Given the vertices of a triangle ABC below, find the midpoint and length of the midsegment. Give your length in simplified radical form.

Given The Vertices Of A Triangle ABC Below, Find The Midpoint And Length Of The Midsegment. Give Your

Answers

Answer 1

Answer:

Midpoint of AC = (-1, 1)

Midpoint of BC = (1, -2)

Length of the midsegment = [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Vertices of a triangle ABC are A(0, 5), B(4, -1) and C(-2, -3).

Midpoint of segment AC = [tex]\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]

                                         = [tex](\frac{0-2}{2},\frac{5-3}{2})[/tex]

                                         = (-1, 1)

Midpoint of BC = [tex](\frac{4-2}{2},\frac{-1-3}{2})[/tex]

                         = [tex](1,-2)[/tex]

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

                                              = [tex]\sqrt{(-1-1)^2+(-2-1)^2}[/tex]

                                              = [tex]\sqrt{4+9}[/tex]

                                              = [tex]\sqrt{13}[/tex]


Related Questions

Solve for the value of x.

Answers

Step-by-step explanation:

9x-4+6x+4=180 ( being straight angle)

15x=180

x=180/15

x=12

I hope it help you

Find the 69th term of the arithmetic sequence -13, -33, -53, ...​

Answers

Answer:

-1,373

Step-by-step explanation:

a69 = -13 + (69-1)(-20)

= -13+(68)(-20)

= -13 - 1,360

= -1,373

Answer:

-1373

Step-by-step explanation:

GIVEN :-

A.P. = -13 , -33 , -53 , ...

TO FIND :-

69th term of A.P.

FACTS TO KNOW BEFORE SOLVING :-

Lets say there's an A.P. whose :-

First term = aCommon Difference = dTotal number of terms = nnth term = aⁿ

Formula for finding nth term of A.P. = aⁿ = a + (n - 1)d

SOLUTION :-

According to the question ,

First term = -13Common difference = -33 - (-13) = -20Number of terms needed to find = 69

By using the formula for finding nth term ,

69th term of A.P. = -13 + (69 - 1)×(-20) = -13 + (-1360) = -1373

Which is equivalent to the expression (3x^2 – 2x + 14) – (6x² + 3x – 9)?
A) -3X^2 - x +5
B) -3X^2-5x+5
C) -3x^2-5x+23
D) 18x^4-6x^2-126

Answers

correct answer is c i think so

Solve.
3x+4y=−15

2x−2y=−3

Answers

The solution is (-3,-3/2)
point form: (-3, -3/2)

equation form: x=-3, y=-3/2

let me know if you need the work!

A race horse runs one lap around a lake in 10 minutes.

How long will it take for the horse to run 6 laps around the lake at the same pace?

Answers

Answer:

1 hour or 60 minutes.

A basketball tosses a ball to a teammate. The ball reaches a maximum height of 11 feet 3 seconds after it was released. If the ball is thrown from a height of 6 feet, write a quadratic equation that represents the height of the ball as a function of time

Answers

Answer:

h = - 16t² + 49.67t + 6

Step-by-step explanation:

The expression for the height of the basketball, h at time, t is given by

h - h₀ = u₀t - 1/2gt² where h₀ = initial height of ball = 6 feet, h = maximum height of ball = 11 feet, u₀ = initial vertical velocity of ball, t = time taken to reach maximum height = 3 s and g = acceleration due to gravity =9.8 m/s².

We need to find u₀ from u = u₀ -

So, h - h₀ = u₀t - 1/2gt²

h - h₀ + 1/2gt² = u₀t

u₀ = (h - h₀)/t + 1/2gt

substituting the values of the variables into the equation, we have

u₀ = (h - h₀)/t + 1/2gt

u₀ = (11 ft - 6 ft)/3s + 1/2 × 32 ft/s² × 3 s

u₀ = 5 ft/3s + 1/2 × 96 ft/s

u₀ = 1.67 ft/s + 48 ft/s

u₀ = 49.67 ft/s

Using h - h₀ = u₀t - 1/2gt² where h is the height of the basketball at time, t

h = u₀t - 1/2gt² + h₀

substituting the values of the variables into the equation, we have

h = u₀t - 1/2gt² + h₀

h = (49.67ft/s)t - 1/2(32 ft/s²)t² + 6 ft

h = 49.67t - 16t² + 6

h = - 16t² + 49.67t + 6

Taylor invested $2500 in an account that pays 3.7% interest compounded monthly. If Taylor does not touch the money, what will the balance of the account be after 7 years?

Answers

Answer:

hehe

Step-by-step explanation:

A backpack normally costs $25 but it is on scale for $16.25. What percentage is on discount? Please help, I have a test rn:((​

Answers

Answer: 16%

Step-by-step explanation:

$25 - $21 = $4

Percentage = 100[discount / (original price)] % = 100($4 / $25) % = 16%

Zahra reads 45 words per minute. at this rate. how many minutes will it take for her to read 180 words

Answers

Answer:

4 minutes

Step-by-step explanation:

I will use ratios for this equation:

[tex]\frac{1}{45} =\frac{x}{180} \\\\45x=180\\x=4[/tex]

It will take Zahra 4 minutes to read 180 words because she reads 45 words PER minute.

