Given: Y is the midpoint of XZ
Prove: XY = 1/2 XZ
Statements
Reasons

Answers

Answer 1

Answer:

The proposition If Y is the midpoint of XZ, then XY = 1/2 XZ is true.

Step-by-step explanation:

We proceed to present the demonstration of the following proposition:

If Y is the midpoint of XZ, then XY = 1/2 XZ.

1) Y is the midpoint of XZ. Given.

2) [tex]XY + YZ = XZ[/tex] Definition of line segment.

3) [tex]XY = YZ[/tex] By 1)

4) [tex]2\cdot XY = XZ[/tex] 3) in 2)

5) [tex]XY = \frac{1}{2}\cdot XZ[/tex] Algebra/Result

Therefore, the proposition If Y is the midpoint of XZ, then XY = 1/2 XZ is true.


Related Questions

Are the given
equations parallel,
perpendicular, or
neither?
y = 3x + 5
y = 3x - 7

Answers

Answer:

parallel

Step-by-step explanation:

They have the same slope, just different y-intercepts. The two lines never cross, making them parallel.

What percentage of 80 is 67

Answers

Answer:

83.75%

Step-by-step explanation:

67/80 = 83.75%

7.
If 3 tickets to a certain show cost $13.20, what would 7 tickets cost?

What is this answer?

Answers

Answer:

$ 30.8

Step-by-step explanation:

ratio and proportion:

3 tickets  = 7 tickets

$13.20            x

then cross multiply:  3 (x) = 13.20 (7)

simplify: 3x = 92.4

solve for x = 92.4 / 3

x = $ 30.8

therefore,

7 tickets costs $ 30.8

Evaluate 0.1m + 8- 12n when m=30 and n = 1/4 answer

Answers

Answer:

8

Step-by-step explanation:

Original equation:

0.1m + 8 - 12n

Plug in the values of m and n

0.1(30) + 8 - 12(0.25)

Multiply.

0.1 x 30 = 3

3 + 8 - 12(0.25)

Multiply.

-12 x 0.25 = -3

3 + 8 - 3

Add.

3 + 8 = 11

11 - 3

Subtract.

11 - 3 = 8

Hope I helped :)

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You bike 16.2 miles in 1.8 hours at a steady rate. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you​ travel?

Answers

Answer:

9x

Step-by-step explanation:

You have to subtract both of the numbers and simplify it.

Simplify

8a-8b
a2-b2

Answers

Answer:

 -8a2b + 8a - b2

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (8a -  23a2b) -  b2

STEP  2 :

STEP  3 :

Pulling out like terms

3.1     Pull out like factors :

-8a2b + 8a - b2  =   -1 • (8a2b - 8a + b2)  

Trying to factor a multi variable polynomial :

3.2    Factoring    8a2b - 8a + b2  

Try to factor this multi-variable trinomial using trial and error  

Answer:

-8a^2b - b^2 + 8a

Have a nice day and stay safe. Pls rate me and like.

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The table represents the relationship between a length measured in meters and the same length measured in kilometers.

1. Complete the table.

Type the answers in the boxes below.

meters kilometers
1,000 1
3,500
500
75
1
x


2. Write an equation for converting the number of meters to kilometers. Use x for number of meters and y for number of kilometers.

Type the answer in the box below.

Answers

Answer:

Q1 1000     1

    3500    3.5

   500       .5

   75   .075

   1        .001

   x       1/1000x or .001x        Q2    Y=  1/1000x

Step-by-step explanation:

just search up 1000 meters to 1 kilometer and go from there :)  

PLZ HELP WILL MARK BRAINLEST 2 or more have to answer and its timed 1 hour

Answers

Answer:

z=77

Step-by-step explanation:

z/7−9=2

Step 1: Simplify both sides of the equation.

z−9+9=2+9

1/7z=11

z=77

(✿◠‿◠)

Which expression is equivalent to 6a + 15?

6(a + 5)
3(2a + 5)
3(3a + 12)
6(a + 12)

Answers

The answer is going to be 3(2a+5)


Explanation:

6(a+b) = 6a +30 (it is not equivalent to 6a+15)

You have to multiply what’s in the brackets by 6

3(2a+5) = 6a+15 ( it is equivalent )


3 (3a+12) = 9a+36 (not equivalent)


6(a+12) = 6a+12 (not equivalent)

I hope this helps:))

Pool #1 is a rectangle that is 14 feet wide. The length is (14– 8)2ft.

The dimensions of the pool are: Length=________ ft Width=_________ft

Answers

Answer: the length is 6 feet. The width is 2 feet

Step-by-step explanation:

The garden pool is rectangular in shape.

