find the length of midsegment YZ in trapezoid ABCD when A(-5,-6) B(-6,-2) C(-4,0) and D(3,2)

Find The Length Of Midsegment YZ In Trapezoid ABCD When A(-5,-6) B(-6,-2) C(-4,0) And D(3,2)

Answers

Answer 1

Answer:

Option C

Step-by-step explanation:

Since, Y and Z are the midpoints of sides AB and CD of the given trapezoid.

Segment YZ will the midsegment of trapezoid ABCD.

By the theorem of midsegment,

m(YZ) = [tex]\frac{1}{2}(AD+BC)[/tex]

By using expression for the length of a segment between two points,

Length of a segment = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between two points A(-5, -6) and D(3, 2),

AD = [tex]\sqrt{(3+5)^2+(2+6)^2}[/tex]

AD = [tex]\sqrt{64+64}[/tex]

AD = [tex]\sqrt{128}[/tex]

AD = [tex]8\sqrt{2}[/tex]

Distance between B(-6, -2) and C(-4, 0)

BC = [tex]\sqrt{(-6+4)^2+(-2-0)^2}[/tex]

BC = [tex]\sqrt{8}[/tex]

BC = [tex]2\sqrt{2}[/tex]

Therefore, m(YZ) = [tex]\frac{1}{2}(8\sqrt{2}+2\sqrt{2})[/tex]

                             = [tex]\frac{1}{2} (10\sqrt{2})[/tex]

                             = [tex]5\sqrt{2}[/tex]

Option C will be the answer.

Answer 2

The length of the midsegment YZ is [tex]5\sqrt 2[/tex]

The coordinates are given as:

A(-5,-6) B(-6,-2) C(-4,0) and D(3,2)

Start by calculating distance AD and CB using:

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

So, we have:

[tex]AD = \sqrt{(3 +5)^2 + (2 +6)^2} = \sqrt{128}[/tex]

[tex]CB = \sqrt{(-6 +4)^2 + (-2 -0)^2} = \sqrt{8}[/tex]

The length of the midsegment is then calculated as:

[tex]YZ = \frac 12 * (AD + CB)[/tex]

This gives

[tex]YZ = \frac 12 * (\sqrt{128} + \sqrt 8)[/tex]

Simplify

[tex]YZ = \frac 12 * (8\sqrt{2} + 2\sqrt 2)[/tex]

[tex]YZ = \frac 12 * (10\sqrt 2)[/tex]

Simplify

[tex]YZ = 5\sqrt 2[/tex]

Hence, the length of the midsegment YZ is [tex]5\sqrt 2[/tex]

Read more about midsegments at:

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Related Questions

Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions. please help ​

Answers

Answer:

(-9/2t + 3) +( 7/4t + 33) = -11/4t + 36

5(2t + 1)+(-7t +28) = 3t+ 33

Step-by-step explanation

Those are the ones i could solve hope this helps!

1. Problem  

(-9/2t + 3) +( 7/4t + 33)

-9/2t + 7/4t

-18/4t +7/4t= -11/4t

3+ 33= 36

-11/4t + 36

2. Problem

5(2t + 1)+(-7t +28)

10t + 5 + ( -7t +28)

10t - 7t= 3t

5+ 38= 33

one solution of x^2 - 64 = 0 is 8. what is the other solution​

Answers

Answer:

- 8

Step-by-step explanation:

Given

x² - 64 = 0 ( add 64 to both sides )

x² = 64 ( take the square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8

Solutions are x = 8 and x = - 8

The fun guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The game bank charges an annual fee of $20 plus $2.50 per game. for how many game rentals will the cost be the same at both stores?​

Answers

Answer: 5


You would need to buy 5 game rentals for the cost to be the same at both stores
Answer :


5 i just wanted to answer

please some help me .

