Answers
Triangle proportionality theorem and the segment addition postulate, indicates that A_F : AT = A_F : 4×A_F, therefore;
A_F : AT = 1 : 4
What is the triangle proportionality theorem statement?The triangle proportionality theorem states that a segment drawn in a triangle, such that it is parallel to one side of the triangle and intersects the other two sides at two distinct points, then the proportion in which the segment divides the other two sides are the same.
The specified details of the triangle ΔABC are;
The location of the point D = AB, the location of the point B = AC
The point of intersection of the angle bisector of angle ∠A and DE = F
The point of intersection of the angle bisector of angle ∠A and BC = Point T
AD = 1, DB = 3, AE = 2, EC = 4
Drawing a line CU parallel to DE from point C to intersect AB at U, according to the triangle proportionality theorem, we get;
AE : EC = 2 : 4 = AD : DU = A_F : FV
AD : DU = 1 : 2
A_F : FV = 1 : 2
Therefore; FV = 2 × A_F
FV : VT = DU : BU = 2 : 1
FV = 2 × VT
2 × VT = 2 × A_F by substitution property, therefore;
FV = 2 × A_F
AT = A_F + FV + VT (segment addition postulate)
Therefore; AT = A_F + 2 × A_F + A_F = 4×A_F
A_F : AT = A_F : 4 × A_F = 1 : 4
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Related Questions
1. the very first step in verifying a statement about a product is represented by the c in claim. what does the letter c stand for?
Answers
Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.
What do the other letters stand for?L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.
A - Attribution: Identifying the source of the assertion and assessing its reliability.
I - Investigation: Research and evidence collecting to support or reject the allegation.
M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.
Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.
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what ratio is equivalent to 2
Answers
Two numbers' multiples are shown by a ratio. The required equivalent ratio will therefore be 2a:a
What are ratio of expressions?A ratio displays the multiples of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
a/b can be termed as a ratio b. In order to determine a ratio that is equivalent to 2, the value at the numerator must be twice that of the denominator.
Let the value at the denominator be "a", hence the numerator will be '2a'. The required equivalent ratio will therefore be 2a:a
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Please the inverse of this function!!
Answers
Answer:
[tex]\frac{5x-3}{4}[/tex]
Step-by-step explanation:
[tex]x=\frac{4y+3}{5} \\ 5x=4y+3\\ 5x-3=4y\\ \frac{5x-3}{4} =y[/tex]
Find the z-score for the value 93, when the mean is 100 and the standard deviation is 3.
Answers
The required z-score of the value 93 when the mean is 100 and the standard deviation is 3 is z = -2.3.
What is the Z -a score?A Z-score is stated as the fractional model of data point to the mean using standard deviations.
here,
z = x - μ / σ
Where,
μ = mean and σ = standard deviation
From the question substitute the value in the given above formula,
z = 93 - 100 / 3
z = -2.3
Thus, the required z-score of the value 93, when the mean is 100 and the standard deviation is 3 is z = -2.3.
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Diana had a coupon for c dollars off of
each box of crackers. Diana bought 2
boxes of crackers for 4.50 – c dollars
each. She also bought 8 cans of soup
for s dollars each. The total amount, in
dollars, she spent on the cans of soup
and boxes of crackers is represented by
the expression below.
2(4.50 – c)+8s
Which expression also represents the
total amount, in dollars, she spent?
A.6.50 – 2c + 8s B. 6.50 – 2c + 10s
C. 9 – c + 8s D. 9–2c + 8s
Answers
Answer:
d. 9 - 2c + 8s
Step-by-step explanation:
we can distribute the two by multiplying it by both 4.50 and -c. our result will be 9 and -2c. simply combine that with the 8s that we already had, and we end up with 9 - 2c + 8s.
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ), y = sec(θ), (1,√2)
Answers
The equation of the tangent to the curve x=tan(θ) and y=sec(θ) at the point (1,√2) can be found by both eliminating the parameter and without eliminating the parameter.
Find an equation of the tangent to the curve?Eliminating the parameter: y = x + √2Without eliminating the parameter: dy/dθ = sec(θ) + tan(θ) × csc(θ); y = sec(θ) + tan(θ) × (x - tan(θ)).Without eliminating the parameter:The equation of the tangent line at (1,√2) is given by y = (sec(θ)cos(θ))x - (sec^2(θ)) + √2, where θ is the parameter.This is derived from the slope of the tangent line, which is equal to the derivative of the function at the given point, or sec(θ)cos(θ).By eliminating the parameter:The equation of the tangent line at (1,√2) is y = x + (1/√2). This equation is derived from the slope of the tangent line, which is equal to the derivative of the function at the given point.Since the derivative of x = tan(θ) and y = sec(θ) is sec(θ)cos(θ), by setting θ = π/4, we get sec(π/4)cos(π/4) = 1/√2. Therefore, the equation of the tangent line is y = x + (1/√2).To learn more about tangent line approximation refer to:
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Each number in the first table represents the points scored by a player on the AOP Academy basketball team. Make a frequency distribution, including relative frequency.
percent of total = frequency/total x 100%
1 5 8 10 11 12
1 6 9 10 12 13
3 7 9 11 12 13
4 8 10 11 12 14
For the relative frequencies below, round to the nearest hundredth. If applicable, include a leading zero.
