1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Keith_Richards [23]
3 years ago
13

I really need help with this! Thank you!!

Mathematics
1 answer:
photoshop1234 [79]3 years ago
7 0
<h3>Answer:</h3>
  1. x = 13; NP = 2 18/23 ≈ 2.8; NL = 5 5/23 ≈ 5.2
  2. D. x = 17, y = 5
<h3>Step-by-step explanation:</h3>

1. In order for this problem to be workable, we need to assume PQ ║ ML. Then ΔPNQ ~ ΔLNM and ∠L = ∠P = 60°.

... ∠L = 60°

... (3x+21)° = 60°

... 3x = 39 . . . . . . . divide by °, subtract 21

... x = 13 . . . . . . . . .divide by 3

The side lengths of similar triangles are proportional, so we have ...

... (3.2 cm)/y = (6 cm)/(8-y)

Multiplying by the product of the denominators, and dividing by (cm), we have ...

... 3.2(8 -y) = 6y

... 3.2×8 = 9.2y . . . . . add 3.2y

... y = 3.2×8/9.2 = 64/23 = 2 18/23 ≈ 2.78 = NP

Then ...

... 8-y = NL ≈ 5.22

In summary: x = 13; NP ≈ 2.8; NL ≈ 5.2

_____

2. If we assume figures ABCD and PSRQ are similar, we can find the values of the variables. We assume ∠C ≅ ∠R, so ...

... 4x +27° = 95°

... 4x = 68° . . . . . subtract 27°

... x = 17° . . . . . . . divide by 4

___

AB/AD = PS/PQ . . . . . corresponding sides of similar figures are proportional

... 4y/(3y-5) = 10/5 . . . . . units of ft cancel

... 5×4y = 10(3y -5) . . . . . multiply by 5(3y-5)

... 20y = 30y -50 . . . . . . simplify

... 50 = 10y . . . . . . . . . . . add 50-20y

... 5 = y . . . . . . . . . . . . . . divide by 10

Using this value of y, we have ...

AB = 4y ft = 20 ft; AD = (3y-5) ft = 10 ft. Both these values are double the corresponding lengths on PSRQ.

In summary, x = 17°, y = 5. . . . . . (note that the ° symbol is appropriate for x)

_____

You should have your teacher show you how to work these problems <em>using only the given information</em>.

In the second problem, you cannot start with the assumption that the figures are similar, as that is what you're being asked to prove. Please note, too, that two sides and one angle of a quadrilateral are insufficient to show similarity.

You might be interested in
If sin(theta) =4/5 and is in quadrant 2, the value of cot(theta
iren [92.7K]
\sin\theta= \frac{4}{5} &#10;\\&#10;\\\sin^2\theta+\cos^2\theta=1&#10;\\ \cos\theta=\pm \sqrt{1-\sin^2\theta} =\pm \sqrt{1-( \frac{4}{5})^2 } =\pm \sqrt{1- \frac{16}{25} } =\pm \sqrt{\frac{9}{25} }=\pm \frac{3}{5}}

\theta \in II \Rightarrow \cos\theta\ \textless \ 0 \Rightarrow \cos\theta=-\frac{3}{5}

\cot\theta= \frac{\cos\theta}{\sin\theta}= \frac{-\frac{3}{5}}{\frac{4}{5}}  =- \frac{3}{4}

5 0
3 years ago
Describe the steps that transform the graph of the function y=x^2 to y=2(x+3)^2. Which attributes are not affected by the transf
dolphi86 [110]

Step-by-step explanation:

y=2(x+3)² y=x²

x²=2(x²+9+6x)

x²=2x²+18+12x

0=x²+18+12x

x²+18+12x=0

7 0
3 years ago
Read 2 more answers
Solve this system of equations: 2x - y = 7 5x + y = 21
JulsSmile [24]
7x= 28 so x is 4 and y is 1.. So (4,1)
7 0
3 years ago
2. In what ratio does the point (5, 4) divide the given line joining the points (2,1) and (7,6)​
Darya [45]

Answer:

3/2

Step-by-step explanation:

Let it be

C (5;4) , A (2;1) ; B(7;6)

Suppose that C divide the line AB in ratio m/n from point A (AC is m, CB is n)

Use the formula xc=(m*xb+n*xa)/ (m+n)

5=(m*7+2n)/(m+n)

5m+5n= 7m+2n

2m=3n

m/n=3/2

5 0
3 years ago
PLEASE PLEASE PLEASE I ALMOST DONE AND I NEED THIS QUESTION
sukhopar [10]

Answer:

107

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Which value is the 10th term in the sequence:-62,-47,-32,-17,-2?
    15·1 answer
  • How do u take 40% off on something
    15·2 answers
  • How many thousands equal 500 tens
    15·2 answers
  • If f(x) = (x - 1) / (x + 2), then the range of f is given by the interval
    6·2 answers
  • Helpppppp 10points some plz help
    5·1 answer
  • 4 3/10 - ( 2 2/5x+ 5 1/2) = 1/2(-3 3/5x + 1 1/5)
    7·1 answer
  • V/12 = 6/9 simplify and find v
    6·1 answer
  • SOMEONE PLEAS HELP ME OUTTTTT!!!
    8·2 answers
  • PLS HELP I WILL GIVE BRAINLIEST <br><br> HELP ASAP
    12·2 answers
  • What's 2.537 rounded to the nearest hundred?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!