The diagram shows FGH, its medians, centroid P, and the lengths of some of the subsegments. Apply the Centroid Theorem to find other lengths.
Answers
Answer:
Step-by-step explanation:
We will use two properties to solve this problem,
1). Medians of a triangle bisect the sides of a triangle.
2). Centroid of a triangle divides the medians in the ratio of 2 : 1.
Length of FH = 2 × Length of HX
= 2 × 12
FH = 24
PF : PZ = 2 : 1
[tex]\frac{PF}{PZ}=\frac{2}{1}[/tex]
[tex]\frac{PF}{4}=\frac{2}{1}[/tex]
PF = 8
GX = GP + PX
GP = 9 [Given]
Since, [tex]\frac{GP}{PX}=\frac{2}{1}[/tex]
PX = [tex]\frac{9}{2}[/tex] = 4.5
Therefore, GX = 9 + 4.5
GX = 13.5
The other lengths using the centroid theorem gives us;
FH = 24
PF = 8
GX = 13.5
The centroid of a triangle is defined as the point where the three medians intersect each other.
Now, the centroid theorem states that the centroid is ²/₃ of the distance from each vertex to the midpoint of the opposite side.
Thus, applying the centroid theorem to the given triangle gives;
FH = 2(HX)
We see that HX = 12.
Thus; FH = 2 * 12
FH = 24
Also; PF = 2(PZ)
We see that; PZ = 4
Thus;
PF = 2(4)
PF = 8
Also, GP = 2(PX)
We have GP = 9.
Thus;
9 = 2(PX)
PX = 9/2
PX = 4.5
GX = GP + PX
GX = 9 + 4.5
GX = 13.5
Read more at; https://brainly.com/question/24246680
Related Questions
The relationship between the elapsed time t, in days, since the mass of the sample was initially measured, and its mass, M(t), in grams, is modeled by the following function:
M(t)=900⋅(8/27)^t
Complete the following sentence about the rate of change of the sample. Round your answer to two decimal places.
The sample loses 1/3 of its mass every ___ days.
Answers
Answer:
The sample Loses .33 mass every day
Step-by-step explanation:
PLSSSS I NEED HELP
Evaluate 35a when a=7.
Answers
Answer:
[tex]35x \\ 35 \times 7 = 245[/tex]
Answer:
245
Step-by-step explanation:
All you have to do is replace a with 7.
So, 35a=35*7= 245
PLEASE HELP!!!!!
Solve, showing and explaining all steps in the process. 7(y + 2) – (2y – 5) = 41
Answers
Answer:
Step-by-step explanation:
Remove parentheses.
7(y+2)-2y+5=41
2 Expand.
7y+14-2y+5=41
3 Simplify 7y+14-2y+5 to 5y+19.
5y+19=41
4 Subtract 19 from both sides.
5y=41-19
5 Simplify 41-19 to 22
5y=22
6 Divide both sides by 5.
y= 22/5
Answer:
y=6.4
Step-by-step explanation:
distribute:
7y+14-2y-5=41
then combine like terms:
5y+9=41
subtract 9 from both sides:
5y=32
divide 5 by both sides:
y=6.4
how many times bigger is 6.4*10^9 than 1.3*10^9
Answers
Answer:
at least four times bigger
Don’t get it help me !
Answers
Answer:
a > 12
Step-by-step explanation:
To ride the go karts you need to be OVER 12 years old. We are going to use < and > because you can't be 12 and younger. The hint is OVER because this essentially means that the variable a HAS to be bigger than 12. Thus is why the ineuality is a > 12.
Best of Luck!
PLEASE HELP 10 BRAINLY POINTS
Find SA for this triangular prism: DON'T FORGET TO SHOW ALL WORK
Answers
Answer: 872
10 times 16 = 160
12vtimes 10 = 120
20 times 20 = 400
12 times 16 = 192
*with the area of triangles, you have to divide your number by 2, but there is 2 triangles, so 192, instead of 96*
Step-by-step explanation:
What is the diameter of the inscribe circle of the triangle?
