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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Step-by-step explanation:

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Step-by-step explanation:

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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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Answers

Answer:

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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.

You put the values on the second power and add them. So the equation would be 6^2 + 8^2. The answer would be 100.  Because the Pythagorean Theorem is a^2 + b^2= c^2, you would square root would be 10. The distance between the two points is 10.

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C
B
A
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Answers

Answer:

B

Step-by-step explanation:

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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

so options A,B and C are incorrect

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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.

[tex] \therefore \: x = \frac{ \sqrt{3} }{2} \times 18 \\ \\ \therefore \: x = \sqrt{3} \times 9 \\ \\ \huge\therefore \: x =9 \sqrt{ \boxed{3}} [/tex]

Answer:

3

Step-by-step explanation:

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Answers

Answer:

The answer would be 30 the second one is 180

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Answers

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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Answers

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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:

Junior author = $800

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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:

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3 parts = $2400

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

1 part = $800

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Step-by-step explanation:

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Answer:

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Answers

Answer:

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Answers

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Step-by-step explanation:

-8x + 10y = -22

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

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=====

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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

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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:

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-8x + 10(1) = -22

-8x + 10 = -22

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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:

He has 672 nails

Step-by-step explanation:

168/.25

Answer:

He has 672 nails.

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Answer:

Ans 26

Step-by-step explanation:

F(x) = x/2

proof:

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Answers

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Step-by-step explanation:

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1 = <

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Step-by-step explanation:

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Answers

Step-by-step explanation:

(i) 2x = 5

compare with ax+by+c = 0

→ 2x + 0.y - 5 = 0

» a = 2 ,b = 0 ,c = -5

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compare with ax + by + c = 0

→ 0.x + 1y -2 = 0

» a = 0 , b = 1 , c = -2

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y = 3×7

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y - 21 = 0

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compare with ax + by + c = 0

→ 13x + 0.y + 14 = 0

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Answers

I think you meant, if a = 0.

If a = 0, then,

a³ = 0³

a³ = 0 × 0 × 0

a³ = 0

Any number multiplied by 0 is 0.

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

Answers

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

hope this helps!

A dump truck can hold 2¼ tons of gravel. The pay loader loading the truck puts 750 pounds of gravel in the truck at one time. How many loads does the pay loader need to dump in the truck before it is full?​

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.

Thank you,

Miss Hawaii

Answer:

6 loads

Step-by-step explanation:

3 x 100 + 5 x 10 +6⋅1 + 8 x .1 + 2 x .01



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Answers

your answer is 357.1

7819 rounded to 1 significant figure

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Answer:

8000

Step-by-step explanation:

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