Score Frequency Relative Frequency
Answers
Answer:
1 2 8.33%
3 1 4.17%
4 1 4.17%
5 1 4.17%
6 1 4.17%
7 1 4.17%
8 2 8.33%
9 2 8.33%
10 3 12.5%
11 3 12.5%
12 4 16.67%
13 2 8.33%
14 1 4.17%
total =24
x race to power 4 minus 8x race to power 2 plus 1 equal to zero (Pls can anybody solve this)
Answers
Answer:
×⁴-8ײ+1
Explanation:
kaya yan ung sagot ksi hnd mo na sya mai-sosolve kasi mag kaiba ung upper right side nya kaya i coppy molng un^_^..hope its help...
The spinner above is used in a game. What is the theoretical probability of the given event with one spin? P(a composite number) a. c. b. d.
Answers
The spinner above is used in a game. the theoretical probability of the given event with one spin is 1/2.
Given that a circular spinner with equal sectors for the numbers 1 through 8 is present.
Therefore, the likelihood of receiving any number from 1 to 8 is equal.
=1/8
Probability that the number is between 2 and 7 is known as the required probability.
The numbers 3,4,5, and 6 fall between 2 and 7.
So, favorable events equal 4,
Events totaling 8 P(a number between 2 and 7)=4/8 =1/2
The result is 1/2.
Theoretically, there is a 0.50 percent chance that the event, which is the number landing in a range between 2 and 7, will occur after one spin.
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what is the answer to 2/3 + 1/3 + 5/3?
Answers
Answer:
8/3
Step-by-step explanation:
Write an equation for the line that passes through (8, 2) and is parallel to the graph of y = 3/4x + 2.
Answers
Answer: do it youself
Step-by-step explanation:
How do you write a ratio table in 7th grade?
Answers
A ratio table is a way to compare two or more related quantities. To write a ratio table in 7th grade, you need to:
1. Identify the two or more related quantities you are comparing.
2. Create a table with two columns. Label the first column with the first quantity and the second column with the second quantity.
3. Put the combined ratio in the first row of the table.
4. Put the ratio for the first quantity in the second row of the table.
5. Put the ratio for the second quantity in the third row of the table.
6. In the fourth row, put the combined ratio of the ratios from the previous rows.
7. Repeat steps 4-6 until you have the desired number of rows.
8. Check to make sure that all of the ratios in the table are equivalent.
Once you have completed these steps, you should have a completed ratio table
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A plane flying at 2000 ft altitude begins a 25 degree angle of depression to land. What
is the distance the plane will travel before it lands?
Answers
The distance the plane will travel before it lands cannot be determined from the information given. You would need to know the speed of the plane and the time it takes to travel in order to calculate the distance.
A system of equations is shown below. y = 3x + 4 y = 7x – 2 What is the solution to the system?
Answers
The solution to the system of equations is x = 3/2 and y = 11/2.
What is the linear equation?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b
We are given two equations:
y = 3x + 4
y = 7x – 2
We can set the two equations equal to each other and solve for x:
3x + 4 = 7x - 2
Subtracting 3x from both sides:
4 = 4x - 2
Adding 2 to both sides:
6 = 4x
Dividing both sides by 4:
x = 3/2
Now we can substitute this value of x back into either of the original equations to find the corresponding value of y. Using the first equation:
y = 3(3/2) + 4 = 9/2 + 4 = 11/2
Therefore, the solution to the system of equations is x = 3/2 and y = 11/2.
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If you work 45 minutes a day for 90 days in row and add an additional 20 hours how many hours do you have?
Answers
Let’s break down the math to arrive at this answer. You said that you worked 45 minutes each day for 90 days. To calculate the total number of hours, we can multiply 45 minutes by 90 days. 45 minutes is 0.75 of an hour, so we can convert the minutes to hours and multiply by 90. 0.75 multiplied by 90 is 67.5 hours.
You also noted that you added an additional 20 hours of work. When we add these two numbers together, we get 67.5 hours plus 20 hours, which equals a total of 87.5 hours.
To get to the answer of how many total hours you have worked, we must round up the 87.5 hours to the nearest whole hour. If we round up 87.5 hours, we get a result of 88 hours. To calculate the final answer, we need to add the 88 hours to our original number of 67.5 hours, which gives us a total of 105 hours.
