triangles abc, dbe, and fbg are all symmetric about the y-axis. what are the coordinates of the centroid?
please help
Answers
Answer:
The coordinates of the centroid are (0, 5)
Step-by-step explanation:
The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are ([tex]\frac{x1+x2+x3}{3}[/tex] , [tex]\frac{y1+y2+y3}{3}[/tex])
In Δ ABC
∵ A = (-20, 0), B = (0, 15), C = (20, 0)
∴ x1 = -20, x2 = 0, x3 = 20
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ([tex]\frac{-20+0+20}{3}[/tex] , [tex]\frac{0+15+0}{3}[/tex]) = ([tex]\frac{0}{3}[/tex] , [tex]\frac{15}{3}[/tex]) = (0, 5)
∴ The coordinates of the centroid of Δ ABC are (0, 5)
In Δ DBE
∵ D = (-15, 0), B = (0, 15), E = (15, 0)
∴ x1 = -15, x2 = 0, x3 = 15
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ([tex]\frac{-15+0+15}{3}[/tex] , [tex]\frac{0+15+0}{3}[/tex]) = ([tex]\frac{0}{3}[/tex] , [tex]\frac{15}{3}[/tex]) = (0, 5)
∴ The coordinates of the centroid of Δ DBE are (0, 5)
In Δ FBG
∵ F = (-5, 0), B = (0, 15), G = (5, 0)
∴ x1 = -5, x2 = 0, x3 = 5
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ([tex]\frac{-5+0+5}{3}[/tex] , [tex]\frac{0+15+0}{3}[/tex]) = ([tex]\frac{0}{3}[/tex] , [tex]\frac{15}{3}[/tex]) = (0, 5)
∴ The coordinates of the centroid of Δ FBG are (0, 5)
∵ The three triangles are symmetric about the y-axis
→ That means they have the same centroid and it lies on the y-axis
∴ The coordinates of the centroid are (0, 5)
Related Questions
Question in picture please use the picture and write it down
Answers
Answer:
Radius is 2.
2πr= 4π
r=4π/2π
r=2
A cookie recipe that yields 48 cookies calls for 2 cups of flour. How much flour would be needed for a cookie recipe that yields 144 cookies? help asap!!!!! :(
Answers
Answer: 6 cups
Step-by-step explanation:
You need to find a unit rate...
48/2= 1 cup for 24 cookies (unit rate)
144/24=6 so you need to multiply 1 and 24 each by 6
1*6=6
24*6
to get...
6 cups for 144 cookies
Determine the x- and y- intercepts for the graph equation y = -8
a. x-intercept is (0, -8) No y-intercept
b. No x-intercept y-intercept is (0, -8)
c. x-intercept is ( x8, 0) NO y-intercept
d. NO x-intercept is ( -8,0)
Please select the best answer from the choices prov
Answers
Answer:
b. No x-intercept y-intercept is (0, -8)
Answer:b
Step-by-step explanation:
Find the distance between the points (-3,- 2.2) and (-3,2.6).
Plz explain I want to see if I got it right.
Answers
Answer:
d = 4.8 units
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
d = [tex]\sqrt{(x_{2} -x_{1} )^2 + (y_{2} -y_{1} )^2}[/tex]
~~~~~~~~~~~
( - 3, 2.6 )
( - 3, - 2.2 )
d = [tex]\sqrt{(-3+3)^2 +(-2.2-2.6)^2 }[/tex] = √(- 4.8)² = 4.8 units
What is 2 divided by 3/4
Answers
Answer:
1/2
Step-by-step explanation:
2 / (3/4) = 1/2 * 3/4
= 3/6
= 1/2
Answer:2.6 with the 6 repeating
or 2.66666666667
Step-by-step explanation:
i am fast with a calculator.
Evaluate the expression when a=1\4 and b=6. -8ab
Answers
Answer:
-12
Step-by-step explanation:
-8 * ( 1/4) * (6)
= -12
Answer:
-12
Step-by-step explanation:
You must multiply 8 x 1/4 x 6 to get your answer
please awnser use images for question
Answers
Answer:
coordinate points
Step-by-step explanation:
variables: a symbol for a value we don't know yet. ex: x or y
numbers: I hope you know what they are cuz i dunno how to describe it ex: 2
coordinate points: a set of numbers that show position on a graph ex: (2,4)
operations: adding, subtracting, multiplying, dividing
Please help me ASAP it’s times THANK U
Answers
Answer:
Only choices C and D are solutions
Step-by-step explanation:
6x + 3y = -15
y = -2x - 5
6x + 3y = -15
6x + 3(-2x - 5) = -15
6x - 6x - 15 = -15
0 = 0
Since 0 = 0 is a true statement, both equations of this system are the same equation and represent a single line on the coordinate plane.
