Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Help Me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1
i am pretty sure it is A
Answer 2

Answer:

ye you have it correct

Step-by-step explanation:

it shows 2 gs fitting into 20

g=10 btw


Related Questions

WHAT IS THE ANSWER PLS HELPPPPP!!!!!

WHAT IS THE ANSWER PLS HELPPPPP!!!!!

Answers

Answer:

5^x - 5^-x

Step-by-step explanation:

g(x) = 5^-x

h(x) = 5^x

We want h(x) - g(x)

h(x) - g(x) = 5^x - 5^-x

This cannot be simplified

Amy has 364 pieces of candy. She is making gift bags and wants to put 8 pieces of candy in each bag. If Amy makes as many bags as she can, how many pieces of candy will she have left?​

Answers

Answer:

Step-by-step explanation:

If you do the division needed to figure out this answer, you will find out she is able to make 45.5 bags. :)

PLEASE ANSWER ASAP!!

PLEASE ANSWER ASAP!!

Answers

A equation of a cosecant curve that have the asymptotes given is csc(3x) = 1 / sin(3x).

How to find the cosecant curve equation ?

To write an equation of a cosecant curve with asymptotes at x = 0, x = π/3, x = (2π)/3, and x = π, we first notice that the distance between consecutive asymptotes is π/3.

The general equation for a cosecant curve is:

csc(A(x - h)) + k

Because the first asymptote is at x = 0, we don't need any horizontal phase shift (h = 0).

The equation for the sine function is:

sin(3x)

Now, we need to find the reciprocal of the sine function to obtain the cosecant curve:

csc(3x) = 1 / sin(3x)

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assume that the histograms are drawn on the same scale. which of the histograms has the largest interquartile range (iqr)?

Answers

The interquartile range (IQR) is a measure of variability in a data set and is calculated as the difference between the first and third quartiles.

A larger IQR indicates a greater spread of data. Assuming that the histograms are drawn on the same scale, the histogram with the largest IQR would be the one with the widest spread of data. This can be determined by examining the width of the boxes in each histogram. The box represents the IQR, with the bottom of the box being the first quartile and the top of the box being the third quartile. The histogram with the widest box would have the largest IQR. It is important to note that a larger IQR does not necessarily mean that the data is more spread out than other histograms, as it only measures the middle 50% of the data and ignores outliers. Therefore, it is important to consider other measures of variability and the overall shape of the distribution when interpreting histograms.

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Your professor gives a true/false quiz with 10 questions. The minimum score required to pass is 60% correct. You were too busy to study for the quiz, so you just randomly guess on each question. Let X be the number of questions you guess correctly. Theoretically, how many questions should you expect to get correct?

Answers

Theoretically, you should expect to get 5 questions correct by randomly guessing on a 10-question true/false quiz.

Since this is a true/false quiz with 10 questions, if you were to guess randomly on each question, you would have a 50/50 chance of getting each question correct. Therefore, the probability of guessing correctly on any one question is 0.5.

Let X be the number of questions you guess correctly. Since each question is independent of the others, we can use the binomial distribution to calculate the expected value of X.

The formula for the expected value of a binomial distribution is:

E(X) = n * p

where n is the number of trials (in this case, the number of questions) and p is the probability of success on each trial (in this case, the probability of guessing a question correctly, which we calculated to be 0.5).

So, plugging in the numbers:

E(X) = 10 * 0.5 = 5

Therefore, theoretically, you should expect to get 5 questions correct if you randomly guess on each question. However, since the minimum score to pass is 60%, you would need to get at least 6 questions correct to pass.


To answer your question, let's consider the terms "minimum score", "questions", and "true/false". You have a true/false quiz with 10 questions, and you need a minimum score of 60% correct to pass. Since you're randomly guessing, the probability of getting each question correct is 50% or 0.5.