If the quadrilateral below is a trapezoid, find the missing measures.

PLEASE HELP

Answers

Answer:

101°

46°

Step-by-step explanation:

The sum of angle C and angle F should be 180°as they are parallel.

Hence, angle C ;

Angle C + angle F = 180°

Angle C + 79° = 180°

Angle C = 180° - 79°

Angle C = 101°

Sum of angle in Trapezoid = 360°

Hence,

C + D + E + F = 360°

101° + 134° + E + 79° = 360°

314° + E = 360°

E = (360 - 314)°

E = 46°

Please help I am confused explain your answer and brainliest

Answers

Answer:

Technically Andrew since his sum is technically "higher" than the rest of the negative numbers.

Answer:

Andrew

Step-by-step explanation:

Andrew since his sum is practically greater than the rest of the negative numbers.

I need help please it would really make my day



no links or zooms please !!!!

Answers

Answer:

267.45 sq units

Step-by-step explanation:

Area of shaded region = Area of Square minus Area of Circle

the sides of the square are twice the radius of 9, therefore 18

A(square) = 18² = 324

A(circle) = π9² = 81π ≈ 56.55

324 - 56.55 = 267.45

Problem Page Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.

Answers

Note: Consider we need to find the possible number of ways to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.

Given:

Number of letters = 4

Number of letters selected without replacement = 2

To find:

The total possible number of ways.

Solution:

We have 4 letters A, B, C and D.

So, the number of ways to select first letter is 4.

After selecting a letter the number of remaining letters is 3.

So, the number of ways to select second letter is 3.

Now, the total number of ways to select 2 letters, without replacement, from the 4 letters A, B, C, and D is:

[tex]4\times 3=12[/tex]

Therefore, the required number of ways is 12.

Johnny wants to buy a set of drums that cost $2000, it requires a 15% down payment. The remainder plus an additional finance charge is paid back on a monthly basis of 25 months. the monthly payment is $80. What is the finance charge.

Answers

Answer: The finance charge = $ 300

Step-by-step explanation:

Given: cost of drums = $ 2000

Down payment = 15% of 2000

= 0.15 x 2000

= $300

Total installments = (Number of months) x (Monthly charge)

= 25 x $ 80

= $ 2000

Finance charge  = Down payment + Total installments - cost of drums

= $ (300+2000-2000)

= $ 300

Hence, the finance charge = $ 300

HELP ASAP

A pair of equations is shown below:

y = 2x + 9
y = 4x − 3

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show the first step you would use. (4 points) Write the solution. (2 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intrsect? Explain your answer. (4 points)

Your answer:

Answers

Answer:

(6,21)

Step-by-step explanation:

Given that,

y = 2x + 9 .....(1)

y = 4x − 3 .....(2)

From equations (1) and (2),

2x + 9 = 4x − 3

Taking variables both sides and constants to another side.

9+3 = 4x-2x

12 = 2x

x = 6

Put the value of x in equation (1).

y = 2(6) + 9

y = 12 + 9

y = 21

The solution of the given equations is x = 6 and y = 21. If we graph them, they will intersect at (6,21).

Sasha borrows $100 at 12% simple interest, to be paid back in one year . How much does she pay back

Answers

Answer:

$289 I think

Step-by-step explanation:

$289 I think

sorry if I am wrong

please help this is due at 8 i'll mark you brainlist

Answers

Answer:

Surface Area = 1633.63 square yd

Step-by-step explanation:

[tex]r = 10, \ h = 16\\\\Surface \ Area = 2 \pi r^2 + 2 \pi r h\\\\[/tex]

[tex]= 2 \pi \times 10^2 + 2 \pi \times 10 \times 16\\\\=200 \pi + 320 \pi\\\\= 520 \pi\\\\ =1633.63 \ yd ^2[/tex]

If quadrilateral WXYZ is a rhombus and ZY = 25, VX = 15, WY = 40 find each measure

Answers

Answer:

Size of the side of the square = 25

Step-by-step explanation:

Here WY is the diagonal

VZ = ZX = 15

and VW = VY = 20 (bisector of diagonal)

The diagonals intersect each other at 90 degrees

Hence the side of the Rhombus

Sqrt ( 15^2 + 20^2)

Sqrt (225 +400)

Sqrt (625)

= 25

Find the side length x

Answers

Answer:

x = 10

Step-by-step explanation:

8² + 6² = x²

64 + 36 = x

64 + 36 = 100

√100 = 10

[tex]\huge\bold{To\:find:}[/tex]

The length of the hypotenuse ''[tex]x[/tex]".

