Find the centroid of the triangle with these vertices: P (-1,7), Q (9,5), and R (4,3).
The coordinates of the centroid are?
Answers
Answer:
The coordinates of the centroid are:
[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]
The diagram is also attached below.
Step-by-step explanation:
Given the vertices
P (-1, 7)Q (9, 5)R (4, 3)We know that the intersection of medians brings the centroid of the triangle.
The centroid of a triangle is given by
[tex]O\:=\:\left(\frac{P_x+Q_x+R_x}{3},\:\frac{P_y+Q_y+R_y}{3}\:\right)[/tex]
In this example,
[tex]P_x=-1,\:P_y=7[/tex]
[tex]Qx=9,\:Q_y=5[/tex]
[tex]Rx=4,\:R_y=3[/tex]
substituting in the formula
[tex]O\:=\:\left(\frac{-1+9+4}{3},\:\frac{7+5+3}{3}\:\right)\:\:[/tex]
[tex]O\:=\:\left(\frac{12}{3},\:\frac{15}{3}\:\right)\:\:[/tex]
[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]
Therefore, the coordinates of the centroid are:
[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]
The diagram is also attached below.
We've been given with the co-ordinates of vertices of the triangle and asked to calculate the co-ordinates of the centroid.
★ Centroid of a triangle :-
[tex]\red{\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} } \: , \: \dfrac{y_1 \: + \: y_2 \: + \: y_3}{3} }} \: \pink\bigstar [/tex]We have :
x₁ = -1x₂ = 9x3 = 4y₁ = 7y₂ = 5y3 = 3Substituting the values :
★ For x co-ordinate:-
[tex]: \: \implies \: \sf{x\: = \: \dfrac{x_{1} \: + \: x_2 \: + \: x_3}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ - 1 \: + \: 9 \: + \: 4}{3}} \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 8 \: + \: 4}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \cancel\dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: 4 }[/tex]
★ For y co-ordinate:-
[tex]: \: \implies \: \sf{y\: = \: \dfrac{y_{1} \: + \: y_2 \: + \: y_3}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 7 + 5 + 3}{3}} \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 10 \: + \: 5}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \cancel\dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: 5 }[/tex]
★ Henceforth,
Co-ordinates are (4 , 5)Additional Information :
★ Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]★ Distance Formula :-
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]★ Visit more :-
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Related Questions
The hemmings borrowed $3 000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay
Answers
Answer:
5%
Step-by-step explanation:
Given that:
Principal = $3000
Simple Interest paid = $600
Period = 4 years
Simple interest = principal * rate * time
$600 = $3000 * rate * 4
$600 = $12000 * rate
Rate = $600 /$12000
Rate = 0.05
Hence, simple interest rate paid = (0.05 * 100%) = 5%
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Answer:
It is 52
Step-by-step explanation:
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What is the slope of this line? please explain because it is confusing if I only got the number of the slope:)
Answers
Answer:
8/3
Step-by-step explanation:
Use rise over run. Find two points that are at perfect points. For example (3,2). Don't use something like (2.45, 7.34), That will make it difficult. I used (0, 4) and (-3, 4). To get from (-3,4) to (0,4), you have to go up 8 and to the right 3. Always count up or down first and then side to side.
In the equation y=2X+7 which
number is the slope?
Slope (m)
Answers
Answer:
2 is the slope
Step-by-step explanation:
the equation is y=mx+b so if it is
y= 2x+7 that means the slope is 2
Answer:
2
Step-by-step explanation:
This equation is in y=mx+b form.
Slope = m
Y-intercept = b
This will give you the slope of 2 :)
I’ll mark you brainlist write in y=mx+b form
Answers
Answer:
y=-1/8x +4
Step-by-step explanation:
1. First, write the equation in point-slope form: y-y1=m(x-x1)
y-1=-1/8(x-24)
2. Distribute -1/8 to x and -24
-1/8 times x = -1/8x
-1/8 times -24 = 3
y-1=-1/8x+3
3. Add 1 to both sides
y=-1/8x +4
What is an equation of the line that passes through the points (4, -2) and (8, – 7)?
