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oee [108]
3 years ago
10

Suppose lines EF and GH are reflected over the line Y equals X to form the lines JK and LM which statement would be true about t

he lines
A) jk and lm will be parallel

B) jk and lm will be perpendicular

C) jk will be same slope as ef

D) lm will be negative reciprocal of gh

Mathematics
1 answer:
katrin [286]3 years ago
5 0

Answer:

A) JK and LM will be parallel to each other.

Step-by-step explanation:

On reflection on y=x line the x co-ordinate changes with y co-ordinate and y co-ordinate changes with x co-ordinate

(x,y)\rightarrow (y,x)

Points on line EF

(0,6) , (-5,-2)

On reflection of this line on y=x the new points we get for line JK are

(6,0),(-2,-5)

Points on line GH

(-4,9),(-9,1)

On reflection on y=x line the new points we get for line LM are

(9,-4),(1,-9)

Slope of line JK

m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-5)-0}{(-2)-6} \\m=\frac{-5}{-8}=\frac{5}{8}

Slope of line LM

m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-9)-(-4)}{1-9} \\m=\frac{-9+4}{-8}=\frac{-5}{-8}\\m=\frac{5}{8}

For two line to be parallel, their slopes will be same.

m_{JK} =\frac{5}{8} , m_{LM}=\frac{5}{8}

Since slopes of lines JK and LM are same therefore we can say that these are parallel to each other.

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sp2606 [1]
Solving
  S = 3F - 24
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  S + 24 = 3F
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The best choice is the last one:
  F = (S + 24)/3
6 0
3 years ago
Allen's daily regular wage is P1,420. This coming Christmas, his boss is asking him to work for 14 hours. How much is his DAILY
VMariaS [17]

Using proportions, it is found that his DAILY RATE on that particular day is of Php 2,420 .

  • This question is solved by proportions, using a <em>rule of three.</em>
  • In a regular 8-hour day, Allen earns Php 1420. How much will he earn on a 14 hour day?

The <em>rule of three</em> is:

8 hours - Php 1420

14 hours - x

Applying cross multiplication:

8x = 1420 \times 14

x = \frac{1420 \times 14}{8}

x = 2485

The closest option is Php 2,420.

A similar problem is given at brainly.com/question/24372153

7 0
3 years ago
24 is 31.25% of what number? Prove your answer in the show your workbox.
FinnZ [79.3K]

Answer:

76.8

Step-by-step explanation:

1. We assume, that the number 31.25 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 31.25, so we can write it down as 100%=31.25.

4. We know, that x% equals 24 of the output value, so we can write it down as x%=24.

5. Now we have two simple equations:

1) 100%=31.25

2) x%=24

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=31.25/24

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 24 is what percent of 31.25

100%/x%=31.25/24

(100/x)*x=(31.25/24)*x       - we multiply both sides of the equation by x

100=1.3020833333333*x       - we divide both sides of the equation by (1.3020833333333) to get x

100/1.3020833333333=x

76.8=x

x=76.8

now we have:

24 is 76.8% of 31.25

6 0
3 years ago
Read 2 more answers
An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15
NeTakaya

Answer:

D. 22,417 feet

Step-by-step explanation:

Fine the diagram in the attachment for proper elucidation. Using the SOH, CAH, TOA trigonometry identity to solve for the distance (x) from the plane (P) to the observer (O), the longest side x is the hypotenuse and the side facing the angle of elevation is the opposite.

Hypotenuse = x and Opposite = 15,000feet

According to SOH;

sin 42^0 = \frac{Opposite}{Hypotenuse} \\\\Sin42^0 = \frac{15000}{x}\\ \\x = \frac{15000}{sin42^0}\\\\ \\

x = \frac{15000}{ 0.6691} \\\\x = 22,417 feet

Hence the distance (x) from the plane P to the observer O is approximately 22,417 feet

3 0
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ollegr [7]

Answer:

The home printer is faster.

Step-by-step explanation:

25 photos in 12.5 minutes

12.5 is half of 25 and therefore this is a two to one ratio.

So 2 photos print in 1 minute with the office printer.

And 4 photos in 2 minutes(this is relevant later)

The home printer prints 15 photos in 6 minutes. Since 15 is not divisible by 6 without a remainder divide both by 3.

So 5 photos in 2 minutes. This is faster than the office printer.

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