. The area of triangle LPQ is 16cm^2. Work out the area of triangle
Answers
Answer:
The area of LQM is [tex]48cm^2[/tex]
Step-by-step explanation:
Given
Area of PNQ = 8
Area of LPQ = 16
See attachment for triangles
The area of PNQ is calculated as:
[tex]Area = \frac{1}{2} * PQ * PN[/tex]
Substitute 8 for Area
[tex]8 = \frac{1}{2} * PQ * PN[/tex]
[tex]PQ * PN = 16[/tex]
The area of LPQ is calculated as:
[tex]Area = \frac{1}{2} * PQ * LP[/tex]
Substitute 16 for Area
[tex]16= \frac{1}{2} * PQ * LP[/tex]
From the attachment:
[tex]PN + LP =LN[/tex]
Make LP the subject
[tex]LP = LN -PN[/tex]
So:
[tex]16= \frac{1}{2} * PQ * (LN -PN)[/tex]
We have:
[tex]16= \frac{1}{2} * PQ * (LN -PN)[/tex] and [tex]PQ * PN = 16[/tex]
Equate both expressions:
[tex]\frac{1}{2} * PQ *(LN - PN) = PQ * PN[/tex]
Divide both sides by PQ
[tex]\frac{1}{2} (LN - PN) = PN[/tex]
Multiply both sides by 2
[tex]LN - PN = 2PN[/tex]
[tex]LN= 3PN[/tex]
Since PNQ is similar to LNM, the following equivalent ratios exist:
[tex]\frac{LM}{PQ} = \frac{LN}{PN}[/tex]
Substitute [tex]LN= 3PN[/tex]
[tex]\frac{LM}{PQ} = \frac{3PN}{PN}[/tex]
[tex]\frac{LM}{PQ} = 3[/tex]
[tex]LM = 3PQ[/tex]
Area of LQM is:
[tex]Area = \frac{1}{2} * LM * LP[/tex]
This gives:
[tex]Area = \frac{1}{2} * 3PQ * LP[/tex]
[tex]Area = 3 *\frac{1}{2} *PQ * LP[/tex]
Recall that:
[tex]16= \frac{1}{2} * PQ * LP[/tex]
So:
[tex]Area = 3 *16[/tex]
[tex]Area = 48cm^2[/tex]
Related Questions
Find f(x)=(x^2)+x+39, when x=50. (don't write a comma in answer.)
Answers
f(x) = x² + x + 39
f(50) = 50² + 50 + 39
f(50) = 2500 + 89
f(50) = 2589
Between which two numbers is √8 located on a number line?
Answers
Answer:
√8 is between 2 and 3.
Step-by-step explanation:
♡ im sorry if its wrong ♡
Find the greatest common factor of 9n² and 6m⁴?
Answers
please help me on this math I have been trying to solve it but I can't please please help me!!!!!!
Answers
Answer:The first table would be a proportional relationship.
Step-by-step explanation:
It's the only table with a constant, which is required in a proportional relationship. The constant would be 1300 which you can find by divided the two numbers in each row.
PLEASE HELP!!!!! 50 POINTS!!!! REAL ANSWERS ONLY!!!!!! PLEASE HELP!!!!!! I NEED TO GET THIS DONE
finding angle measures with trig. Find the missing angle measures. Round to the nearest whole number
Answers
Answer:
#1
30° as opposite side is half of the hypotenuse#2
7/16 = tan xx = arctan (7/16) = 24°#3
31/50 = tan xx = arctan (31/50) = 32°#4
5/7 = cos xx = arccos (5/7) = 44°#5
4/14 = sin xx = arcsin (4/14) = 17°#6
6/7 = cos xx = arccos (6/7) = 31°#7
29/37 = tan xx = arctan (29/37) = 38°#8
43/60 = sin xx = arcsin (43/60) = 46°#9
32/44 = cos xx = arccos (32/44) = 43°Answer:
let angle be x
Step-by-step explanation:
relationship between perpendicular and hypotenuse is given by sin anglesin x =p/h
sin x=13/26
x=sin-¹(13/26)=30°
2.relationship between perpendicular and base is given by tan angle
tan x =p/b
tan x =7/16
x=tan -¹(7/16)=23.63°
3.relationship between between perpendicular and base is given by tan angle
tan x =p/b
tanx=31/50
x=tan-¹(31/50)=31.8°
4.relationship between base and hypotenuse is given by cos angle
cos x =b/h
cos x=5/7
x=cos-1(5/7)=44.4°
5.relationship between perpendicular and hypotenuse is given by sin angle
sin x =p/h
sin x=4/14
x=sin-¹(4/14)=16.6
6..relationship between base and hypotenuse is given by cos angle
cos x=6/7
x=cos-¹(6/7)=31.0027
7.relationship between perpendicular and base is given by tan angle
.tanx=29/37
x=tan-¹(29/37)=38.09
8.relationship between perpendicular and hypotenuse is given by sin angle
.sin x=43/60
x=sin-¹(43/60)=45.78
9..relationship between base and hypotenuse is given by cos angle
cos x=32/44
x=cos-¹(32/44)=43.34
Dvide if the polynomial does not divide evenly. Include the remainder as a fraction (18u^2 - 142u - 11) ÷ (u - 8)
Answers
Answer:
18u + 2 + 5/(u - 8)Step-by-step explanation:
(18u^2 - 142u - 11) ÷ (u - 8) 18u^2 - 142u - 11 = 18u^2 - 8*18u + 2u - 11 = 18u(u - 8) + 2u - 16 + 5 =18u(u - 8) + 2(u - 8) + 5 =(18u + 2)(u - 8) + 5(18u^2 - 142u - 11) ÷ (u - 8) = 18u + 2 + 5/(u - 8)Answer:
18u + 2 + 5/u - 8.