Now, let's calculate the expected number of correct questions, X. To do this, we multiply the probability of getting a question correct (0.5) by the total number of questions (10):

X = 0.5 * 10

X = 5

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Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results.
t-Test for Acue Care Occupancy Rates
MaxHealth HealthPro Mean 62.5462 68.4800 Variance 108.2377 98.3707 Observations 13 10 Hypothesized Diff 0 df 20 t Stat −1.3923 P(T<=t) one-tail 0.0896 t Critical one-tail 1.7247 P(T<=t) two-tail 0.1791 t Critical two-tail 2.0860 Which conclusion is correct in a two-tailed test at α = .05?
Multiple Choice
There appears to be no difference in the mean occupancy rates.
There is a significant difference in the mean occupancy rates.
HealthPro has a significantly higher mean occupancy rate.
Carver Memorial Hospital’s surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test for equal means (assume equal variances), the critical value at α = .10 is
Multiple Choice
2.120
2.754
1.746
1.337

Answers

The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

How to solve

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

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Derek wants to order some roses online. Florist A charges $4.75 per blue
rose plus $40 delivery charge. Florist B charges $5.15 per red rose plus $25
delivery charge. If Florist B increases the cost per rose to $5.20, for what
number of roses is it less expensive to order from Florist A? From Florist B?

Answers

Step-by-step explanation:

let the total charge be y

and the number of rose be x

Florist A charges

y=40+4.75x---------1

Florist B charges

y=25+5.2x--------2

to solve for the number of roses we need to equate 1 and 2

40+4.75x=25+5.2x

40-25=5.2x-4.75x

15=0.45x

x=15/0.45

x=33.33

The number of roses that will be less expensive to order from A is 33.33

Answer:

 

Step-by-step explanation:

33.33

the parcel is in the n1/2 of the s1/2 of the e1/2 of the w1/2. what is the acreage of the parcel and how many lots can it be divided into if each lot needs to be at least 5 acres? which quadrant is the parcel to be divided located in?

Answers

The parcel is located in the northeast quadrant of the quarter section, based on the description given, since it is in the north half of the south half, the east half of the west half, and so on.

The parcel is in the n1/2 of the s1/2 of the e1/2 of the w1/2.

The first step in finding the total acreage of the parcel is

To determine how much land is in each quadrant.

An acre is a unit of area measurement that equals 43,560 square feet, and half of a quarter section is 80 acres,

so each quadrant is 40 acres.

In each quadrant, the parcel takes up one-eighth of the total area, which is 5 acres.

As a result, the total acreage of the parcel is 5 acres.

Each lot must be at least 5 acres in size, so the number of lots is determined by dividing the total acreage by 5.

There are 1 lot in the parcel, according to this calculation.

A quadrant is any of the four sections into which a plane is divided by the x-axis and y-axis of a Cartesian coordinate system.

There are two perpendicular axes, the x-axis and the y-axis, in the Cartesian coordinate system.

The x-axis is the horizontal line, while the y-axis is the vertical line.

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Mike saves $2,000 at a yearly simple interest rate of 2%. He earns $280 in interest. For how many years did he save this money?

Answers

Answer:

7 years.

Step-by-step explanation:

To find this, we need to find 2% of 2,000. To do this, we mulitply 2,000 by .02. This gets us 40. Now, we need to divide 280 by 40 to find the amount of years it took for Mike to get this money. When we do that, it gets us 7. That means Mike saved that money for 7 years.

The number of years that he saves this money will be 7 years.

What is simple interest?

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Mike saves $2,000 at a yearly simple interest rate of 2%. He earns $280 in interest. Then the number of years is calculated as,

$280 = ($2,000 x 2 x T) / 100

$28,000 = $4,000 x T

T = $28,000 / $4,000

T = 7 years

The number of years that he saves this money will be 7 years.

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LOGIC, Use the model universe method to show the following invalid.
(x) (AxBx) (3x)Ax :: (x) (Ax v Bx)

Answers

The conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

To show that the argument is invalid using the model universe method, we need to find a counterexample where the premises are true, but the conclusion is false.

Let's consider the following interpretation:

Domain of discourse: {1, 2}

A(x): x is even

B(x): x is odd

Under this interpretation, the premises "(x)(A(x) ∧ B(x))" and "(∃x)A(x)" are true because all elements in the domain satisfy A(x) ∧ B(x), and there exists at least one element (e.g., 2) that satisfies A(x).

However, the conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

In this counterexample, the premises are true, but the conclusion is false, demonstrating that the argument is invalid using the model universe method.

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A passenger train can travel, on average, 20 miles per hour faster than a freight train.
If the passenger train covers 390 miles in the same time it takes the freight train to cover 270 miles, then how fast is each train?

Answers

Answer:

The speed of the passenger train is 65 miles per hour and the speed of the freight train is 45 miles per hour.