OPTIONS: 75 degrees, 30, 90, or 45

Answers

Answer:

x = 45

Step-by-step explanation:

x + 45 + 2x = 180

3x + 45 = 180

3x = 135

x = 45

Answer:

x = 45

Step-by-step explanation:

We know that the three angles of a triangle add up to 180. So we can add all the points equal to 180 to find the value of x.

a + b + c = 180

45 + x + 2x = 180

Combine terms.

45 + 3x = 180

Subtract 45 from both sides.

3x = 135

Divide both sides by 3 to get

x = 45.

To prove this, put x into the original addition of the angles.

45 + x + 2x = 180

Substitute 45 into x.

45 + 45 + 2(45) = 180

Multiply 2 and 45.

45 + 45 + 90 = 180

Add terms.

180 = 180.

I need help!!!! Please

Answers

the answer is

y≥2x/5+2

Step-by-step explanation:

we moved the y to the right site and the -10 to the left site

so we had

2x+10≤5y

and then we devided by 5

2x/5+10/5≤y

y≥2x/5+2

hopefully its correct

Answer:  Choice D

[tex]y \ge \frac{2}{5}x +2\\\\[/tex]

=======================================

Work Shown:

[tex]2x - 5y \le -10\\\\-5y \le -2x-10\\\\y \ge \frac{-2x-10}{-5} \ \text{ ... see note1 below}\\\\y \ge \frac{-2x}{-5} - \frac{10}{-5}\\\\y \ge \frac{2}{5}x +2 \ \text{ ... answer is choice D}\\\\[/tex]

Note1: when dividing both sides by a negative number, the inequality sign flips.

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

Here's another approach that doesn't involve dividing both sides by a negative number.

[tex]2x - 5y \le -10\\\\2x \le -10+5y\\\\2x +10\le 5y\\\\5y \ge 2x+10 \ \text{ .... see note2 below}\\\\y \ge \frac{2x+10}{5}\\\\y \ge \frac{2x}{5} + \frac{10}{5}\\\\y \ge \frac{2}{5}x +2\\\\[/tex]

Note2: I swapped the left and right sides. Doing this swap means that the inequality sign must flip as well.

Can someone help me out my grads are bad

Answers

Answer:

shen's new area will be 1200 ft ^ 2

It will be 2 times the original

Donna should increase the length by 5 times

Step-by-step explanation:

Original length = 40

New length = 30 x 4 = 120

Original width = 20

New width = 20 x 5 = 100

120 x 100 = 12000 ft^2

12000/600 = 20

It will be 20 times larger

For Donna:

ex:

length = 1

width = 2

Area = 2

He wants it to be 15 times 2

Lisa says increase 4 times

2 x 3 = 6

30/6 = 5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

a) 120 ft x 100 ft = 12000 [tex]ft^{2}[/tex]

b) 20 times

c) 5 times

Step-by-step explanation:

a) 30x4 = 120

20x5 = 100

120x100 = 12000

b) 12000/600 = 20

c) 15/3 = 5

SOMEONE HELP ME PLSSS ASAP

Answers

It’s D :)))))))$))))

please help me i need this grade

Answers

The answer is C. (2,6)

Solve for x, given: x2−4x+29=0

Answers

Answer:

X= 5i-2, x=5i-2

Step-by-step explanation:

Step-by-step explanation:

[tex] {x}^{2} - 4x + 29 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{4± \sqrt{ - 100} }{2} \\ x = \frac{4±10i}{2} \\ x = 2±5i \\ x = 2 + 5i \: \: or \: \: x = 2 - 5i[/tex]


Anita's father is 5 ft. 9 in. tall, How many inches tall is anita's father​

Answers

Answer:

He would be about 69 inches

Answer:

69 inches tall

Step-by-step explanation:

add 5ft = 60 inches + the other 9 inches which is

69 inches all together

hello please help i’ll give brainliest

Answers

Answer:

Option B) His teachings became government philosophy.

Answer:

His teachings became government philosophy ..

hope it is helpful to you.