Let L represent the length of the rectangular garden.

Let W represent the width of the rectangular garden.

The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that

L× W = 12 - - - - - - - - - - 1

The length of the pool needs to be 2ft more than twice that width. This means that

L = 2W + 2 - - - - - - - - - - - 2

Substituting equation 2 into equation 1, it becomes

W(2W + 2) = 12

2W^2 + 2W = 12

2W^2 + 2W - 12 = 0

W^2 + W - 6 = 0

W^2 + 3W - 2W - 6 = 0

W(W + 3) - 2(W + 3) = 0

W - 2 = 0 or W + 3 = 0

W = 2 or W = - 3

Since the Width cannot be negative, then the width is 2 feet

Substituting W = 2 into equation 2. It becomes

L = 2×2 + 2 = 6 feet

Alecia placed the numbers 0, 2, 14, -8, and -11 on the number line. Which of the numbers is furthest from zero?

Answers

Answer:

14

Step-by-step explanation:

Write an equation in standard form of the line that passes through (4,−1) and has the slope m=3.

Answers

Answer :

m = 3

Point = (4,-1)

x1 = 4

y1 = -1

Formula =

y - y1 = m (x-x1)

y - (-1) = 3 (x -4)

y + 1 = 3x -12

y - 3x + 1 + 12 = 0

y - 3x + 13 = 0

The line = y - 3x + 13 = 0 or -3x + y + 13 = 0

I'm sorry if I'm wrong.

Cmiiw

Good luck

Love from Indonesia

y=3x-13 is the equation in standard form of the line that passes through (4,−1) and has the slope m=3.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=3

We need to find slope intercept form, for this we should know the y intercept with slope m =3 and point (4,-1)

-1=3(4)+b

-1=12+b

-1-12=b

b=-13

y intercept is -13

Hence, y=3x-13 is the equation in standard form of the line that passes through (4,−1) and has the slope m=3.

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the area of a trapezium is given by the formula A=1/2h(a+b), where h is the height and a and b are the measures of the two bases. what is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches?

Answers

Answer:

[tex] h = 4.8 \: inches.[/tex]

Step-by-step explanation:

[tex]A= \frac{1}{2} h(a+b) \\ h(a + b) = 2A \\ h = \frac{2A}{(a+b)} = \frac{2 \times24 }{4 + 6} \\ h = \frac{48}{10} \\ h = 4.8 \: inches.[/tex]

Answer:

h=4.8

Given:

area=24 , a=4 , b=6

To find:

height

Step-by-step explanation:

A = [tex]\frac{1}{2}[/tex] × h(a+b)

24 = [tex]\frac{1}{2}[/tex] × h(4+6)

24 × 2 = h(10)

48 = 10h

48/10 = h

h=24/5

h=4.8

therefore, height of the trapezium is 4.8

hope it helps you!

In triangle QRS, angle Q measures 33.7°, angle R measures 52.3°, and angle S measures 94º. Based on the information that is provided, which could be a correct set of sides for this set of angles?

O side QR = 7 cm. side RS = 10 cm , side QS = 12.6 cm

O side QR = 10 cm, side RS = 7 cm, side QS = 12.6 cm side

O QR = 12.6 cm, side RS = 10 cm, side QS = 7 cm

O side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm​

Answers

You know, it's easier to draw it out to figure out the answer!

It's side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm. So, it's D. (last option)

Answer:

D

Step-by-step explanation:

I got it right on the test. 100%

please I need answer asap!!

Where is the point (5,-1) located in the coordinate plane? O A. In quadrant IV B. In quadrant II C. On the y-axis OD. In quadrant Ill​

Answers

I’m pretty sure that it is located in quadrant II

Answer:

A. In quadrant IV

Step-by-step explanation:

I checked it and it’s right on A P E X hope this helps:)

Which is better to buy 4.20 for 6 cans or 8.00 for 10 cans

Answers

Answer:

4.20 for 6 cans is better

Step-by-step explanation:

4.20 / 6 = 0.70 per can  

8.00 / 10 = 0.80 per can

0.70 per can is cheaper/less expensive than 0.80 per can.

I need help finding the slope, the y-intercept and the equation?

Answers

Answer:

y is (0,-2) thats all i know sorry

Step-by-step explanation:

The equation of line will be;

⇒ y = x + 2

And, The y - intercept will be 2.

What is Equation of line?

The equation of line with slope 'm' and y - intercept at point 'b' is given as;

⇒ y = mx + b

Given that;

The points on the graph are (0, 2) and (- 2, 0).