We need to check each choice in just one equation.
Let's use the second equation.
y = -2x - 5
A.
(2, 7)
7 = -2(2) - 5
7 = -4 - 5
7 = -9 False
Not a solution
B.
(5, 0)
0 = -2(5) - 5
0 = -10 - 5
0 = -15 False
Not a solution
C.
(-3, 1)
1 = -2(-3) - 5
1 = 6 - 5
1 = 1 True
Solution
D.
-13 = -2(4) - 5
-13 = -8 - 5
-13 = -13 True
Solution
Answer: Only choices C and D are solutions
3√7×2√3×2√21
simplify
Answers
Answer:
root 7 × root 7= root 21
Step-by-step explanation:
root21×root21=21 now 12×21 =252
For every pound a company spends on advertising, it spends 43 pence on its website. Express
the amount spent on advertising to its website as a ratio in its simplest form.
Answers
Answer:
43:100
Step-by-step explanation:
this is the simplest form
Answer:
The answer is 100:43
Step-by-step explanation:
Write a formula that estimates the change in the volume Vx of a cube when the edge lengths change from a to ax. Then use the formula to estimate the change in volume when x changes from cm to cm.
Answers
Answer:
a. [tex]dV = 3x^2\ dx[/tex]
b. See Explanation
Step-by-step explanation:
Given
Shape: Cube
Solving (a); Formula that estimates the change in edge length
The volume (V) of a cube is:
[tex]V = x^3[/tex]
Where
[tex]x = edge\ length[/tex]
The change in volume is got by:
[tex]dV = \frac{d}{dx}(x^3)[/tex]
Differentiate [tex]x^3[/tex]
[tex]dV = 3x^2\ dx[/tex]
Where
[tex]dx = x_2 - x_1[/tex] i.e. change in x
Solving (b):
The initial and final edge lengths are not given.
In order to solve this question, I'll assume that x changes from 5cm to 5.01cm
So, we have:
[tex]x = x_1 = 5cm[/tex]
[tex]x_2 = 5.01cm[/tex]
Substitute these values in [tex]dV = 3x^2\ dx[/tex]
[tex]dV = 3 * (5cm)^2 * (5.01cm - 5cm)[/tex]
[tex]dV = 3 * (5cm)^2 * 0.01cm[/tex]
[tex]dV = 3 * 25cm^2 * 0.01cm[/tex]
[tex]dV = 075cm^3[/tex]
Solve the following problems using linear functions.
a. Suppose there’s a linear relationship between your height and your shoe size: s = (1/10)h + 5, where h is measured in inches. If you’re 5 feet, 10 inches tall, what size shoes do you take? (Remember that 1 foot = 12 inches.)
b. Runner A and Runner B are competing in a race. Runner B is given a 10-meter head start and is therefore positioned 10 meters in front of the starting line. The starting gun sounds, and Runner B runs at a constant speed of 2.5 meters per second (m/s). After 10 seconds, how far is Runner B from the starting line?
Answers
Answer: a.) I take a shoe size 12
b.) Runner B is 35 m from starting line
Step-by-step explanation:
a) The variable h (height) is in inches, so, first, transform feet in inches:
1 ft = 12 in
5ft = 5.12 = 60 in
My height is 5ft 10in, then, my height in inches is: h = 60 + 10 = 70
To determine my shoe size:
[tex]s=\frac{1}{10}(70)+5[/tex]
s = 12
For me, who is 5ft 10in tall, my shoe size is 12.
b) Runner B is 10m in front of the starting line, which means runner's initial position is 10. Linear relationship between speed and position is given by:
[tex]x=x_{0}+v.t[/tex]
where
x₀ is initial position
v is speed
t is time
Replacing and solving:
x = 10 + 2.5t
x = 10 + 2.5(10)
x = 35
After 10s, Runner B is 35 meters ahead of the starting line
give two ways to write the expression as a phase for 15-b
Answers
Answer:
((c)) man so simple. bye
Sandra walks 13 miles in 3 hours. At what unit rate does Sandra walk?
Answers
PLEASE HELP ME!!!! PLEASE PLEASE!!! 40 POINTS a rectangular toy box has a length of x + 1 feet a width of 2x - 5 feet if the volume is 90 cubic feet what are the dimensions of the toy box
Answers
Answer:
the dimensions of the toy box:
Step-by-step explanation:
x+1=2x
2x-5
90
like terms;
- crossing over becomes + and vice versa
soo 2x-2x +90-5
2x^2 cancels it self out leaving 90-5
=85.
A plane is flying from city A to city B, which is 70 miles away. After flying 25 miles, the pilot realizes they were 15 ∘ off course .