Step-by-step explanation:

A passenger train can travel, on average, 20 miles per hour faster than a freight train.If the passenger
A passenger train can travel, on average, 20 miles per hour faster than a freight train.If the passenger

solve pls brainliest

solve pls brainliest

Answers

Answer:

1)3 meters/second

2)-16°C

Step-by-step explanation:

Hope it can help you lovelots

a party of fishermen rented a boat for $240. two of the fishermen had to withdraw from the party and, as a result, the share of each of the others was increased by $10. how many were in the original party? provide a numerical answer.

Answers

Answer:a party of fishermen rented a boat for $240. two of the fishermen had to withdraw from the party and, as a result, the share of each of the others was increased by $10. how many were in the original party? provide a numerical answer.

Step-by-step explanation:

Now ,Let original number in party be "x"::

Average cost per person = 240/x

New number in the party:: x-2

New Average cost per person:: 240/(x-2)

Equation::

10 dollars =New average - old average

240/(x-2) - 240/x = 10

240x - 240(x-2) = 10x(x-2)

480 = 10x^2-20x

x^2 - 2x - 48 = 0

X = 8 (ORIGINAL)

The graph shows depth of water in a tank over time.
Calculate the rate at which the depth is decreasing.
Give your answer as a decimal.
PLEASE HELP ASAP!!!

The graph shows depth of water in a tank over time.Calculate the rate at which the depth is decreasing.Give

Answers

74 is the answer to this question

Gwen runs back and forth along straight track: During the time interval 0 < t < 45 seconds, Gwens 250ain velocity; In feet per second, is modeled by the function given by v (t) What is the first time;t1 , that Gwen changes direction? Find Gwens average velocity over the time interval 0 < t

Answers

The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.

Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.

Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.

Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.

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Select the correct answer.
Mateo teaches a continuing education class at the library on Tuesday nights. He estimates that 75% of his students are satisfied or very satisfied with the class.

Last week, he asked a random sample of students to take a survey on their experience in the class. However, the results showed that only 70% indicated that they are satisfied or very satisfied with the class. He decides to randomly survey more of his students. How will Mateo know whether his model is valid or not?

A.
It is valid if the result from all the surveys and the model get closer together.
B.
It is impossible to determine whether the model is valid.
C.
It is valid if the result from all the surveys and the model stay the same.
D.
It is valid if the result from all the surveys and the model get farther apart.

Answers

Answer:

A

Step-by-step explanation:

Getting closer together means that both are becoming more accurate.

A valid model is such model whose calculated value approximates to the actual value. If it doesn't approximate to the actual value, it must be close to the actual value.

The model is valid if the results from the survey are close enough, together.

Given that:

\(p_1 = 75\%\) -- the actual estimation of satisfied students

\(p_2 = 70\%\) -- the second estimation of satisfied students

For a model to be valid, the calculated value must be close to the actual value.

If after Mateo's survey of more students, the result of satisfied or very satisfied students is still close to 75%, then Mateo's model is valid.

If otherwise, then the model is invalid.

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Find an equation of the tangent line to the curve at the given point. y = V 8 + x3, (1, 3)

Answers

The equation of the tangent line to the curve y = 8 + x^3 at the point (1, 3) is y = 3x.

To find the equation of the tangent line to the curve at the given point (1, 3), we need to find the derivative of the function y = 8 + x^3 and evaluate it at x = 1.

First, let's find the derivative of y with respect to x:

dy/dx = d/dx (8 + x^3)

= 0 + 3x^2

= 3x^2

Now, evaluate the derivative at x = 1:

dy/dx = 3(1)^2

= 3

The slope of the tangent line at x = 1 is 3.

To find the equation of the tangent line, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Plugging in the values (1, 3) and m = 3, we get:

y - 3 = 3(x - 1)

Now simplify and rearrange the equation:

y - 3 = 3x - 3

y = 3x

Therefore, the equation of the tangent line to the curve y = 8 + x^3 at the point (1, 3) is y = 3x

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Select all that apply to the following statement. There is a LOW correlation between cheating and final grades in Math256. Group of answer choices Correlation requires both variables to be either qualitative or quantitative. The correlation has no unit of measurement; it is just a number. The correlation must specify which is the explanatory variable and which is the response variable Correlation requires both variables to be quantitative

Answers

Answer:

The correlation has no unit of measurement; it is just a number.

