C is the centroid of △ABD. find the following:
1. If CD = 12, find FC.
2. If BG= 15, find BC.
3. If AE = 21, find EC.
4. If FA = 6, find BA.
5. If CG = 3.5, find BC.
Answers
Answer:
1. FC = 6
2. BC = 10
3. EC = 7
4. BA = 12
5. BC = 7
Step-by-step explanation:
⭐What is the centroid of a triangle?
the intersection of the medians of a trianglethe medians bisect each side in halfeach median is split in the ratio of 2:1each median has a segment from the vertex to the centroid. that segment is 2/3 the distance from said vertex to the opposite side of said vertexeach median has a segment from the centroid to a side opposite of a vertex. that segment is 1/3 the distance from said vertex to said opposite sideUsing the properties of a centroid, we can determine the lengths the problem is asking us for.
1. If CD = 12, find FC.
each median is split in the ratio of 2:1So if the median we need to look at is FD,
then CD : FC = 2:1
[tex]\frac{CD}{FC} = \frac{2}{1}\\\\\\\\[/tex] . . . . . . . . write the proportion
[tex]\frac{12}{FC} = \frac{2}{1}[/tex] . . . . . . . . . substitute the known values
[tex]12 = 2FC[/tex] . . . . . . cross multiply
[tex]FC = 6[/tex] . . . . . . divide both sides by 2 to isolate FC
∴ FC = 6
2. If BG = 15, find BC
each median has a segment from the vertex to the centroid. that segment is 2/3 the distance from said vertex to the opposite side of said vertexSo if BG = 15, and BC is the distance from a vertex to the centroid, then BC is 2/3 of BG.
[tex]BC = \frac{2}{2}BG[/tex] . . . . . write equation
[tex]BC = \frac{2}{3}(15)[/tex] . . . . . substitute known values
[tex]BC = \frac{30}{3}[/tex] . . . . . . . . multiply numerators
[tex]BC = 10[/tex] . . . . . . . . compute
∴ BC = 10
3. If AE = 21, find EC
each median has a segment from the centroid to a side opposite of a vertex. that segment is 1/3 the distance from said vertex to said opposite sideSo if AE is the full median, and EC is the distance from the centroid to the opposite side of a vertex, then EC is 1/3 of AE.
[tex]EC = \frac{1}{3}AE[/tex] . . . . . . . . write equation
[tex]EC = \frac{1}{3}(21)[/tex] . . . . . . . . substitute known values
[tex]EC = \frac{21}{3}[/tex] . . . . . . . . . . . multiply the numerators
[tex]EC = 7[/tex] . . . . . . . . . . . . compute
∴ EC = 7
4. If FA = 6, find BA
the medians bisect each side in halfIf BA is a side length that is bisected by a median, then FA is 1/2 of BA.
[tex]FA = \frac{1}{2}BA[/tex] . . . . . . . make equation
[tex]FA = \frac{1}{2}(6)[/tex] . . . . . . . . substitute known values
[tex]FA = \frac{6}{2}[/tex] . . . . . . . . . . . multiply the numerators
[tex]FA = 3[/tex] . . . . . . . . . . . compute
∴ FA = 3
5. If CG = 3.5, find BC
each median is split in the ratio of 2:1each median is split in the ratio of 2:1So if the median we need to look at is BG,
then BC : CG = 2:1
[tex]\frac{BC}{CG} = \frac{2}{1}[/tex] . . . . . . . . . . create the proportion
[tex]\frac{BC}{3.5} = \frac{2}{1}[/tex] . . . . . . . . . . substitute the known values
[tex]BC = 2(3.5)\\[/tex] . . . . . . . . cross multiply
[tex]BC = 7[/tex] . . . . . . . . . . . . . compute
∴ BC = 7
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Related Questions
Which is a recursive formula for the sequence 99. 4, 0, –99. 4, –198. 8, where f(1) = 99. 4? f(n 1) = f(n) 99. 4, n ≥ 1 f(n 1) = f(n) – 99. 4, n ≥ 1 f(n 1) = 99. 4f(n), n ≥ 1 f(n 1) = –99. 4f(n), n ≥ 1
Answers
A recursive formula for the sequence is: f(n+1) = f(n)-99.4, n ≥ 1
Consider the given sequence.
99.4, 0, -99.4, -198.8, . . .