Answers
============================================
Work Shown:
The two angle bisectors intersect to form the incenter. The incenter is the center of the inscribed circle (aka "incircle"). This circle is the largest possible, but is completely inside the triangle. No portions of the circle spill outside the triangle.
The two segments marked with lengths x+8 and 2x-5 are two radii of the incircle. This is because the sides of the triangle are tangent to the incircle.
Since all radii are the same length, we can set those expressions equal to one another and solve for x
x+8 = 2x-5
x-2x = -5-8
-x = -13
x = 13
This x value then leads to
x+8 = 13+8 = 212x-5 = 2*13-5 = 26-5 = 21Both radii are 21 units long, which helps confirm we have the proper x value. We double the length of the radius ot get the diameter.
So the diameter of the incircle is 2*21 = 42 units long.
When the supplies are endless, prices tend to O A. fluctuate O B. stay the same O C. decrease O D. increase
Answers
the answer is c. decrease
Dan buys a car for £1700.
It depreciates at a rate of 4% per year.
How much will it be worth in 4 years?
Answers
Answer:
Step-by-step explanation:
100%-4%=96%
96/100=0.96
£1700*0.96^4=£1443.89
Answer:
1143.89Step-by-step explanation:
I HOPE it's help you
How wide is a pool that has a length of 25/2 feet and area of 225/2 square feet?
Answers
Answer:
16 feet for pool and 12 for square feet
Step-by-step explanation:
Identify the first step when evaluating the expression 11 – 10 ÷ 2 + 6 × 1
Answers
using bedmas, the division comes first
Answer: 6.5
Step-by-step explanation: You first substract 11-10 that would be 1 so, you divide it by 2, that tyhe answer of that is 0.5 so we add 6, the total owuld be 6.5, times 1, it would be the samen cantity because each number multiple by 1 give the same answer.
Convert 0.245 into a percent and choose the appropriate result.
А
24.5%
B
2.45%
245%
D) 0.245%
Answers
Answer:
A. 24.5
Step-by-step explanation:
HOPE THIS HELPS!!!!
Can I have Brainliest???
Answer:
Its A, 24.5%
Step-by-step explanation:
I remember doing this before
Which of the following sentences could not be used to represent the equation x-5=-10?
A number subtracted from five is equal to negative ten.
A number less five equals negative ten
Ave less than a number is negative ten.
fa number is decreased by five, the result is negative ten.
plz help
Answers
Answer:
A number less five equals negative ten
Step-by-step explanation:
sorry if it is wrong
hope it helped
Simplify the expression by removing symbols of grouping and combining like terms.
7(2s − 1) + s + 5
Answers
Answer:
=15s−2
Step-by-step explanation:
sorry if its not correct i tried
Consider an example of an apartment: The number of bedrooms, bathrooms, and the floor of an apartment determines its price. Which is the dependent variable in this example
Answers
Answer: The price of the apartment.
Step-by-step explanation:
We know that for a given apartment, the number of bedrooms, bathrooms, and floor determines the price.
Then we could define the variables:
x = number of bedrooms.
y = number of bathrooms
z = floor.
And define the price of the apartment as a function of these variables:
p(x, y, z) = price
Then the independent variables are x, y, and z.
And the dependent variable (this is, the variable that changes in response to the changes in the independent variables) will be the price of the apartment.
Using function concepts, it is found that the dependent variable in this example is the price.
The standard format of a function is: [tex]y = f(x)[/tex].In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.In this problem, price depends of the number of bedrooms, bathrooms, and the floor of an apartment, hence, the function is:
[tex]p = f(be, ba, fl)[/tex]
Which means that the dependent variable is the price.
You can learn more about dependent and independent variables at https://brainly.com/question/1429012
Marie about six books for total $360 math books cost 80 and science books cost 50 how many science books did she buy
Answers
Answer:
4 books are science
2 are math
:)
what is 2 + 2 - 90 + 40
Answers
Answer:
-46
Step-by-step explanation:
hope this helps ;)
Answer:
Pemdas makes it -46
Step-by-step explanation:
since this is only addition and subtraction it doesn't matter really what order you do it in
2+2=4
-90+40=-50
4+-50=-46
this is thanks to the Commutative property of addition which states that "Changing the order of addends does not change the sum."