The height h and the base area B of a cylinder are given. Find the volume of the cylinder. Write your answer in terms of it. h=2 units B=25pi symbol square units​

Answers

here's the solution,

[tex] \boxed{\small{volume = area \: \: of \: base \: \: \times height}}[/tex]

so,

=》

[tex]v = 25\pi \times 2[/tex]

=》

[tex]v = 50\pi[/tex]

if you solve for π then the value will be :

157

but in terms of π the value will be :

50 π

The volume of the cylinder is 157 unit³.

What is volume?

The amount of space occupied by a three-dimensional figure as measured in cubic units.

Given: B= 25π, h= 2 units

Base area= 25π

πr²=  25π

r²=25

r=±5 units

Now, Volume of cylinder= πr²h

                                         = 3.14* 5* 5* 2

                                         = 157 unit³

Hence, the volume of cylinder is  157 unit³.

Learn more about volume of cylinder here:

https://brainly.com/question/16134180

#SPJ2

PLEASE HELP I AM BEGGING YOU EXTRA POINTS AND BRAINLIEST I DONT UNDERSTAND NO WORK JUST ANSWER :)!!!!!!!!!!!!!!!!!!!!!!!1

Answers

Answer:

1.    x > -3

2.    8 > 0.5

3.    x < -4

6. x < 2

7. Yes

8. No

9. Yes

10. Yes

1. p=packs of gum

inequality = 35 > 10+2p

Benny can buy 6 packs of gum.

The circumference of a circular painting is 43.96 feet. What is the diameter of the painting? Use 3.14 for π and do not round your answer.

Answers

Answer:

14 feet

Step-by-step explanation:

c = πd

Plug in the givens

43.96 = 3.14d

Divide both sides by 3.14

14 = d

Answer:

Diameter = circumference ÷π

43. 96÷3. 14 =14 feet

32 + 4 × [12 - (2 + 4)]

Answers

Answer:

32+4×[12-(2+4)]

=32+4×[12-6]

=32+4×6

=32+24

=56,,answer

hope this will help you more

Put the values into the correct order from GREATEST on the top to LEAST on the bottom. ​

Answers

2134 second box first and some on

9514 1404 393

Answer:

  C, D, B, A

Step-by-step explanation:

The values shown are ...

-π ≈ -3.14√5 -5 ≈ -2.76√9+√2 ≈ 4.418/3 ≈ 2.67

So, from greatest to least, the values are ...

  √9 +√2 ≈ 4.41

  8/3 ≈ 2.67

  √5 -5 ≈ -2.76

  -π ≈ -3.14

Which number is closest to the value of the upper quartile?​

Answers

Answer:

180 is closest to upper quartile

Step-by-step explanation:

Simplify the algebraic expression: 4n + 19 + 3n - 2n - 5 A. 19n B. 33n C. 5n + 14 D. 9n + 24

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{4n + 19 + 3n - 2n - 5}[/tex]

[tex]\large\text{COMBINE the LIKE TERMS}[/tex]

[tex]\large\text{(4n + 3n - 2n) + (19 - 5)}[/tex]

[tex]\large\text{4n + 3n - 2n}\\\large\text{4n + 3n = \bf 7n}\\\large\text{7n - 2n = \bf 5n}[/tex]

[tex]\large\text{5n + (19 - 5)}[/tex]

[tex]\large\text{19 - 5 = \bf 14}[/tex]

[tex]\large\text{= \bf 5n + 14}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf Option C. 5n + 14}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

what is the volume of the rectangular prism​

Answers

Answer:

it might be 7yd^3 im not to sure.

Step-by-step explanation:

The coordinates of point S are (-5, 2). In which quadrants does point S lie?

