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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Step-by-step explanation:
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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,
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where ,w = number of weeks
example, find out rice after 6 weeks
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Answers
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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.
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Slope = (y₂ - y₁)/(x₂ - x₁)
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The inequality representing p, the number of people who can go to the amusement park, is given as follows:
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How to build the inequality?The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:
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10.5p + 16.5 ≤ 90.
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Answers
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Answer:
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distance = 99 kilometers/hours × 2/3 hours
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Answers
Answer:
6.2300, 6.2030, 6.1031, 6.1000
Step-by-step explanation:
Answer:
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Answers
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Step-by-step explanation:
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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.
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Consequently, the garden's roses represent a mathematical progression.
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When Sₙ = 150, we get;
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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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,
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Therefore, recursive formula: f(n+1) = f(n) - 99.4
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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
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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
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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:
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Answers
Answer:
rectangular prism, 6 faces, 8 vertices
Answer:
The figure is a rectangular prism with 6 faces, moreover, it has 8 vertices.
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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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
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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...
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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.
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