Given the vertices of a triangle ABC below, find the midpoint and length of the midsegment. Give your length in simplified radical form.
Answers
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
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
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.
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 = aⁿFormula 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 = 69By using the formula for finding nth term ,
69th term of A.P. = -13 + (69 - 1)×(-20) = -13 + (-1360) = -1373
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
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:
(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.
please help!! choices for for the first one is $5, $15, $10, $20
Answers
Answer:
5, 240
Step-by-step explanation:
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°
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).
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.
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.
PLS HELP
What is the value of x ?
A. 42
B. 43
C. 84
D. 86
Answers
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 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%
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
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]
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
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
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
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
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]
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.
Pls help.
Question above
Answers
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]
Write the equation of the line in fully simplified slope-intercept form.
Answers
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:
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
Please help!!!!!!
BRainliest.
Answers
Answer:
4.974
Step-by-step explanation:
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.
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
Solve.
3x+4y=−15
2x−2y=−3
Answers
equation form: x=-3, y=-3/2
let me know if you need the work!
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 2011Given:
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
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