Now,

Since, The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Thus, The slope of the line with the points (0 , 2) and (-2, 0) is;

m = (0 - 2) / (- 2 - 0)

m = - 2/- 2

m = 1

So, The equation of line passing through the points (0 , 2) and (-2, 0) with slope 1 is defined as;

y - y₁ = m (x - x₁)

y - 2 = 1 (x - 0)

y - 2 = x

y = x + 2

Now, Compare with the equation y = mx + b, we get;

The y - intercept = 2

Thus, The equation of line will be;

⇒ y = x + 2

And, The y - intercept will be 2.

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ryan deposited 4,000$ into his savings account at the interest rate of 4%for 5 years ate the end of the 5 years how much money would be in ryan's account worksheet

Answers

Answer:

$4,800

Step-by-step explanation:

you take $4000 and multiply by .04 to get interest for one year. Then multiply by 5 for the years and that is $800. and $800 + $4000 - $4800.

Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.

y= 1/3 x− 2/3

Answers

Answer:

y-intercept = (0,-2/3)

x-intercept = (2,0)

Step-by-step explanation:

*X-intercept touches the x-axis & y-intercept touches the y-axis*

You can identify the y-intercept by looking at the equation.

The slope is 1/3x and the y-intercept is -2/3.

I'm not sure how to solve for the x-intercept, but you can make a graph with the y-intercept and the slope points. By doing this you should be able to find the x-intercept.

Hope this helped!!!  :)

PS: Check out the Desmos Graphing Calculator

This website helps a lot with these types of problems. You can type the equation, and it will show you a graph. If you look at the graph, you'll be able to determine the slope, the x-intercept, and the y-intercept.

i need help with this asap!homework is due tomorrow.

Answers

Heyyy!!

HERE'S YOUR ANSWER!

AB²+BC²=AC²

Answer:

If triangle ABC is a right angled triangle,right angled at C

AB²=AC² + BC²

Pls mark me brainliest

Step-by-step explanation:

A coordinate grid with 2 lines. The first line is labeled f(x) and passes through (negative 4, 3), (0, 3) and (4, 3). The second line is labeled g(x) and passes through the points (negative 2, negative 5), (0, negative 2), and (2, 1)

Determine the input value for which the statement

f(x) = g(x) is true.


From the graph, the input value is approximately (2) (2.5) (3.5) or (4)

.


f(x) = 3 and g(x) = 3/2x – 2


3 = 3/2x – 2


5 = 3/2x


The x-value at which the two functions’ values are equal is (2/3) (3/2) (5/3) or (10/3)

.

Answers

Answer:

3.5 and 10/3

Step-by-step explanation:

just took the quiz

Answer: C.) 3.5 and D.) 10/3

Step-by-step explanation: i hope this helps :)

what is the answer to :
4 x 10³÷ 2 x 10∧12

Answers

Answer:

2x10^15x^2

Step-by-step explanation:

Find the surface area of this rectangular solid.
7cm 5cm 4cm

A. 138
B. 166
C. 168
D. 16
E. 140​

Answers

E:The answer is 140 because seven times five times four equals 140.

whats the slope between these points (3,2) and (6,5)

Answers

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

Answer:

1

Step-by-step explanation:

What is the domain of h^-1(x)

Answers

Answer:

(-∞,∞)

Step-by-step explanation:

Given the following sequence: {x. 3x, 5x, 7x, 9x .... ). what will the value of
the TENTH term be?

Answers

Answer:

The tenth trem will be 21x considering 3x as one 1 + 10x2=21

The distance between two asteroids was calculated at 37,500,000,000 kilometers. What is this value expressed in scientific notation?

Answers

I believe that the answer is 3.75x10^10

Find all whole values for y for which the double inequality is true: -5

Answers

Answer:

The values of y for which the inequality is true are;

-4,-3,-2,-1,1,0,1

Step-by-step explanation:

Here, we want to give all the values of y for which the given inequality is true

We have the inequality as;

-5 < y < 2

This can be read as -5 is less than 5 which is less than 2

This means that the correct y-values lie between -5 and 2 which are not inclusive

So the correct values of y in this case are;

-4,-3, -2, -1 , 0, 1

multiply (3-6i)^2 write in standard form

Answers

-27-36i .................................................................... not sure

The result of (3 - 6i)² will be -27 -36i .

Given,

(3 - 6i)²

Now,

The multiplication is of complex number .

So,

(3-6i)(3 - 6i)

So,

Multiply the terms ,

9 - 18i - 18i -36

Simplifying further,

-27 - 36i

Thus the resultant will be  -27 -36i  .

Know more about complex numbers,

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Why is brainliest so important and why is leveling up so important

Answers

Answer:

Its is so u get points make me he brainlst thx

Step-by-step explanation:

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