Correlation requires both variables to be quantitative.

Step-by-step explanation:

Correlation refers to the measure of the relationship between two variables. The correlation between two variables is measured using the correlation Coefficient which may take any value between - 1 and 1 ; the closer the correlation Coefficient is to either 1 or - 1, the greater the relationship with negative depicting a negative association and positive depicting a positive relationship between the variables. The correlation Coefficient requires that both variables are numeric (quantitative). The correlation Coefficient has no unit of measurement.

Help me with this, it’s due in a bit!

Help me with this, its due in a bit!

Answers

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

The expression p2/p1=(T2/T1)^k/(k-1) relates two states of an ideal gas with constant specific ratio k and equal

Answers

By answering the presented question, we may conclude that This is the expressions phrase used in the question. It connects the pressure ratio to the temperature ratio and the gas's specific ratio k.

what is expression ?

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

quantities of petrol. It specifically connects the pressure and temperature of the gas in two states, represented by subscripts 1 and 2.

T2/T1 = (nRT2/V) / (nRT1/V) P2/P1

The adiabatic process equation, which connects the pressure and temperature of an ideal gas passing through an adiabatic process with a constant specific ratio k:

(T2/T1)(k/(k-1)) = P2/P1

We may eliminate the pressure ratio by merging these two equations, yielding the expression:

T2/T1 = (nRT2/V) / (nRT1/V) = T2/T1 = (k/(k-1)) = P2/P1 = (nRT2/V) / (nRT1/V) = T2/T1

When we simplify this expression, we get:

(T2/T1)(k/(k-1)) / P2/P1 (k-1)

This is the phrase used in the question. It connects the pressure ratio to the temperature ratio and the gas's specific ratio k.

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Solve each of the following equations.

a.
24 = -3 + 3n

b.
11 + 4x = x - 10

c.
-216 = 1 + 7(1 + 8m)

d.
3p - 3(2 - 2p) = 34 + 4p

You must show all of your work to receive credit.
I will give you 27 points if you solve this by showing your work plz

Answers

Answer:

A) n=9

B)X=-7

C)m=-4

D)P=8

Step-by-step explanation:

A)24=-3+3n

move variable to the lefthand side &change its sign

-3n+24=-3

move the constant to the righthand side &change its sign

-3n=-3-24

calculate the difference

-3n=-27

devide both sides by-3

Solution:

n=9

B)11+4x=x-10

11+4x-x=-10

move variable to the lefthand side &change its sign

4x-x=-10-11

move constant to the righthand &change its sign

4x-x=-10-11

collect like terms

3x=-21

devide both sides of the equation by 3

solution :

x=-7

C)-216=1+7(1+8m)

multiply the parentheses by 7

-216=1+7+56m

add the numbers

-216=8m+56m

move variable to the lefthand side &change its sign

-56m-216=8

move constant to the righthand side &change its sign

-56m=8+216

add the numbers

-56m=224

devide both sides of the equation by -56

solution:

m=-4

D)3p-3(2-2p)=34+4p

multiply the parentheses by -3

3p-6+6p=34+4p

collect like terms

9p-6=34+4p

move the variable to the lefthand side &change its sign

9p-4p-6=34

move the constant to the righthand side &change its sign

9p-4p=34+6

collect like terms &calculate the sum

5p=40

devide both sides by 5

solution:

P=8

HiI hope this helps..

the area of a square field is 50625 meter square find its perimeter

Answers

Answer:

900

Step-by-step explanation:

A=S^2

50265=SxS

S=√50265

S=225

P=Sx4

P=225x4

P=900

Need help with this for school

Need help with this for school

Answers

Answer: 135

Step-by-step explanation:

Counting by 5 The last point at the end of the box and whisker plot is 135


Which values of x, if any, prove that the graph below is not a function?

Which values of x, if any, prove that the graph below is not a function?

Answers

Answer:

3

Step-by-step explanation:

For a graph not to be a function, it means that a particular value of x has more than one corresponding value of y. Looking at the graph, at the point where x = 3 on the horizontal axis, there are so many value of y. Plus, the graph below is not a function at x = 3

The correct option is 3

what is 9-3 divied by 1/3 + 1 =

Answers

Answer:

1

Step-by-step explanation:

3 divided by 1/3 is 9, and 9-9=0

0+1=1

1

Step-by-step explanation:

Find the area of the composite figure.

