Given that rectangle LMNO with coordinates L(0,0), M(3,0), N(3,7), O(0,7), P is the midpoint of LM⎯⎯⎯, and Q is the midpoint of NO⎯⎯⎯, which of the following proves that PQ=LO?

Answers attached

Given That Rectangle LMNO With Coordinates L(0,0), M(3,0), N(3,7), O(0,7), P Is The Midpoint Of LM, And

Answers

Answer 1

The midpoint of a line divides the line into equal segments.

The option that proves PQ = LO is (a)

The given parameters are:

[tex]\mathbf{L = (0,0)}[/tex]

[tex]\mathbf{M = (3,0)}[/tex]

[tex]\mathbf{N = (3,7)}[/tex]

[tex]\mathbf{O = (0,7)}[/tex]

P is the midpoint of LM.

So, we have:

[tex]\mathbf{P = \frac{LM}{2}}[/tex]

[tex]\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}[/tex]

[tex]\mathbf{P = (\frac{3}{2},0)}[/tex]

Q is the midpoint of NO.

So, we have:

[tex]\mathbf{Q = \frac{NO}{2}}[/tex]

[tex]\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}[/tex]

[tex]\mathbf{Q = (\frac{3}{2},7)}[/tex]

Distance PQ is calculated as follows:

[tex]\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]

This gives:

[tex]\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}[/tex]

[tex]\mathbf{PQ = \sqrt{ 7^2}}[/tex]

[tex]\mathbf{PQ = 7}[/tex]

Distance LO is calculated as follows:

[tex]\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}[/tex]

[tex]\mathbf{LO = \sqrt{ 7^2}}[/tex]

[tex]\mathbf{LO=7}[/tex]

So, we have:

[tex]\mathbf{PQ = 7}[/tex]

[tex]\mathbf{LO=7}[/tex]

Thus:

[tex]\mathbf{PQ = LO}[/tex]

Hence, the correct option is (a)

Read more about distance and midpoints at:

https://brainly.com/question/11231122


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Answer:

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Answer:

The error is that the question equals -13-13.

Step-by-step explanation:

This is absolute value, so anything inside of the bars is positive. Since the first -13 has bars around it it would be positive. But since the second - is outside of the 13 with bars, the 13 stays negative, so it would be 13-13. Hope this helps! :)

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In the given problem, x represents the exterior angle, while the m < 65° and m < 48° are the non-adjacent interior angles.

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A hardware dealer has 168kg of nails, if one nail weighs 0.25kg, how many nails he have?​

Answers

Answer:

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Step-by-step explanation:

168/.25

Answer:

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Step-by-step explanation:

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Answers

Answer:

Ans 26

Step-by-step explanation:

F(x) = x/2

proof:

at x=0, f(x)=0

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and x = -4 , f(x) = -2

that's it.

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Answers

Answer:

looks like your understanding is pretty good! I'm not sure how you missed the first 2... you should check those two against your understanding.

Step-by-step explanation:

a) 2

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Answers

Answer:

the answer is option D

Step-by-step explanation:

if you add the no of students in favour of the survey

32+42+58+64=192

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The opinion of tenth and eleventh graders are not identical.

11th and 12th graders gave a favourable response

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Answers

Answer:

The next term is 64, a is 2, and the common ratio is 2.

Step-by-step explanation:

Look at what's happening from each number to the next. What do you need to do to get from 2 to 4, or 4 to 8? Multiply by 2. That's your common ratio. To get the next number in the sequence, multiply the last number by the common ratio of 2. 32 x 2 = 64, so the next number in the sequence is 64. "a" is just the very first term, meaning it's 2.

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Answer:

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Step-by-step explanation:

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Answer:

(i. -15<-9)

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Answer:

1 = <

2= >

Step-by-step explanation:

This is a 30-60-90 triangle.
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Answers

Answer:

[tex] \huge\: x =9 \sqrt{ \boxed{3}} [/tex]

Step-by-step explanation:

Given is a 30°-60°-90° triangle and x is the length of side opposite to 60° angle.