We can observe that each next term of the sequence is decreased by -99.4
i.e., f(0) = 99.4
f(1) = f(0) - 99.4
f(1) = 99.4 - 99.4
f(1) = 0
f(2) = f(1) - 99.4
f(2) = 0 - 99.4
f(2) = -99.4
From these calculations we can say that the n-th term would be,
f(n) = f(n - 1) - 99.4
Therefore, recursive formula: f(n+1) = f(n) - 99.4
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Question 1
Find the distance: Speed = 99 km/h,
Time = 40 mins
Answers
Distance = 99 x 40
Distance = 3,960
Answer:
40 minute = 40 : 60 hours
= 4/6 [÷10]
= 2/3 [÷2]
distance = speed × time
distance = 99 kilometers/hours × 2/3 hours
distance = 33 × 2
distance = 66km
The owner of a mall retaurant bought 75 kilogram of rice. Each week, the retaurant ue 4. 5 kilogram of rice. Function r give the remaining amount of rice, in kilogram, a a function of the number of week ince the retaurant owner bought the rice. 1. Complete the table. Clear All
Answers
function f(x) = 75 - 4.5 w.
where w = number of weeks.
this question is related to function and solution is as follows,
The owner of a mall Restaurant bought rice = 75 kg
Each week, the restaurant use rice = 4. 5 kg
so we have to make an equation of function by which we can find out the remaining rice after w number of weeks,
f(x) = 75 - 4.5 w
where ,w = number of weeks
example, find out rice after 6 weeks
number of weeks (w) = 6
put it in the function,
f(x) = 75 - 4.5(6)
f(x) = 75 - 27
f(x) = 48.
so the function is ,f(x) = 75 - 4.5 w.
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Is 5'2 a solution to a system of equations?
Answers
Yes, the lines intersect at the point (5, -2) so it is the solution to the system.
Now, According to the question:
Let's know:
Solution to a System of Linear Equations:-
A system of linear equations consists of the equations of two lines. The solution to a system of linear equations is the point which lies on both lines. In other words, the solution is the point where the two lines intersect. To verify whether a point is a solution to a system or not, we will either determine whether it is the point of intersection of two lines on a graph or we will determine whether or not the point lies on both lines algebraically.
Let's determine whether the given points are a solution to the systems of equations below.
Is the point (5, -2) the solution of the system of linear equations shown in the graph below?
Yes, the lines intersect at the point (5, -2) so it is the solution to the system.
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convert 20% profit into profit amount
Answers
Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.
Let's say,
You have revenue of $1000
So,
20/100 * 1000 = $200
So the 20% profit on the revenue of $1000 is $200.
It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.
Step-by-step explanation:
The Burj Khalifa building in Dubai, United Arab Emirates, is one of the tallest buildings in the world at 2,722 feet tall. An American football field is 360 feet in length. Approximately how many football fields tall is the Buri Khalifa building? Round to the nearest tenth.
Answers
Answer:
7.5 which rounds to 8
Step-by-step explanation:
2,722 divided by 360 equals 7.56
check if needed <3
Dodie wants to plant roses in her triangular plot. There will be 11 plant at a corner. Starting from that corner, each row will have 55 more plants than the row before it. She has 160160 rose plants and wants the plot to have as many rows as possible. How many rows will Dodie's plot have
Answers
Solving provided question, we can say that by arithmetic progression number of rows Dodie's plot has, n ≈ 7.3965
what is arithmetic progression?The difference between succeeding terms in a sequence is always the same, and this is known as an arithmetic progression. An arithmetic progression with a tolerance of 2 is, for instance, the sequence 5, 7, 9, 11, 13, and 15. The term "arithmetic progression" (A.P.) refers to a progression with a fixed tolerance between any two consecutive values. Mathematic progression can be of two different types: arithmetic series with finite length A series with a finite amount of terms is a finite geometric progression. The terms in the series can be used to determine the early, late, tolerance, and number of terms.
d = 6 is the difference between subsequent rows.
The value increased to a = 1 at the top vertex.
Consequently, the garden's roses represent a mathematical progression.
A = 1 is the first phrase.
d = 6 is the common difference.
The sum of the n terms in an arithmetic progression,, is what determines how many rows Bill's plot will contain.