Find the area of the composite figure.

Answers

Answer:

42cm

Step-by-step explanation:

I'm sry if I'm wrong

Answer:

42 square centimeters

Step-by-step explanation:

We know all the sides of the square is 6 cm.

The side of a square and the triangle on the bottom add to 8 cm.

The bottom part of the triangle must be 2 cm.

The area of the square is 36 square centimeters as we use the formula Area = side x side for a square.

The height of the triangle is 6cm as it is as tall as the square.

The formula of a triangle is 1/2 * base * height.

1/2*(6)*(2) = 6 square centimetes.

Adding the two together,

36 + 6 = 42

ahhhh i need help like now !!!!!!!!!!!

ahhhh i need help like now !!!!!!!!!!!

Answers

Answer:

x = 2

Step-by-step explanation:

Simplify both sides of the equation.

−20 = − 4x − 6x

−20 = −4x − 6x

−20 = (−4x − 6x)(Combine Like Terms)

−20 = −10x  

Flip the equation.

−10x = −20

Divide both sides by -10.

-10x/-10 = -20/-10

x = 2

What is the domain of x )= â x 1?

Answers

The domain of the function f(x)= -x+1 is (-∞, ∞).

What is domain?

The collection of all conceivable independent values that a function or relation may take is known as its domain.

Given:

Function f(x)= -x+1

To find the domain:

Find the domain by finding where the function is defined.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input.

When x = 1, f(x) = 0

When x = 2, f(x) = -1

x = 0, f(x) = 1

And so on.

And the function is defined over (-∞, ∞)

And the graph is given in the attached image.

From the graph, we can see that the function is defined over  (-∞, ∞)

Therefore,  (-∞, ∞) is the domain.

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The complete question:

What is the domain of f(x)= -x+1?

What is the domain of x )= x 1?

Explain in words why there are 9 square feet in 1 square yard and 27 cubic feet in 1 cubic yard. Then describe generally how to find conversion factors involving squares or cubes.

Answers

To find the conversion factor for converting from one unit to another involving squares or cubes, we need to use the relationship between the units that are being converted and the appropriate power of the conversion factor.

The conversion from yards to feet and vice versa involves the concepts of squares and cubes.

There are 3 feet in 1 yard, so the number of feet squared in one square yard is (3 feet)² = 9 square feet (because 3² = 9). This is why there are 9 square feet in 1 square yard.

Similarly, there are 3 feet in 1 yard, so the number of feet cubed in one cubic yard is (3 feet)³ = 27 cubic feet (because 3³ = 27). This is why there are 27 cubic feet in 1 cubic yard.2.

To find conversion factors involving squares or cubes, we need to use the relationship between the units that are being converted.

For example, to convert from square feet to square yards, we know that there are 9 square feet in 1 square yard. So the conversion factor is:1 square yard / 9 square feet

Similarly, to convert from cubic feet to cubic yards, we know that there are 27 cubic feet in 1 cubic yard. So the conversion factor is:1 cubic yard / 27 cubic feetIn general, to find the conversion factor for converting from one unit to another involving squares or cubes, we need to use the relationship between the units that are being converted and the appropriate power of the conversion factor.

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Final answer:

A yard is equivalent to 3 feet. Hence, a square yard is equivalent to 9 square feet (3^2) and a cubic yard is equivalent to 27 cubic feet (3^3). Conversion factors for squares or cubes are found by squaring or cubing the base conversion factor.

Explanation:

In terms of measurement conversion, 1 yard is equivalent to 3 feet. When dealing with square units like square feet and square yard, we square this conversion factor, thus 1 square yard is equivalent to 3^2 or 9 square feet.

Similarly, for cubic measurements, we cube the conversion factor. Therefore, 1 cubic yard is equivalent to 3^3 or 27 cubic feet.

To find conversion factors involving squares or cubes, you typically square or cube the base conversion factor. For example, if converting inches to feet, the base conversion is 1 foot is 12 inches. For square inches to square feet, you'd square the conversion so 1 square foot is 144 (12^2) square inches. Finally, for cubic feet to cubic inches, you'd cube the base conversion thus 1 cubic foot is 1728 (12^3) cubic inches.

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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=

Given Triangle ABC with FC=5, you want to find BF. First, find the value that y must have for the Triangle

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

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