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3

Step-by-step explanation:

Solve each system of linear equations using the elimination mehod
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Answers

Answer: y = 1 and x = 4

Step-by-step explanation:

-8x + 10y = -22

8x - 15y = 17

-----------------------

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y = 1 Solve for y

=====

8x - 15y = 17 (y = 1) Use y=1 in either equation

8x - 15 = 17

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x = 4 Ta da

Answer:

solution:  x = 4, y = 1 or (4, 1)

Step-by-step explanation:

To solve the system of linear equations using the elimination method, simply add both equations together (since the coefficeints of x have opposite signs):

-8x + 10y = -22

+ 8x -  15y =  17

       - 5y  = -5

Divide both sides by -5 to solve for y:

[tex]\frac{-5y}{-5} = \frac{-5}{-5}[/tex]

y = 1

Next, substitute the value of y into one of the equations to solve for x:

-8x + 10y = -22

-8x + 10(1) = -22

-8x + 10 = -22

Subtract 10 from both sides

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-8x = -32

Divide both sides by -8 to solve for x:

[tex]\frac{-8x}{-8} = \frac{-32}{-8}[/tex]

x = 4

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Answers

Answer:

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Step-by-step explanation:

Create a right triangle, in which A is the right angle, and mZC is approximately 60°. What is the approximate measure of _B? m_B = What is the sum of m_A, m_B, and m_C?​

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Answer:

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mark me brainlyest plz

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Answers

Step-by-step explanation:

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Answer:

5)3/2

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8)13

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Step-by-step explanation:

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Use the Pythagorean Theorem to find the distance between the point (1,4) and (-5,-4) on the coordinate plane? (FREE RESPONSE)
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Answers

Answer:

12?

Step-by-step explanation:

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Step-by-step explanation:

If you plot (1,4) and (-5,-4) on a graph, you can see that you can form a right triangle.

you would count the values on the X-axis and on the Y-axis. The values are 6 and 8 respectively.

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Answers

Answer:

6 loads would be required to fill the truck with 2¼ tons

Step-by-step explanation:

1 ton= 2000 pounds

2¼ tons= 4500 pounds

4500/750=6

Please allow me to know this helped by clicking thank you, rating or brainly.

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Miss Hawaii

Answer:

6 loads

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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I think you meant, if a = 0.

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a³ = 0³

a³ = 0 × 0 × 0

a³ = 0

Any number multiplied by 0 is 0.

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Answer:

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your answer is 357.1

erome has an app that tracks his running times and distances. He records his distances and times in a table.
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Enter only a number in the space provided. Do not enter words in the box.

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Answer:

IM SMART

Step-by-step explanation:

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u need a protractor

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The answer has to be in y-intercept form. Which is y=mx+b and b can also be neg. y=mx-b. The m is your slope and b is your y-intercept. So A’s slope counting from 3 on the y axis to 1 on the x-axis which is down 2 over 1 so it will be -2/1. And your y intercept is 3. The equation is y=-2x+3. For B its the same thing but no graph. Remember that slope is RISE over RUN. So since the number is on the bottom of the line the rise is 4 and the run is 1. So in this case 10 is your y-intercept. Which means you equation is y=4x+10.

What is the decimal equivalent of 2
- ?
3​

Answers

Answer:

.666

Step-by-step explanation:

The decimal answer of two thirds is zero point six repeating

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Answers

Answer:

18 x^7 y^5

Step-by-step explanation:

Two people wrote a book together. They agreed to share the royalties so that the senior author received twice as much as the
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Answers

Answer:

Junior author = $800

Senior author = $1600

Step-by-step explanation:

The check is split between the senior author and junior author in the ratio of 2:1

2:1 = $2400

Add the ratios together:

2 + 1 = 3

3 parts = $2400

Find one part of the total check by dividing both sides by 3:

1 part = $800

The junior author would get $800, and the senior author would get double, $1600

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Answers

Answer:

8000

Step-by-step explanation:

...
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What is the equation of the line —3x – 2y = 30 in slope-intercept form?

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I believe the first answer shown in the picture because y= mx + b so it's y=3x+30

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