Given Triangle ABC with FC=5, you want to find BF. First, find the value that y must have for the Triangle Proportionality Theorem to apply. Then describe more than one way to find BF, and find BF. The y value for the Triangle Proportionality Theorem to apply is ______. To find BF, you can use the ______ Formula with the coordinates of B and F l, or you use the Trianglr Proportionality Theorem. BF=
Answers
Answer:
Part A
y = 8
Part B
We can find BF by either;
a) Through Pythagoras theorem to find the length of a side in a right triangle
b) The known rate of change of the length of the line FC with height
Step-by-step explanation:
Part A
The given parameters are;
FC = 5
We are to find BF
By the triangle proportionality theorem, we have;
FC:BF = EC:AE
From the given draining we have;
C(10, 2), F(7, 6), B(5.5, y), E(4, 2), A(1, 2)
Points A, E and C are have the same y-coordinate values, therefore, we have;
EC = 10 - 4 = 6
AE = 4 - 1 = 3
Therefore, we have;
5/BF = 6/3 = 2
BF = 5/2 = 2.5
Using the formula for finding the distance between two points, we have;
BF = √((5.5 - 7)² + (y - 6)²)
BF² = 2.5² = (5.5 - 7)² + (y - 6)²
6.25 = 2.25 + (y - 6)²
6.25 - 2.25 = 4 = (y - 6)²
√4 = √(y - 6)² = (y - 6)
±2 = y - 6
y = 6 + 2 = 8, or y = 6 - 2 = 4
Given that from the diagram, y > 6, we have y = 8
Part B
a) To find BF we can use the Pythagoras's theorem given that we know the coordinates of B and F as follows;
BF = √((5.5 - 7)² + (8 - 6)²) = 2.5
b) Given that BF is on the same straight line as FC, BF can be found through the rate of change of the y-values with the length of the line
We can also find BF by using proportion of increase in 'Δy' to the length of the line BFC as follows;
From point C to point F, Δy = 6 - 2 = 4 and the length of the line FC = 5
Therefore, from point B to point F, Δy = 8 - 6 = 2, ∴ BF = 2 × 5/4 = 2.5
Related Questions
Find the simple interes charged on a loan of $26,500 for 8 months at an interest rate of 7%. Show ALL your work or explain
Answers
Answer:
$1236.67
Step-by-step explanation:
I = Prt
P = 26500
r = 0.07
t = 8/12 = 2/3
I = (26500)(0.07)(2/3)
I = 1236.67
Hi can you please help me with my work
Answers
I think it is 1/8 I'm not sure.
Answer:
2 1/4
Step-by-step explanation:
The graph models the value of a vehicle over x years following its purchase for $25,000.
Which interpretation is correct?
(A) The asymptote indicates that the original value of the vehicle approached $25,000
(B) The point (40, 0) contains the x-intercept
(C) The line x=25,000 is an asymptote of the graph
(D)The line y=0 is an asymptote of the graph
Answers
Answer: it’s D. I took the test
The correct interpretation are,
The asymptote indicates that the original value of the vehicle approached $25,000
The line y=0 is an asymptote of the graph
Graph of function:From the given graph,
It is observed that graph is never intersect the x- axis. Therefore, x-axis will be the asymptote.
The equation of x- axis is y= 0.
Since at x= 0, the value of y = 25,000 , It means that the original value of the vehicle approached $25,000.
The x- intercept is the point where graph crosses the x-axis.
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Max's Moving Company charges a $75 loading fee to move your boxes. They also charge $2 per mile that they have to drive the van to move you boxes from one place to another.
Answers
Answer:
y=75+2x
Step-by-step explanation:
Given data
Loading fee=$75
Charge per mile= $2
Let the distance be x
and the total charge be y
Hence the expression for the total charge is
y=75+2x
what is the y-intercept of the equation 6x-3y=36
Answers
Answer:
(0, -12)
Step-by-step explanation:
Using the slope-intercept form, the y-intercept is 12.
plz help me with this question
Answers
Answer:
I think the answer is 8
Step-by-step explanation:
first you do 6 times 6
then you do 36-20
next do 32 divided by 4 and then you subtract that all
[tex] \sqrt{40} [/tex]
Answers
Answer:
√40 = 2√10=6.32455532034
Answer:
2✓10
Step-by-step explanation:
Assuming you'd like to simplify:
✓4✓10
2✓10
please help i suck at math and I am in class
Answers
Answer:84.84m^2
Edit: I redid it doing the base separate and got 84.847 because Pythagorean theorem tells you the sides of the three triangles are 6.998 which is ever so slightly smaller than the base triangle.