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\purple{The\:length\:of\:the\:hypotenuse \:"x"\:is\:10.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

Using Pythagoras theorem, we have

[tex] ( {hypotenuse})^{2} = ( {perpendicular})^{2} + ( {base})^{2} \\ ⇢ {x}^{2} = {6}^{2} + {8}^{2} \\ ⇢ {x}^{2} = 36 + 64 \\ ⇢ {x}^{2} = 100 \\ ⇢ x = \sqrt{100} \\ ⇢x = \sqrt{10 \times 10} \\ ⇢x = \sqrt{ ({10})^{2} } \\ ⇢x = 10[/tex]

[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:10.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex] {x}^{2} = {6}^{2} + {8}^{2} \\⇝ ({10})^{2} = 36 + 64 \\ ⇝10 \times 10 = 100 \\ ⇝100 = 100 \\ ⇝L.H.S.=R. H. S[/tex]

Hence verified. ✔

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

anyone know how to do it?

Answers

Answer:

sorry i dont know how to do this yet moths do a lot of tufff too u know what im sayin

Step-by-step explanation:

Please help!!!!!!
BRainliest.

Answers

Answer:

4.974

Step-by-step explanation:

(4x²y³ + 2xy² - 2y) - (-7x²y³ + 6xy² - 2y)

Answers

Answer:

Simplified it would be 11x^2y^2 - 4xy^

Answer:

11x²y³ - 4xy²

Step-by-step explanation:

is the answer if simplified.

3m=5m-8/5...................................

Answers

Answer:

its m= 4/5

Step-by-step explanation:

Answer:

[tex]m = \frac{4}{5}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

a tin has asquare base whose sides measures 32 cm .the vertical sides are 50cm high.cake mixture is poured into the tin and leveled off at the 38 cm mark above the base


(i)the capacity of the tin


(ii)the volume of the cake mixture in the tin in cm^3

(iii)volume of the space unoccupied by the cake in cm^3

Answers

Answer:

(a) V = 51200 cubic cm

(b) V' = 38912 cubic cm

(c) V'' = V - V' = 12288 cubic cm

Step-by-step explanation:

side of the square base, s = 32 cm

height, h = 50 cm

height of cake mixture, h' = 38 cm

(a) The capacity of the tin is the volume.  

Capacity of tin, V =  s x s x h = 32 x 32 x 50 = 51200 cubic cm

(b) The volume of the cake mixture is

V' =  s x s x h'

V' = 32 x 32 x 38 = 38912 cubic cm

(c) Volume of unoccupied space is

V'' = V - V' = 51200 - 38912 = 12288 cubic cm


Write the equation of the line in fully simplified slope-intercept form.

Answers

12/12 or one whole because if u see the lines end out on the 12’s and if u get the same number is that numb if u want or one whole

An electronics company sells computer monitors
and releases a new model every year. With each
new model, the company increases the screen
size by a constant amount. In 2005, the screen
size was 15.5 inches. In 2011, the screen size was
18.5 inches. Which of the following best
describes how the screen size changed between
2005 and 2011?
A) The company increases the screen size by
0.5 inch every year.
B) The company increases the screen size by 1
inches every year.
C) The company increases the screen size by 2
inches every year.
D) The company increases the screen size by 3
inches every year.

Answers

The statement that best describes how the screen size changed between 2005 and 2011 is: A) The company increases the screen size by 0.5 inch every year.

Screen size changed between 2005 and 2011

Given:

2005= 15.5 inches

2011=18.5 inches

Hence:

2005-2011= 6 years

18.5 inches-15.5 inches=3 inches

Size of screen:

Size of screen=3/6

Size of screen=0.5 increase every year

Therefore the correct option is A.

Learn more about screen size change here:https://brainly.com/question/13261582

#SPJ6

PLS HELP
What is the value of x ?

A. 42

B. 43

C. 84

D. 86

Answers

The value of X would have to be A-42

Answer:

B

Step-by-step explanation:

x+x+94 = 180 (sum of angle of triangle)

2x+94 = 180

2x = 180-94

2x = 86

x = 86÷2

Therefore x = 43

A fish starts at -8 m and jumps up 13 m, what is the fishes new elevation?

Answers

Answer:

the fish is now at 5 m

Step-by-step explanation:

13-8=5

the fish is at 5 meters

Pls help.
Question above

Answers

What is this type of math called please and what year/grade if you don’t mind me asking so I can be prepared

Answer:

[tex]m = \frac{5}{2} [/tex]

Step-by-step explanation:

Here are the laws which would be used in this question:

Indices:

• [tex] \sqrt{a} = {a}^{ \frac{1}{2} } [/tex]

• [tex] \frac{1}{a} = {a}^{ - 1} [/tex]

Logarithm

• [tex] log_{a}( {x}^{n} ) = n log_{a}(x) [/tex]

[tex] log_{m}( \sqrt{2} ) + log_{m}(8) + log_{m}( \frac{1}{2} ) [/tex]

[tex] = log_{m}( {2}^{ \frac{1}{2} } ) + log_{m}( {2}^{3} ) + log_{m}( {2}^{ - 1} ) [/tex]

[tex] = \frac{1}{2} log_{m}(2) + 3 log_{m}(2) - log_{m}(2) [/tex]

[tex] = \frac{5}{2} log_{m}(2) [/tex]

please help!! choices for for the first one is $5, $15, $10, $20

Answers

Answer:

5, 240

Step-by-step explanation:

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