Put your answer in fully reduced form.
Answers
Answer:
y= -5x/4 + 3
Step-by-step explanation:
To find slope, use the equation [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], so m(the slope) = (-7+2)/(8-4) = -5/4.
Now let us use (4,-2) in the equation [tex]y-y_1=m(x-x_1)[/tex].
So y - (-2) = (-5/4)(x - 4) (equation of the line)
y + 2 = -5/4(x - 4)
y + 2 = -5x/4 + 5
y= -5x/4 + 3 (slope-intercept form, also known as fully reduced form)
You could also use (8,-7) instead of (4,-2).
Saman drives a truck for $15 an hour. If she worked 40 hours, what would be her gross earnings for one week?
Answers
Answer:
$600
Step-by-step explanation:
because 40 hours at a rate of $15/hours adds up to $600.
(40*15= 600)
This question is worth 100 points please answer now. Algebra 2. I will mark you brainliest.
Show all work to identify the asymptotes and zero of the function f of x equals 4 x over quantity x squared minus 16.
Answers
Answer:
The vertical asymptotes occur at x = 4 and x = -4
The zero of the function is (0, 0)
Step-by-step explanation:
The given function is [tex]f(x) = \dfrac{4\cdot x}{x^2 - 16}[/tex]
Therefore, we have;
[tex]f(x) = \dfrac{4\cdot x}{x^2 - 16} = \dfrac{4\cdot x}{(x - 4) \cdot (x + 4)}[/tex]
The asymptote is given at the value of x for which the denominator = 0, therefore, the asymptote are the values of x that make the denominator of the equation equal to zero, which are given as follows
For the asymptote, the denominator = x² - 16 = (x - 4)·(x + 4) = 0
Therefore, the vertical asymptotes are the lines x = 4 and x = -4.
The zero of the function is given as follows;
[tex]f(x) = \dfrac{4\cdot x}{x^2 - 16} = 0[/tex]
Therefore, 4·x = (x - 4)·(x + 4) × 0 = 0
x = 0/4 = 0
Therefore, when f(x) = 0, x = 0 and the zero of the function = (0, 0).
Which of the following expressions is not equivalent to (-2)(8 + 6 + -3)?
answers:
1. (-2)(8) + (-2)(6) + (-2)(-3)
2. (-2)(8 + 6) + (-2)(-3)
3. (-2)(8) + (-2)(6 + -3)
4. (-2)(8 + 6) + (-3)
Answers
Answer:
4
Step-by-step explanation:
Hope this helps. Pls give brainliest.
(-4,6), (r,10) and m = -2. what is r?
Answers
Answer:
-6
Step-by-step explanation:
The formula of slope Y2-Y1/X2-X1
so you actually use this formula equal to -2
10-6/X-(-4) = -2
what is 15 feet converted to meters
Answers
Answer:
4.572 meters
Step-by-step explanation:
hope it helps, mark brainliest please
Answer:
4.572 meters; 4.6 rounded.
Step-by-step explanation:
Multiply the foot value by 0.3048 or divide by 3.280839895
15x0.3048
=4.572
Simon is selling candy bars for his class fundraiser. In each box of 56 candy bars, 18 are
peanut, and the rest are dark chocolate. Each dark chocolate candy bar costs $2.25.
If Simon raises a total of $117, selling a whole box, how much does each peanut candy bar
cost?
O $4.00
O $4.25
$2.00
$1.75
Nort
Answers
Answer:
it will be 1.75$
Step-by-step explanation:
56-18
38x2.25
117$ - 85.5$
31.5 / 18
b) y = x2 - 10
d) y = x3 - 9
f) y = (x - 2)2
h) y = (2x + 3)
Answers
(1 /a+ 1/b) (a+b-c)+(1/b+1/c) (b+c-a) + (1/c+1/a)(c+a-b)
plz solve this question
Answers
Answer:
(1 /a+ 1/b) (a+b-c)+(1/b+1/c) (b+c-a) + (1/c+1/a)(c+a-b)
plz solve this question
Step-by-step explanation:
3 is the ans
On Monday, Cathy read 1/6 of her book, and on Tuesday, she read 2/6 of the book. How much has she read
Answers
Answer:
1/2 of her book
Step-by-step explanation:
1/6 + 2/6 = 3/6 = 1/2
Answer:
I think that it is 1/2 of her books
Step-by-step explanation:
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sam is 12 in four years his age will be 2/3 the age of his cousin like how old will luke be in two years
Answers
Answer:
he will be 17 in
Step-by-step explanation:
Find the distance between the two points in simplest radical form.