Step-by-step explanation:
This is assuming the triangles are equal. 1/2bh gives you 21.21 for the triangle with the given height and then multiplying that by four for all the sides gives you 84.84m^2. The question doesn’t specify what type of pyramid it is so again I’m assuming it’s equal. Not 100% positive hope it can help at all.
PLEASE HELP ME
Write an equation of a line in slope-intercept form given the slope (m) and the y-intercept (b).
4
Slope, m =-
7
y-intercept, b =7
Answers
Answer:
I believe this should be your answer Y=-7x+7
ill give brainlist who ever get this right
Answers
Answer:
The answer is 1086 in³
Step-by-step explanation:
i need help pls..........
Answers
Answer:
a 14.3
Step-by-step explanation:
23 divided by 4 is 14.3
The dimensions of a right rectangular prism are shown below.
1 in.
in
How many cubes with side lengths of 3 inch are needed to fill the prism without gaps or overlaps?
I will mark brainliest.
Answers
The number of cubes will be 546.
What is the volume?The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.
The volume of the cuboid is,
Volume = (2¹/₆ x 1¹/₆ x 1 )
Volume = ( 13 / 6 ) x ( 7 / 6)
Volume = 91 / 36
The volume of a small cube is:-
Volume = (1/6) x (1/6)
Volume = 1/216
The number of cubes is,
Number = (91/36) ÷ (1/216)
Number = (91 x 216) / 36
Number = 546
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Solve each equation with the quadratic formula.
3p² =-3
Answers
Step-by-step explanation:
3p²=-3
or, 3p²+3=0
a= 3, b=0 and c= 3
x= (-b + √(b²-4ac))/2a
b²-4ac is a negative number.
So, can't be solved.
There are 23 oranges and 16 apples in a basket. Find the ratio of the number of apples to the number of oranges
Answers
Answer:
16:23
Step-by-step explanation:
It's really simple
Plz help
In the diagram, ABC is a straight line.
Work out the size of the angle marked x.
(4 marks)
Answers
Answer:
Why is the picture dark ?
Find the mean and the standard deviation of the data set {2, 3, 6, 7, 6}.
Answers
This is a similar triangle please find the missing length. (?)
Answers
Answer:
33
Step-by-step explanation:
In ΔPQR,
length of side=
77= 7×11
84= 12
Similarly, In ΔFGH
length=
36=3×12
so, the other side= 3×11= 33
Answer:
33
Step-by-step explanation:
[tex]\frac{HG}{FG} =\frac{RQ}{PQ}[/tex], insert given values
[tex]\frac{?}{36}=\frac{77}{84}[/tex], cross multiply
84*?=36*77
84*?=2772, divide both sides by 84 to get ? by itself
?=33
The hypotenuse of a right triangle measures 25. Which could be the lengths of the legs?
A. 3 and 4
B. 5 and 5
C. 7 and 24
D. 10 and 15 ( No links)
Answers
The measure of lengths of the legs are 7 and 24. Therefore, option C is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, the hypotenuse of a right triangle measures 25.
A) 3²+4²= Square of the hypotenuse
25=Square of the hypotenuse
Hypotenuse=5 units
B) 5²+5²= Square of the hypotenuse
50=Square of the hypotenuse
Hypotenuse=5√2 units
C) 7²+24²= Square of the hypotenuse
625=Square of the hypotenuse
Hypotenuse=25 units
D) 10²+15²= Square of the hypotenuse
325=Square of the hypotenuse
Hypotenuse=√325 units
Therefore, option C is the correct answer.
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guys i need help please
i'll give you brainliest if you can help me
this is quadratics
Answers
Please help with this math problem
3x + 6 ≥ 24
Answers
Answer: 1X52=73
Step-by-step explanation:
pls help 30 pts.... answer correctly pls
Answers
Joe runs an M&M's factory and is reviewing the bagging machines. They drop M&M's into bags on a conveyor belt, with 39 M&M's going into each bag. Write an equation for the number of bags 'B' that can be filled from a supply of M&M's 'T'. Write your equation in the form of B=_____________.
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The equation for the number of bags 'B' that can be filled from a supply of M&M's 'T' will be T / 39.
How to explain the equationThe formula to determine how many bags 'B' can be filled with M&M's from a stockpile of 'T', where each bag contains 39 candies, is:
B = T/39
This computation takes the sum of all M&M's in 'T' and divides it by the quantity of candies present in each sack (39), producing the amount of bags 'B' that can be filled.
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A bag contains 5 white marbles and 30 blue marbles. If a representative sample contains 2 white marbles, then how many blue marbles would you expect it to contain? Explain. Because the ratio of white marbles to blue marbles is ▼ 6:5 6:1 5:6 1:6 in the population, the expected number of blue marbles is nothing times the number of white marbles in the representative sample. There should be nothing blue marbles.