When Sₙ = 150, we get;
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
number of rows Dodie's plot has, n = 7.3965
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Someone help plz make sure it’s right plz will mark brainiest
Answers
Answer:
Your answer is B, or the second one from the left
Answer: It would be the 2nd choice
A group of friends wants to go to the amusement park. They have no more than $90 to spend on parking and admission. Parking is $16.50, and tickets cost $10.50 per person, including tax. Use the drop-down menu below to write an inequality representing pp, the number of people who can go to the amusement park.
Answers
The inequality representing p, the number of people who can go to the amusement park, is given as follows:
10.5p + 16.5 ≤ 90.
How to build the inequality?The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:
C(p) = mp + b.
In which the parameters are given as follows:
m is the slope, representing the cost of the ticket per person.b is the intercept, representing the cost of parking.Parking is $16.50, and tickets cost $10.50 per person, hence the numeric values of the slope and the intercept are given as follows:
m = 10.50, b = 16.50.
Thus the cost function is given as follows:
C(p) = 10.5p + 16.5.
They have no more than $90 to spend on parking and admission, hence the inequality is defined as follows:
C(p) ≤ 90.
10.5p + 16.5 ≤ 90.
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Find the missing length. Round to the nearest tenth.
HELP PLEASE!!
Answers
Use the Pythagorean theorem
3^2 + 7^2 = c^2
9 + 49 = 58
square root of 58 =
7.615
Will give brainliest if right
O C. 65
O D. 50
Answers
Answer:
D
Step-by-step explanation:
istg if one of yall roasts my dirty calculator
6x + 2y = 25.92 4x + 3y = 33.93 Solve for x and y
Answers
Answer:
y = -3x + 12.96
y = [tex]\frac{-4}{3}[/tex] x + 11.31
Step-by-step explanation:
6x + 2y = 25.92 Subtract 6x from both sides
2y = -6x + 25.92 Divide all the way through by 2
y = -3x + 12.96
4x + 3y = 33.93 Subtract 4x from both sides
3y = -4x + 33.93 Divide all the way through by 3
y = [tex]\frac{-4}{3}[/tex] x + 11.31
Mr.martland decides the length of his square vegetable garden will be 17 ft. He calculates that the area of the garden is 34 ft^2. is he correct?
Answers
Answer:
Nope
Step-by-step explanation:
If it is a square garden, all sides are equal. Area would be 17x17 and that would equal [tex]289^{2} ft[/tex] not 34
Solve for x. Leave your answer in simplest radical form.
15 in
X
Answers
Answer:
√124
Step-by-step explanation:
a^2+b^2=c^2
x^2+101= 225
x^2= 225-101
x^2= √124
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Answers
Compare the two linear functions listen below
Answers
The slopes of function 1 and function 2 are respectively; -4 and 2. Thus, function 1 has a negative slope
How to find the slope of a linear function?The slope is simply defined as the change in the y-values divided by corresponding change in x-values.
1) Now, the formula for the slope between two coordinates is;
Slope = (y₂ - y₁)/(x₂ - x₁)
Let us take two coordinates from the table as;
(0, 50) and (1, 46). Thus;
Slope = (46 - 50)/(1 - 0)
Slope = -4
2) The general equation for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are given the equation as;
c = 2d + 10
Comparing to the standard form, we have;
Slope = 2
Thus, function 1 has a negative slope
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Find the measure of the indicated angle. Need help please.
I need explanation too
PLEASE NO LINKS I WILL REPORT YOU
Answers
Answer:
AC=35
Step-by-step explanation:
Sin=opposite/hypotenuse
Sin54=AC/43
AC=43sin54
AC=34.78≈35
Make a tree diagram to show sample space. Then select the total number of outcomes.
choosing black, blue or brown socks with boots, gym shoes or dress shoes
a. 3
C. 9
b. 6.
d. 12
PLEASE HELP
Answers
Answer:
C. 9
Step-by-step explanation:
3 sock options, 3 shoe options for each of those sock options.
3 x 3 = 9
Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h(t) at time t seconds after launch is h(t) = -16t2 + 80t. a. Find the vertex. Explain what this means in the context of the situation
Answers
Answer:
Vertex (-2.5,-300)
Step-by-step explanation:
We are given with h(t)=-16 t^2 +80 t. We are asked to find the vertex.
X-coordinate of vertex =[tex]\frac{-b}{2a}[/tex]
Where 'a' is coefficient of [tex]t^{2}[/tex] term
'b' is coefficient of 't' term.