(-3,-2) and (-8,4)
Answer:
Submit Answer
✓
attempt 1 out of 2
Answers
Answer:
y=−2/5x+4/5y
Step-by-step explanation:
Hope's this helps
one factor of 8x^3+1 is 2x+1 The other factor is?
Answers
So that you have 2^3*x^3+1
Multiply the terms with equal exponents by multiply the bases (1 is basically the same as 1^3)
So that it becomes (2x)^3+1^3
Then, using a^3+b^3 equals (a+b)(a^2-2ab+b^2), factor the expression so that it becomes
(2x+1)((2x)^2-2x+1^2)
Expand the second bracket
So the two factors are (2x+1) and (4x^2-2x+1)
The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d
Answers
Answer:Example 1:
Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.
S8=1(1−28)1−2=255
Example 2:
Find S10 of the geometric sequence 24,12,6,⋯.
First, find r.
r=r2r1=1224=12
Now, find the sum:
S10=24(1−(12)10)1−12=306964
Example 3:
Evaluate.
∑n=1103(−2)n−1
(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)
Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023
In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. Then as n increases, rn gets closer and closer to 0. To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.
Example 4:
Find the sum of the infinite geometric sequence
27,18,12,8,⋯.
First find r:
r=a2a1=1827=23
Then find the sum:
S=a11−r
S=271−23=81
Example 5:
Find the sum of the infinite geometric sequence
8,12,18,27,⋯ if it exists.
First find r:
r=a2a1=128=32
Since r=32 is not less than one the series has no sum.
Step-by-step explanation:
Esmeralda received a bag of jellybeans that contained a mixture of regular flavored jellybeans and "surprise" jellybeans. The bag advertised that 15% of the jellybeans were "surprise" flavors. If she counted 40 jellybeans in the bag, how many should she expect to be the "surprise" jellybeans?
Answers
Answer:
6 jellybean
Step-by-step explanation:
Given that:
Esmeralda received a bag of jellybean the contains regular flavored jelly beans and surprise jelly bean.
Consider the regular flavored jellybean to be = r; &
The surprise jelly bean.= s
From the bag, there are 40 jellybeans of which 15% is surprise jellybean.
Therefore the number of expected surprise jellybeans is:
= total number of jellybeans × percentage of surprise jellybean
= 40 × (15 /100)
= 6 jellybean
If 6 surprise jellybean is presented in the bag; then the number of regular flavored jellybean = 40 - 6 = 34 regular flavored jellybean
how can you determine the additive inverse of a number. What is the sum of a number and its additive inverse?
Answers
Answer:
An example can be 14 + (-14) = 0
Whenever you encounter a problem like the one I put, your answer should ALWAYS be 0 because you start with 14. Now take away 14 you end up with 0.
Step-by-step explanation:
Hope this helps!
is 6^p > 0, then p > 0. Is this statement true, sometimes true, or not true?
Answers
Answer:
true
Step-by-step explanation:
What is unit rate of 9 cups and 3 batches
Answers
Answer:
3 cups per batch
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
What is 9 divided by 3.... 3 ok so that is your answer. Hope this helped you!! Give brainliest..
12х - 5 >3х^2 +5
I am confused how to solve this.