Step-by-step explanation:
(18u^2 - 142u - 11) ÷ (u - 8)
= 18u + 2 + 5/u - 8.
What is the volume of the composite object below?
Answers
Answer:
216 cubic inches
Step-by-step explanation:
(9)(3)(3)=81
(3)(3)(9)=81
(3)(3)(6)=54
81+81+54=216
So, it's 216 cubic inches in volume.
brebjfhewiufhuhrehoiwhewiueweobnwqjkfrjoighrf.
Answers
The total cost of a sweater and a pair of pants was $89.47. If the price of the sweater was $8.53 less than the pair of pants, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.
Answers
Answer:
Let S = price of sweater
Let P = price of pants
S + P = 89.47 because that was the total spent
S = P - 8.53 because the sweater is 8.53 less than pants
Substitute P-8.53 in place of S in the
1st equation and solve for P
P - 8.53 + P = 89.47
2P - 8.53 = 89.47 add 8.53 to both sides
2P = 89.47 + 8.53
2P = 98.00 divide both sides by 2
P = 98.00/2
P = $49.00
S = P - 8.53
S = 49.00-8.53
S = $40.47
A sweater costs $40.47 and the pants cost $49.00
Did Sammy eat more blueberries on Monday or on
Monday or on Tuesday? Explain
your reasoning.
Answers
Answer: Sammy says he was hungry on Monday so that's why he ate more blueberries than Tuesday
Step-by-step explanation:
The table below displays the enrollment of freshmen taking Algebra 1. Geometry, or Algebra 2.
The total number of girls enrolled is equal to the number of boys.
There are twice as many boys enrolled in Algebra 1 as boys enrolled in Geometry.
Based on this information, complete the two-way table below.
Answers
Answer:
for the boys it is 92 then 58 and the total is 150 an then 68 for the girls then for the total it is 100
The missing values in the two-way table is shown in the table in the image attached below.
What is a Two-way Table?A two-way table can be described as a table that displays the frequencies of two categorical variables, in such a way that, one category is represented by columns and the other by rows.
Given the information, the missing values in the two-way table would be:
Total number of boys enrolled = 150
Boys that enrolled in Algebra 1 = 2(46) = 92
Boys that enrolled in Algebra 2 = 150 - 92 - 46 = 12
Girls that enrolled in Algebra 1 = 150 - 54 - 28 = 68
Total for boys and girls that enrolled in Geometry = 46 + 54 = 100.
Therefore, the missing values in the two-way table is shown in the table in the image attached below.
Learn more about two-way table on:
https://brainly.com/question/20744563
Which expression is equivalent to the expression below?
7x+5y+x+x+x+x
Answers
Answer:
11x+5y
Step-by-step explanation:
7x+5y+x+x+x+x
Combine like terms
7x+x+x+x+x +5y
11x +5y
hey!!! please answer this asap it is an emergency!!!
whoever answers first and gets it right will be marked brainliest!!!
Answers
Answer:
my bad yall, I seen the comments!! it's 12
Step-by-step explanation:
I'm so sorry!!
Answer:
Okay, i'm not being jugy but it it is super easy... it is 12 only because 1x12=12, 2x12=24, 3x12=36, and 4x12=48!!
it is most definately 12 DON'T WORRY
let's one two and three have the following relationships <1and <2 are adjacent right angles <1 and <3 are vertical angles what is the measurement of <1 plus the measure of <3 minus the measure of two
Answers
Answer:
180 Vertical angles are opposite angles that share only a vertex. Since ∠3 is adjacent to both ∠1 and ∠2, this means that ∠3 shares a side and vertex with both of these angles.