In conclusion, if you work 45 minutes a day for 90 days in a row and add an additional 20 hours, you will have worked a total of 105 hours.
Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
A number line from -5 to 10.
1. Using only addition, write an expression that represents Rebecca's score after these three turns. (Remember that she starts at an energy level of 4.). (2 points)
2. What is Rebecca's energy level after Turn 1? (2 points)
3. What is Rebecca's energy level after Turn 2? (3 points)
4. What is Rebecca's energy level after Turn 3? Will she earn bonus points after Turn 3? Explain why or why not. (3 points)
Answers
In the video game Rebecca is playing using only addition the expression that represents Rebecca's score after these three turns is
= 4 + (-6) + (8) + (-1)
Rebecca's energy level after Turn 1 = -2
Rebecca's energy level after Turn 2 = 6
Rebecca's energy level after Turn 3 = 7
she will not earn bonusHow to find the expression that represents Rebecca's scoreFollowing the rule of the video game the expression is written in steps below
Rebecca is currently at energy level 4
= 4
Turn 1: 6 trees cut
= 4 + (-6)
= 4 - 6
= -2
Turn 2: 8 trees planted
= 4 + (-6) + (8)
= -2 + 8
= 6
Turn 3: 1 tree cut
= 4 + (-6) + (8) + (-1)
= 6 - 1
= 7
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beth and her friends are watching an ice hockey game, so beth decides to buy 4 cups of hot chocolate to share. she figures she'll spend at least $14 on the hot chocolate in all. let x represent how much beth expects each cup of hot chocolate to cost. which inequality describes the problem?
Answers
The inequality that describes the problem is: x*4 >= $14.
This inequality can be read as: "the cost of 4 cups of hot chocolate (x) multiplied by 4 is greater than or equal to $14."
We know that Beth expects to spend at least $14 on the hot chocolate in total, and she's buying 4 cups, so we can set up the inequality with the number of cups and the minimum amount she wants to spend.
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
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Will give 5 star if correct: eden purchased a home for $156,200. the home appreciates about 4.5% each year. what is the value of the home after 17 years? (5 points)
$275,693.00
$71,406.60
$330,109.46
$166,462.16
Answers
The value of the home after 17 years $275,693.00.
The correct option is (A).
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Eden purchased a home for $156,200.
The appreciates percent = 4.5%
So, the appreciates percentage in 17 year
= 4.5 x 17
= 76.5%
Now, the amount increased of home
= 156200 x 76.5%
= $119,493
So, the value of home after 17 year
= 119493 + 156200
= $ 275, 693
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Fill the tables of values for the equation y=2-x
Answers
Explanation: you have to substitute the x values into the formula y=2-x:
y=2-x
y=2- -3
y=5
y=2-x
y=2-0
y=2
y=2-x
y=2-5
y=3
Hope this helps :)
Nicole measured a line to be 10.9 inches long. If the actual length of the line is 10.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answers
Answer: 6.9%
Step-by-step explanation:
Substituting into the percent error formula,
[tex]\frac{|10.9-10.2|}{10.2} \times 100 \approx 6.9\%[/tex]
PLEASE HELP !!!
Question : what do the MAD’s indicate about the vegetables weights?
The weights of the tomatoes vary _____ (less or more) than the weights of the cucumbers since the MAD for tomatoes is ____ (less or greater) than the MAD for cucumbers.
Answers
The weights of the tomatoes vary less than the weights of the cucumbers since the MAD for tomatoes is less than the MAD for cucumbers.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
It is the average distance between each data point and the mean.
The weights of the tomatoes vary less than the weights of the cucumbers since the MAD for tomatoes is less than the MAD for cucumbers.
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Answer:
less & less
Explanation: Because thats how u do it
what is the probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour?
Answers
The probability that the request is received by the server within the first 5 minutes (300 seconds) after the hour would depend on the rate at which requests are made to the server, as well as any other factors that may affect the timing of requests.
In order to find this probability, you would need additional information such as the average rate of requests per second or minute, and the distribution of request timing.
If the requests are Poisson distributed with a mean rate of λ requests per second, the probability that a request is received within the first 5 minutes (300 seconds) after the hour is
P(X<=300) = 1- e^(-300λ)
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This table shows some of the values of x and y that satisfy the equation y=acos0+b, find the value of y when x = 45
Answers
Answer: [tex]4\sqrt{2}+1[/tex]
Step-by-step explanation:
[tex]x=0 \implies y=a+b \implies a+b=9\\\\x=30 \implies \frac{\sqrt{3}}{2}a+b=1+4\sqrt{3}\\\\\implies \frac{\sqrt{3}}{2}a-a=4\sqrt{3}-8\\\\a=\frac{4\sqrt{3}-8}{\frac{\sqrt{3}}{2}-1}=\frac{8\sqrt{3}-16}{\sqrt{3}-2}=8\\\\\implies b=9-8=1\\\\\therefore y=8\cos x^{\circ}+1\\\\x=45 \implies y=8\left(\frac{\sqrt{2}}{2} \right)+1=4\sqrt{2}+1[/tex]
seniors at a certain high school took a survey regarding future plans. all plan to attend college some time; however, 77% plan to go to college immediately following high school. of those who plan to attend college immediately following high school, 17% plan to major in math. of those who do not plan to attend college immediately following high school, 11% plan to major in math. what is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in math.