Answers
Answer (3 different forms):
1st Form:
[tex]2+-\frac{1}{3} \sqrt{6} <x<2+\frac{1}{3} \sqrt{6}[/tex]
2nd Form:
[tex]-\sqrt\frac{2}{3}+2<x<\sqrt\frac{2}{3}+2[/tex]
3rd Form:
[tex]\frac{6-\sqrt{6}}{3}<x< \frac{6+\sqrt{6}}{3}[/tex]
Or
[tex](\frac{6-\sqrt{6}}{3}),(\frac{6+\sqrt{6}}{3})[/tex]
Step-by-step explanation:
You can see that I put three different forms of answers, but they are all still equivalent answers. The reason why I got three different answers is because I put the inequality in three different calculators and they all got me different answers, but all three are still equivalent. The following three attachments are images of the three calculators that I used to solve.
Hope this helps and answers your question! :)
Using PT in the Coordinate System
llus
Find the distance between the two points.
(-1,3)
(4,2)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
Answers
Answer:
The distance between the two points is [tex]\sqrt{26}[/tex]
Step-by-step explanation:
The formula of the distance between two points (x1, y1) and (x2, y2) is
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
∵ The points are (-1, 3) and (4, 2)
∴ x1 = -1 and x2 = 4
∴ y1 = 3 and y2 = 2
→ Substitute them in the formula of the distance above
∵ d = [tex]\sqrt{(4--1)^{2}+(2-3)^{2}}[/tex]
∴ d = [tex]\sqrt{(4+1)^{2}+(-1)^{2}}[/tex]
∴ d = [tex]\sqrt{(5)^{2}+1}[/tex]
∴ d = [tex]\sqrt{25+1}[/tex]
∴ d = [tex]\sqrt{26}[/tex]
∴ The distance between the two points is [tex]\sqrt{26}[/tex]
Please help I don’t get it
Answers
Answer:
Alternate Interior Angles
Step-by-step explanation:
Angle 3 and angle 6 are inside the parallel lines and are opposite sides of the transversal line so, it'd be alternale interior angles.
I just need a favor please use pemdas and if you can write your work thank you so much
Answers
Answer:
Do you need all 6 of them?
Answer and Step-by-step explanation:
w = -1
x = 6
y = 3
z = -2
32. Plug -2 for z and 6 for x.
(9(-2)) / 6
-18 / 6
3
33.
[tex]6^{2} - 3^{2}[/tex]
36 - 9
27
34.
[tex]3^{2} - (-2)^{2}[/tex]
9 - 4
5
35.
[tex]\frac{2(6)+3}{-2 + -1} \\\\\frac{12+3}{-3}\\\\\frac{15}{3} \\\\5[/tex]
36.
[tex]\frac{3(6)-(-2)}{-(-1)} \\\\\frac{18 + 2)}{1)} \\\\\frac{20}{1} \\\\20[/tex]
37.
[tex]\frac{6 + -1}{3 - (-2)} \\\\\frac{5}{5}\\\\1[/tex]
#teamtrees #WAP (Water And Plant) #SPEW (Society for the Promotion of Elfish Welfare)
mga solusyon sa epektibong komunukasyon sa pamilya
Answers
Answer:
Translation: Solutions to effective family education
Step-by-step explanation:
Find the value of h(-67) for the function below.
h(x) = -49x − 125
A.
-3,408
B.
-1.18
C.
3,283
D.
3,158
Answers
Answer:
D. 3,158
Step-by-step explanation:
h(-67) means to plug the x in h(x)=-49x-125 into the function as -67
The function will then be:
h(-67)=-49(-67)-125
Multiply -49 and -67
h(-67)=3283-125
subtract
h(-67)=3158
so the answer is D
Hope this helps!
In a lab experiment, 100 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 26 hours. How long would it be, to the nearest tenth of an hour, until there are 168 bacteria present?
Answers
9514 1404 393
Answer:
19.5 hours
Step-by-step explanation:
The number in the dish at time t (in hours) can be described by ...
n(t) = 100·2^(t/26)
We want to find t such that ...
n(t) = 168
100·2^(t/26) = 168
2^(t/26) = 1.68 . . . . . . divide by 100
(t/26)log(2) = log(1.68) . . . . . take logarithms
t = 26·log(1.68)/log(2) ≈ 19.459992 . . . . divide by the coefficient of t
t ≈ 19.5 . . . hours
It would be about 19.5 hours until there are 168 bacteria.