How far is the plane from city B when the pilot realized the error?
about 74.4 miles
about 21.8 miles
about 46.3 miles
about 84.94 miles
Answers
The graph of the function f(x)=V x+4 is shown below
The domain of the function is
Answers
Answer:
The function domain is:
{x|x ≥ -4}
Hence, option 4 is correct.
Step-by-step explanation:
Given the expression of the function
[tex]f\left(x\right)=\sqrt{x+4}[/tex]
We know that the domain of the function is the set of input values for which the function is real and defined
We know that the value inside the radical expression must be greater than or equal to 0 so that the function remains defined.
so
[tex]x+4\ge \:0[/tex]
subtract 4 from both sides
[tex]x+4-4\ge \:0-4[/tex]
simplify
[tex]x\ge \:-4[/tex]
Therefore, the function domain is:
{x|x ≥ -4}
Hence, option 4 is correct.
4x+20 3x
determine the value of x
Answers
Step-by-step explanation:
[tex]4x + 20 = 3x \\ x = - 20[/tex]
-20 is the right answer.Which table represents a direct variation?
Table A
x
4
6
8
10
y
7
9
11
13
Table B
x
4
6
8
10
y
12
18
24
30
Table C
x
4
6
8
10
y
1
3
5
7
Table D
x
4
6
8
10
y
3
3
3
3
Table A
Table B
Table C
Table D
Answers
Answer:
table c
Step-by-step explanation:
Answer:
The answer is table b
Step-by-step explanation:
Which of the following is the graph of x^2 < 25?
Graph A
Graph B
Graph C
Graph E
Graph D
Graph F
Answers
Answer:
B
Step-by-step explanation:
Graph B represents the values of x when x²<25.
If you take the square root of both sides, you get ±x<5
This means that x is any value in between, but not including, -5 to +5.
Answer:
i think its b
Step-by-step explanation:
PLS HELP
Rita's cat, Pickle, spends 40 percent of his day napping. How many hours does Pickle spend asleep each day?
Answers
he spends 9.6 hours sleeping each day! plz mark me the brainliest!
What did the priests do for the community? a. taught religion c. held mass b. had Indians put on plays d. all of the above Please select the best answer from the choices provided A B C D
Answers
Answer:
I'm pretty sure it's A but I could be wrong
Step-by-step explanation:
Al’s dog breathed 130 times in 5 minutes. At this rate, how many breaths should his dog take in 60 minutes?
Answers
Answer:
1560 breaths
Step-by-step explanation:
130/5=26
26*60
1560 breaths
5-x=3
Work out the value of 3x^2
Answers
Answer:
12
Step-by-step explanation:
[tex]5 - x = 3 \\ \\ 5 - 3 = x \\ \\ 2 = x \\ \\ x = 2 \\ \\ 3 {x}^{2} = 3 {(2)}^{2} = 3 \times 4 = 12[/tex]
x-2y= 1 3x -6y =3 solve this by using the substitution method
Answers
Answer:
im pretty sure its infinite solutions
Step-by-step explanation:
A company sells widgets. The company’s fixed and variable cost are modeled by the function C(x)=0.92x+85000. It’s revenue is modeled by the function R(x)=5.6x.
How many widgets does the company have to sell to break even? Round your answer to the nearest whole number, if needed.
Answers
Answer:
18162 widgets
Step-by-step explanation:
Given
[tex]C(x)=0.92x+85000[/tex]
[tex]R(x)=5.6x.[/tex]
Required
Determine the price at break even point
At breakeven point, the following relationship exists
[tex]Rx = C(x)[/tex]
Substitute values for R(x) and C(x)
[tex]5.6x = 0.92x +85000[/tex]
Collect Like Terms
[tex]5.6x - 0.92x =85000[/tex]
[tex]4.68x =85000[/tex]
Make x the subject
[tex]x = \frac{85000}{4.68}[/tex]
[tex]x = 18162.3931624[/tex]
[tex]x = 18162[/tex] --- Approximated
Which statement about 4 + 2x is true?
Answers
Answer:
What statements, the statements aren't listed in the question?
Step-by-step explanation:
help y'all i need it badly
Answers
Answer:
In other words, the slope of the line tells us the rate of change of y relative to x. If the slope is 2, then y is changing twice as fast as x; if the slope is 1/2, then y is changing half as fast as x, and so on.
Step-by-step explanation:
Hope this helps
I need help ASAP plz help
Answers
Answer:
8:4
7:3
Step-by-step explanation:
p=10-2.5c, find p when c = 3.2
Answers
Answer:
P=2
Step-by-step explanation:
10-2.5(3.2)=P
By order of operations you would multiply 2.5 and 3.2 together giving you 8.
You would then subtract 10-8 giving you 2.
Explanation