Answers
The probability that a randomly chosen senior does not plan to attend college right away and majors in math is 12.5%.
Step 1: Calculate the probability of not attending college immediately after high school:
100% - 77%
= 23%
Step 2: Calculate the probability of majoring in math among those who do not attend college right away: 11%
Step 3: Calculate the probability of not attending college right away and majoring in math:
11% / 23%
= 0.125
The probability of a randomly chosen senior not attending college immediately following high school and majoring in math can be calculated by first determining the probability of not attending college right away. This can be done by subtracting the percentage of seniors who plan to attend college immediately from 100%. This yields 23%. Then, the probability of majoring in math among those who do not attend college right away can be determined by taking the percentage of those who plan to major in math among this group, which is 11%. Lastly, the overall probability of not attending college right away and majoring in math can be calculated by taking the probability of majoring in math among those who do not attend college right away and dividing it by the probability of not attending college right away. This yields 11% / 23%, or 0.125.
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toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat? help
Answers
The number of ways in which exactly one of the toddler triplets to end up with their coat is given as follows:
3.
What is a sample space?A sample space is a set that contains all possible outcomes in the context of an experiment.
The cardinality of the sample space in this problem, considering the Fundamental Counting Theorem, is obtained as follows:
N = 3 x 2 x 1
N = 6.
(the first chosen has 3 possible options, the second has two and the third has one).
The six possible outcomes are given as follows, considering the order Red - Green - Blue:
Red - Green - Blue. (all end with theirs).Red - Blue - Green (one, the red, end with theirs).Green - Red - Blue (one, the blue, end with theirs).Blue - Red - Green (none end with theirs).Green - Blue - Red. (none end with theirs).Blue - Green - Red. (one, the green, end with theirs).Hence there are three outcomes for exactly one of the toddler triplets to end up with their coat.
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F(x) = 2x² +1
g(x) = 3x - 5
f-g
Answers
Answer: The answer is. 2x² - 3x + 6. Step-by-step explanation: f(x) = 2x² + 1. g(x) = 3x - 5. To find f - g(x) subtract g(x) from f(x).
I hope this helps! Have a Wonderful day! <3
A town has three roads that form an obtuse triangle. James wants to set up a refreshment stand so that the shortest distance from his stand to each road is the same for all three roads. Where should he set up the refreshment stand?
A. on the centroid
B. on the circimcenter
C. on the incenter
D. on the median
Answers
James should set up the refreshment stand on the incentre of the obtuse triangle.
The incentre of a triangle is defined as the intersection between the angle bisectors of a triangle. The inradius is the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal.
The inradius is defined as the radius of an inscribed circle in the triangle. Therefore, the required shortest equal distance from his stand to each road so that the stand is at the same distance for all three roads is on the incentre.
Hence, the correct option is C.
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2) Three trucks can carry 240 bags of cement. How many bags of cement can seven trucks carry?
Answers
Answer: 560
Step-by-step explanation:
240 / 3 = 80 x 7 = 560
Digital genius manufactures a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 minutes. the analytics department determined that at a price of $103.00 each, the demand would be 6 thousand pads, and at $53.00 each, the demand would be 16 thousand pads. based on the assumption that a linear relationship exists between price and demand, the price-demand equation is given by where x is the number of thousands of pads in demand. at what price point should they sell the pads to have a demand of 14 thousand pads?
Answers
At $63 price point should they sell the pads to have a demand of 14 thousand pads.
p(x) = -5x + 133
Substitute x with 14,
p(14) = -5(14) + 133
= -70 + 133
= 63.
The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. [1] This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.
The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.
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Which of the following represents 18 = 3 × 6?
A.
18 is 3 times as many as 6
B.
18 is 2 times as many as 9
C.
3 is 6 times as many as 18
D.
6 is 3 times as many as 18
Answers
Answer:
A) 18 is 3 times as many as 6----------------------------
Translate each wording to mathematical expression and compare with the given 18 = 3 × 6.
A) 18 is 3 times as many as 6:
18 = 3 × 6, yes same as givenB) 18 is 2 times as many as 9:
18 = 2 × 9, different from the givenC) 3 is 6 times as many as 18:
3 = 6 × 18, wrongD) 6 is 3 times as many as 18:
6 = 3 × 18, wrong