Answers
Answer:
6:1
Step-by-step explanation:
Answer: 10
Step-by-step explanation:
The expected number of blue marbles in the representative sample is 10. This is because the ratio of white marbles to blue marbles in the population is 5:6, so for every 5 white marbles there are 6 blue marbles. Since the representative sample contains 2 white marbles, the expected number of blue marbles should be 6 times the number of white marbles, or 6 x 2 = 10.
Please help i need it for class thanks
Answers
Answer:
1.a is 3, b is 9, and c is 12
Step-by-step explanation:
Rafael is cutting pieces of wood to make a triangular pyramid like the one shown below. The base of the pyramid is an equilateral triangle, and the faces are isosceles triangles.
Answers
Answer:
[tex]Total = 32.4in^2[/tex]
Step-by-step explanation:
Given
See attachment for triangle
Required
The surface area of the pyramid
To do this, we calculate the surface area of each of the pyramid faces.
For the equilateral triangle.
[tex]Base = 4.5in[/tex]
[tex]Height = 3.9in[/tex]
The area is:
[tex]A_1 = 0.5 * Base * Height[/tex]
[tex]A_1 = 0.5 * 4.5in * 3.9in[/tex]
[tex]A_1 = 8.775in^2[/tex]
There are 3 isosceles triangles of equal dimension.
[tex]Base = 4.5in[/tex]
[tex]Height = 3.5in[/tex]
The area of one of them is:
[tex]A_2 = 0.5 * 4.5in * 3.5in[/tex]
[tex]A_2 = 7.875in^2[/tex]
For the 3, the surface area is:
[tex]3A_2 = 7.875in^2 * 3[/tex]
[tex]3A_2 = 23.625in^2\\[/tex]
The total surface area is:
[tex]Total = 8.775in^2 + 23.625in^2[/tex]
[tex]Total = 32.4in^2[/tex]
Janelle makes a profit of 10% when she sells a bag for $900
i. What is the cost price? ii. find out how much she should have sold it for to make a profit of 15%
Answers
Answer:
i. 818.18
ii. 940.9
Step-by-step explanation:
SP = 900
or, CP + 10% of CP = 900
or, CP + 10/100 × CP = 900
or, 110CP = 90000
or, CP = 90000/110
CP = 818.18
for profit= 15%
SP = 9000/11 + 15% of 9000/11
= 940.9
Pls help..what’s the answer to this question
Answers
Answer:
x = 25
Step-by-step explanation:
53 = 2x + 3
x = (53 - 3)/ 2
x = 25
WILL GIVE BRAINLIEST FOR ANSWER In a 4-by-6-foot Colorado state flag, the gold-colored disk has a 1-foot radius.
How much gold fabric do you need to create the flag?
What percent of the flag is gold?
Answers
Answer:
13%
Step-by-step explanation:
the area of the flag is 4x6=24 the circle has an area of 3.14. 3.14/24 is 13%
The percent of the flag is gold should be considered as the 13%.
Calculation of the percentage:Since
In a 4-by-6-foot Colorado state flag, the gold-colored disk has a 1-foot radius.
So here the area of the flag should be
= (4) (6)
= 24
Now the percentage be like
= 3.14/24
= 13%
hence, The percent of the flag is gold should be considered as the 13%.
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There was a berry-picking contest at the earth day celebration this year. The line plot below shows the number of pints of berries collected by the people participating in the contest.
A. What is the median of the data displaced on the line plot?
B. How many people participated in the contest?
Answers
The work for median is you order the data: 2222113 in Lowest to highest;
1 1 2 2 2 2 3 then find the middle number
The median of the data is 2 and total number of people participated is 13.
The earth day celebration this year. The line plot below shows the number of points of berries collected by the people participating in the contest.
median is the median is the middle value in the set.
number of frequencies are 2,2,1,2,3,1,2
arrange the frequencies in ascending order - 1,1,2,2,2,2,3
median = (n+1/2)th term
= 7+1/2
= 8/2=4th term is the median
median = 2
number of people participated is 13.
Thus,The median of the data is 2 and total number of people participated is 13.
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Do the following set of points represent a function?Explain your answer (2,3),(3,8),(-1,4),(1,8)
Answers
Answer:
Yes.
Step-by-step explanation:
Yes.
To have a function, you cannot use the same value for an x-coordinate more than once. Here, each value of an x-coordinate is used only once, so it is a function.
Answer:
Yes.
Step-by-step explanation:
It is a many-to-one function. Both 3 and 1 map to 8.
2 maps to to 3 and -1 maps to 4 which is one-to-one.
There are no one to many mappings so it is a function.