Point A, located at (-11, - 7) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C. What are the coordinates of points B and C?
Answers
Answer:
Answer: B(-11,7) C(11,7)
Step-by-step explanation:
Reflections In The Coordinate Plane
Reflect over the x-axis:When we reflect a point over the x-axis, the x-coordinate remains the same, but the y-coordinate is mapped to its opposite.
The reflection of the point (x,y) over the x-axis is the point (x,-y).
Reflect over the y-axis:When reflecting a point over the y-axis, the y-coordinate remains the same, but the x-coordinate is mapped to its opposite (its sign is changed).
The reflection of the point (x,y) across the y-axis is the point (-x,y).
Point A is at (-11,-7). When reflected over the x-axis, it maps to Point B located at B(-11,7).
Point B is now reflected over the y-axis and maps to C(11,7).
Answer: B(-11,7) C(11,7)
What is the lowest form of 32:28?
Answers
Answer:
to lowest terms of 32:28 is 8/7 or 8:7
Step-by-step explanation:
3x + 2y = 5
5x + 2y = 7
Based on the given system of equations, which of the following is not true?
8x=12
4y=4
2x=2
Answers
Answer:
I am guessing the 1st one.
Step-by-step explanation:
8x does NOT equal 12 I believe. I am sorry if I am incorrect
An environmental club is raising money to preserve habitat for local owls. They are keeping track of their progress using the “thermometer” shown. Which is the best estimate of the progress they have made in reaching their goal?
what's the answer
A
30%
B
14
C
12
D
0.95
Answers
Answer:
is there an image?
Step-by-step explanation:
if no then i guess B
The Quality Assurance department at a gear company
found that there were 3 defective gears for every 500
produced. Express this as a percent.
Group of answer choices
Answers
0.6%??
I did 3 divided by 500 and got 0.006 then moved the decimal places to transform the decimal to fraction which ends up being 0.6%
Help!!!!!!!! Pls?????
Answers
Answer:
220 newtons
Step-by-step explanation:
The hole for a support needs to be 6 feet deep. It is currently 2 feet 5 inches deep. How much deeper must the hole be? Use pencil and paper. Show two ways to solve this problem. Use the conversion factor
12 inches
________
1 foot.
The hole needs to be nothing inches deeper.
Answers
Answer:
43 inches deeper and it will be 6 feet deep
Answer:
3feet 7inches
Step-by-step explanation:
2feet + 3feet=5feet 5inches+7inches =1 feet
5feet + 1 feet=6feet
63 is 11% of what number?
Answers
Answer:
572.7272
572.73 (rounded)
Step-by-step explanation:
used calc
just to make sure what is 9 x 2/3
Answers
9 times 2 equals 18 and 18 divided by 3 equals 6
Answer:
6
Step-by-step explanation:
48 oz. for $3.99
36 oz. for $2.59
12 oz. for $1.99
which is the best deal
Answers
Answer:
Step-by-step explanation:
12 oz for 1.99$
Answer:
12 oz. for $1.99
Step-by-step explanation:
16, 3, 3, 14, 10, 8, 11
Find the mean.
If necessary, round your answer to the nearest tenth.
Answers
Step-by-step explanation:
divide all the numbers and the add about ow many number their are
Answer: 9.3
Step-by-step explanation:
Find an equation of the line with the given y-intercept and slope m.
10, m= 5
The equation of the line is
(Type your answer in slope-intercept form.)
Answers
Answer:
y = 5x + 10
Step-by-step explanation:
Use formula: y = mx + b
1. Since m = 5, plug it into where m is
2. 10 has no variable so it's b ( the y-intercept)
the product of 34 and z
Answers
Answer:
its 34z
Step-by-step explanation:
Answer: 34z
Step-by-step explanation:
34 × z = 34z