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lozanna [386]
3 years ago
12

If MN=14, NO=11, and QR=27, find the length of PQ. Round your answer to the nearest tenth if necessary. Figures are not necessar

ily drawn to scale.

Mathematics
1 answer:
allsm [11]3 years ago
4 0

Answer:

PQ = 34.4

Step-by-step explanation:

First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74

Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)

This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.

We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that

NO/QR = MN/PQ

Thus,

11/27 = 14/PQ

multiply both sides by PQ to remove a denominator

PQ * 11/27 = 14

multiply both sides by 27 to remove the other denominator

PQ * 11 = 14 * 27

divide both sides by 11 to isolate the PQ

PQ = 14 * 27 /11

PQ = 34.4

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Aanand earns Rs 80 in 7 hours and pramode earns Rs 90 in 12 hours. find their ratio​
My name is Ann [436]

Answer:

1.671:1

Step-by-step explanation:

80/7=11.99(9) or ~12

90/12= 7.177(7)

11.99(9)/7.177(7)=1.671

1.671:1

6 0
4 years ago
Fill in the missing work and justification for step 5 when solving 4(x + 1) = 8.
vlada-n [284]

4(x + 1) = 8

4x+4=8

4x=8-4

4x=4

x=4/4

x=1

5 0
3 years ago
Help please! Identify an equation in point slope form for the line perpendicular to Y =-4x + 8 that passes through (-2, 7)
777dan777 [17]

Answer:

D. y-7=\frac{1}{4}(x+2)

Step-by-step explanation:

The point-slope form of a line is given by:

y-y_1=m(x-x_1)

The line given to us has equation; y=-4x+8.

The slope of this line is -4. The of the line perpendicular to this line is the negative reciprocal of the slope of the given line.

Our slope of interest is therefore; m=\frac{1}{4}

Since the point goes through (-2,7), we have x_1=-2,y_1=7.

We plug in the slope and the point into the point-slope formula to obain;

y-7=\frac{1}{4}(x--2)

The required equation is:

y-7=\frac{1}{4}(x+2)

3 0
3 years ago
A freight elevator can hold a maximum weight of 3,500 pounds.
Brrunno [24]

Answer:

C

Step-by-step explanation:

200 + 48c \leqslant 3500

48c \leqslant 3300

c \leqslant 68.75

5 0
2 years ago
Please help WHAT IS THE PERCENT OF 39.8 out of 200 QUICK PLEASE
Masteriza [31]

Answer:

19.9%

Step-by-step explanation:

39.8/200 = 0.199 (move decimal two times)

19.9%

or you can just see what number get 200 to 100, which is by dividing by 2. What you do to the bottom you do to the top so 39.8/200 (divide both sides by 2)  = 19.9/100

which is 19.9%.

<u><em>Ace Carlos</em></u>

7 0
3 years ago
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