Answers

By the 2 because it goes up more than 5 or put 5.2 on 7

16. What is the image of (2, -2) rotated 270° counterclockwise about the origin?
A (-2,-2)
B (-2, 2)
C (2,-2)
D (2, 2)
w

Answers

it’s D. a 270* rotation is basically switching them around. i cant rlly explain it

Actividades.
Iniciamos la clase leyendo atentamente la
siguiente situación
Joaquin compró un tanque para agua que tiene
forma de prisma rectangular, cuyas dimensiones
son √5m, √6m y √ 10m


¿Cual es el volumen del tanque de agua?
. Ancho- √5m
Largo - √6m
Altura - √10m

Answers

Answer:

ancho de ese culotote

Step-by-step explanation:

(No linkssss)Pls help me if your good at math I’ll mark brainliest if correct

Answers

The answer should be D bc the others don’t make sense. Hope this helps!

Solutions to a quadratic equation are -7 and 1. What is the equation of its axis of symmetry?

Answers

Answer:

Axis of symmetry: x=-4

Step-by-step explanation:

If x=-7 and x=-1 are solutions to a quadratic equation, then that quadratic equation must be (x+1)(x+7)=0 -> x^2+8x+7=0 as both solutions satisfy the Zero Product Property where the function is f(x)=x^2+8x+7. The axis of symmetry would be the line x=-b/2a which means the axis of symmetry is x=-(8)/2(1)=-8/2=-4 -> x=-4. It can also be found by turning f(x)=x^2+8x+7 into f(x)=(x+4)^2-9 by completing the square, and since h=-4, then the axis of symmetry would be x=h=-4. Refer to the graph.

trig///HELPP PLEASE!! i’ve been stuck on this for 30 minutes!!

Answers

Answer: There are two solutions and they are

theta = 135

theta = 225

=============================================================

Explanation:

Recall that x = cos(theta). Since the given cosine value is negative, this indicates x < 0. Theta is somewhere to the left of the y axis, placing it in quadrant 2 or quadrant 3.

It turns out there are two solutions, with one solution per quadrant mentioned above. Use the unit circle to find that the two solutions are:

theta = 135

theta = 225

You're looking for points on the unit circle that have x coordinate equal to x = -sqrt(2)/2. Those two points correspond to the angles of 135 and 225, which are in quadrants 2 and 3 respectively.

--------

I recommend using your calculator to note that

-sqrt(2)/2 = -0.70710678

cos(135) = -0.70710678

cos(225) = -0.70710678

The decimal values are approximate. Make sure your calculator is in degree mode. Because those three results are the same decimal approximation, this indicates that cos(135) = cos(225) = -sqrt(2)/2.

HELPP PLEASEEE
NO LINK!!

Answers

Answer:

the graph increases

Step-by-step explanation:

Explain the benefits of data analysis in weather systems.

Answers

Made open and interprated in the right way! Weather warnings, forecasts to protect life and property. Weather's forecast is important to agriculture and therefore traders within commodity markets.

Huge volumes of data on the present state of environmental conditions, notably temperatures, moisture, and wind, are gathered in order to predict weather forecasts, and via the atmospheric procedure, meteorology data analysts assess how the atmosphere will change.

Barometers. Measuring devices are used by meteorologists to monitor compressed air. A barometer can hold water, air, or mercury, although most barometers, like thermometers, have become digital. A shift in barometric pressure signals that the weather is about to change.

Learn more:

https://brainly.com/question/19015263?referrer=searchResults

(−4x−2)−(5x+10)
Please helppppp

Answers

Answer:

-9x-12

Step-by-step explanation:

Answer:

Factor Awnser....  -3(3x+4)

Simplify Awnser.... -9x-12

Step-by-step explanation:

not sure which you needed

(x²- 3x) + (-2x²+ 5x - 3)

Answers

Answer:

[tex]-x^{2} +2x-3[/tex]

Answer :

-2x^2 + 2x - 3

A trapezoid has an area of 140 square centimeters with bases of 12 and 10 centimeters. What is the length of the height? Round to the nearest tenth place.

Answers

Answer:

12.7 cm

Step-by-step explanation:

Area of a trapezium = 1/2 x ( a + b) x height

a and b represents the bases

140 = 1/2 x (12 + 10) x h

140 = 11h

h = 140 / 11

h = 12.727 cm

h = 12.7 cm to the nearest tenth

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

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