This means that ∠3 and ∠1 form a straight line; this makes them a linear pair, which makes their sum 180°.
pease help me i really need this
Answers
Answer:
2:140
1:70
Step-by-step explanation:
:)
70 x 2 is 140
70 x 1 is 70
he drove 140 miles in 2 hours, and 70 miles in an hour
CAN SOMEONE PLEASE HELP ME WITH THIS??
Answers
Answer:
12
Step-by-step explanation:
6x12=72
3x12=36
36+36=72
Answer: 23.
Step-by-step explanation:
A dog shelter has 22 poodles. The number of poodles is doubling every year. How long before the shelter has 22,528 poodles?
Please help
Answers
Answer:
I think 1024 days? Which is around 2 years...
a part of a line with endpoints on both ends a(n):
Answers
The answer is line segment
Answer:A part of a line with endpoints on both ends is a(n):
A line with 2 endpoints is called a line segment. We know that it is a segment because the endpoints make the line finite
Step-by-step explanation:
Select the ratios that are equivalent to 11:1.
Choose 3 answers:
A-1:11
B-22:2
C-55:5
D-9:99
E-110:10
Answers
Answer:
i think the answer is B . 22::2
(2+h)^4 is equal to what
Answers
Answer:
16+32h+24h²+8h³+[tex]h^{4}[/tex]
Step-by-step explanation:
Solve for the nearest tenth
Answers
Answer:
426.9
Step-by-step explanation:
Find the missing number in the proportion.
23 over 50 = ___ over 100
Answers
Answer:
46
Step-by-step explanation:
let that number x
so [tex]\frac{23}{50} =\frac{x}{100}[/tex]
I do cross multiplication so 23*100=2300 and 50*x=50x
so 50x=2300 divide both by 50
x=46
Answer:
46
Step-by-step explanation:
since 100 is 50×2 you just do the same thing to 23 and multiply it by 2.
4x - 7y = -40
3x - 2y = -4
Answers
How many significant figures will the answer to the following problem have? You do not have to solve the problem. 8.82 -3.4 =
Answers
Answer:
5.42
Step-by-step explanation:
8.82 -3.4 = 5.42
The solution to the problem will have two significant figures.
What are significant figures?The number of digits in a value, generally a measurement, that contributes to the degree of precision of the value is referred to as significant figures. At the first non-zero digit, we begin calculating significant numbers.
The given problem 8.82 -3.4 has two digits after the decimal place. Hence, The solution to the problem will have two significant figures.
Learn more about Significant Figures:
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jamie wants to treat some friends to lunch. He has $45 and know that the lunch will cost about $7 per person, p. He will also have to pay a $5.10 delivery fee. How many people can jamie buy lunch for?
Write and solve a inequality to represent the situation:
Answers
Answer:
5 people
Step-by-step explanation:
1. I subtract 5.10 from 45 which gave me 39.90
2. I divided 39.90 by 7 to figure out how many people he could buy for
3. I had gotten 5.7 so I had to round
4 final answer is 5
Answer:
Jamie can buy lunch for 5 people.
7p≤40
Step-by-step explanation:
Given:
Jamie has $40.
Lunch cost per person = $7
Solution:
Jamie wants to treat some friends to lunch.He has $40 and knows that lunch will cost about $7 per person, p.
So, an inequality to represent this situation is written as:
Hence, the answer is 5
Therefore, Jamie can buy lunch for 5 people.
I hope this helps :)
please be as soon as possible.
Answers
Answer:
Really?
Step-by-step explanation:
Answer:
Ik
Step-by-step explanation:
help me please fast i’m in need
Answers
Answer:
es la
A
Step-by-step explanation:
Are the fractions 3/8 and 9/27 equivalent? If yes, explain how you know they are equivalent. If they are not equivalent, what is a fraction that would be equivalent to 3/8.
Answers
Answer:
Step-by-step explanation:
The factors are 9 and 27 are 1,3,9,27
With that, 9/27 is undoubtedly reducible to 1/3
Before now,we were told that when a number divides itself,the result is zero...now,⅜÷⅓ should give us 1 but 3/8×3/1 = 9/8 and 9/8≠1 hence,they aren't same!
Help me pls pls help
Answers
This means (8x2)-(4x2) is the correct answer!!
Hope this helps :)
Answer:
The last one
Step-by-step explanation:
This is because 8x2 is doubling8 and then it also asks to multiply 4 and 2
Lastly it says subtract second number from first which means subtract 4 by 2 from 8 by 2
Hope this makes sense
Find the measure of.. (image included)
I need help please! My teacher changed the due date to today and I don't understand it.
Answers
Answer:
B) 50
Step-by-step explanation:
<A = x + 53
x + 53 + x + 83 + 50 = 180
2x + 186 = 180
2x = -6
x = -3
<A = x + 53
-3 + 53
50