From given function, a= -16
b=80
So,
x-coordinate of vertex =[tex]\frac{-80}{2(-16)}[/tex]
=-2.5
y-coordinate of vertex =[tex]-16(-2.5)^{2} +80(-2.5)[/tex]
Simplify it,
=-100 -200
= -300
So, vertex is at (-2.5, -300).
3x + 2y = 5
x = 2y + 7
Answers
Answer:
I hope this helps you...
please mark me as brainliest..
david mowed 2/3 of the yard in 1/2 hour how long will it take him to mow the whole yard?
Answers
Answer:
Step-by-step explanation: It would take him 15 minutes more to mow the whole yard
1/2 hour is 30 mins divided by 2 which is 15 mines times 3 is 45 mins total mins
What are the roots of the equation x² - 10x +34 = 0 in simplest
a + bi form?
Answers
x = (10 +/- sqrt(10^2 - 4134)) / (2*1)
This simplifies to:
x = (10 +/- sqrt(100 - 136)) / 2
The square root of a negative number is equal to a complex number in the form a + bi, where a and b are real numbers and i is the square root of -1. Therefore, the roots of the equation x^2 - 10x + 34 = 0 are:
x = (-10 + sqrt(-36)) / 2 = (-5 + 3i) / 2 = -2.5 + 1.5i
x = (-10 - sqrt(-36)) / 2 = (-5 - 3i) / 2 = -2.5 - 1.5i
In simplest a + bi form, the roots of the equation are -2.5 + 1.5i and -2.5 - 1.5i.
Order of operation help I have 4 min left on my timer . NO LINKS
Answers
Answer:
13
Step-by-step explanation:
Just In case you want explanation-
1. 4 squared Meaning 4 x 4 = 16
2. 16 x 6 = 96
3x 6 = 18
96- 18 = 78
in the denominator, 25/ 5 = 5
11 minus 5 = 6
78 divided by 6
it gives you 13
Answer:
13
Step-by-step explanation:
Order of operations:
Parenthesis, exponents, multiplication and division, addition and subtraction
Math
On a grid, a middle school is located at ( − 5 , 3 ) , and a library is located at ( 2 , 3 ) . If 1 unit represents 1 mile on the grid, how far is the library from the middle school?
Answers
Answer:
14 miles
Step-by-step explanation:
there are 14 units in between point (-5,3) and (2,3), and since each unit is 1 mile it would be 14 miles.
Carmen uses 2/7 of a bag of flour to make 1/2 of a batch of her special homemade cookies. How many bags of flour does it take to make 3 batches of the cookies?
Answers
Answer:
12/7 or 1 5/7
Step-by-step explanation:
2/7=1/2, so 4/7=1. multiply 4 by three, since one times three equals three.
Order these numbers from least to greatest.
6.1031, 6.203, 6.1, 6.23
Answers
Answer:
6.2300, 6.2030, 6.1031, 6.1000
Step-by-step explanation:
Answer:
6.1, 6.1031, 6.203, 6.23
PLEASE HELP 10 POINTS
Answers
Answer:
9.75
Step-by-step explanation:
3/4 |1/3x+2| < 6
you can turn the < into a =
then subtract 3/4 from 6 which leaves you with 5.25. And since you know 2 will always be positive because it's in an absolute value bracket 5.25-2=3.25. Which leaves you with
|1/3x| = 3.25
then do 3.25/(1/3) which leaves you with 9.75
:)
A car is traveling at a speed of 61 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will the car travel in 20 minutes? Do not round your answers.
Answers
The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
A car is traveling at a speed of 61 kilometers per hour.
Convert the speed into a kilometer per minute. Then we have
Speed = 61 / 60
Speed = 1.01667 kilometers per minute
Then the number of kilometers will the car travel in 20 minutes will be given as,
1.01667 = d / 20
d = 1.01667 x 20
d = 20.33 kilometers
The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.
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please help:
find BP
Answers
Answer:
so i will be honest I've done this before and it may be 64 or 120
Step-by-step explanation:
It may be one of these answers I'm doing as much as I can to help
help ill give brainiest <3 dont guess
Answers
Answer:
rectangular prism, 6 faces, 8 vertices
Answer:
The figure is a rectangular prism with 6 faces, moreover, it has 8 vertices.