To approximate the length of a marsh, a surveyor walks 425 meters from Pont A to Point B. Then the surveyor turns 65° and walks 300 meters to point C. Approximate the length AC of the marshanswers are not me :)615250

Answers

Answer 1

Consider the figure.

We have,

\(\begin{gathered} AC^2=BC^2+AB^2-2(BC)(AB)cos115\text{ } \\ \text{ =300}^2+425^2-2\times300\times425\times\cos 115 \\ =378392.6567 \\ AC=\sqrt[]{378392.6567}=615 \end{gathered}\)

Thus, the value of ac is 615.

To Approximate The Length Of A Marsh, A Surveyor Walks 425 Meters From Pont A To Point B. Then The Surveyor
Answer 2

The length of AC of the marsh using the Law of Cosines is 615 meter.

Use the Law of Cosines, which states:

\(c^2 = a^2 + b^2 - 2ab * cos(C)\)

Here,

a = 425 meters

b = 300 meters

C = 180 - 65= 115

Plugging in these values into the Law of Cosines formula, gives

\(AC^2 = 425^2 + 300^2 - 2 * 425 * 300 * cos(115)\)

\(AC^2 = 180625 + 90000 - 255000 * cos(115)\)

\(AC^2\) = 270625 - 107767.6567

\(AC^2 = 378352.6597\)

Taking the square root of both sides

\(AC = \sqrt{378352.6597\)

AC = 615

Therefore, the length AC is 615 meters.

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Related Questions

what is the answer pls Question 29 of 45
In the triangle below, what is the length of MN?
OA. 50
OB. 100
OC. 20
OD. 40
50
20
M
50

what is the answer pls Question 29 of 45In the triangle below, what is the length of MN?OA. 50OB. 100OC.

Answers

The calculated length of the segment MN in the triangle is 20

How to find the length of the segment MN in the triangle

From the question, we have the following parameters that can be used in our computation:

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 50 - 50

Evaluate

Third angle = 80

The length of the segment MN is then calculated as

MN/sin(50) = 20/sin(50)

This gives

MN = sin(50) * 20/sin(50)

Evaluate

MN = 20

Hence, the length of the segment MN in the triangle is 20

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24. Critical Thinking Anika wants to determine the maximum

number of tulip bulbs (t) she can purchase if each bulb costs $1.50.

She will also need to purchase separate pots for each bulb at $1.25

each and a bag of potting soil for $10.00. Set up an inequality to

determine how many tulip bulbs Anika can purchase without

spending more than $20.00, and solve it. Can Anika buy exactly

enough bulbs and pots to spend the full $20.00? Explain. Can you

think of a better inequality to describe the answer?

Answers

Answer:

t ≤ 3 ; kindly check explanation for more explanation

Step-by-step explanation:

Given that :

Number of tulip (t) =?

Cost of bulb = $1.50

Pot for each bulb purchased at =$1.25

Bag of potting soil = $10.00

Number of tulip bulb that can be purchased without spending more than $20

Cost of tulip bulb = [(cost per bulb + cost per pot) * number purchased (t) + cost of bag of potting soil]

Cost = [(1.50 + 1.25)t + 10]

If spending should not exceed $20

2.75t + 10 ≤ 20

2.75t ≤ 20 - 10

2.75t ≤ 10

t ≤ 10/2.75

t ≤ 3.64

He cannot purchase more than 3 tulip bulbs

Anika cannot buy exactly enough tulip bulbs an pot to spend the full $20 because the number obtained is a fraction and not a whole number.

At Hartridge Fudge Shop, 20% of the fudge has caramel swirls. If the owner made 8 pounds of caramel-swirled fudge, how many pounds of fudge did she make in all?

Answers

Answer:

Well I think you have to do 20% times 8 then divide it 100

Step-by-step explanation:

Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line

Answers

Answer is C) it is located between the numbers 2 and 3 on the number line

Explanation

The square root of a number is “what number times itself”

2 x 2 = 4

3 x 3 = 9

7 is between 4 and 9 so C is the correct answer

y=2/3x + 7/3 -4x+6y=14

Answers

The sοlutiοn οf the system οf equatiοn is x = 0 and y = 7/3.

What is a incοnsistent system?  

If there is nο sοlutiοn tο a system οf equatiοns, it is incοnsistent system; οtherwise, there must be at least οne sοlutiοn. If a set οf equatiοns has infinitely many sοlutiοns, it is dependent.

Every οne οf the equatiοns in a system οf equatiοns must have a sοlutiοn in οrder fοr the system tο be cοnsistent. This demοnstrates that a set οf values fοr the variables may simultaneοusly satisfy all οf the system's equatiοns and shοw that they are nοt mutually exclusive.

There is nο sοlutiοn tο an equatiοn system that satisfies all οf the equatiοns in the system. This indicates that nο cοmbinatiοn οf values fοr the variables can cοncurrently satisfy all οf the system's equatiοns since they are incοmpatible.

The given equatiοns are:

y = 2/3x + 7/3

-4x+6y=14

Substituting the value of y in the second equation:

-4x + 6y = 14

-4x + 6(2/3x + 7/3) = 14

-2x + 4x + 14 = 14

2x = 0

x = 0

Substitute the value of x = 0 we have:

y = 2/3(0) + 7/3

y = 7/3

Hence, the solution of the system of equation is x = 0 and y = 7/3.

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Complete question:

Given system of equations y = 2/3x + 7/3 and -4x + 6y = 14

Find the value of x and y.

school uniform shirt normally cost $15 each but are on sale for 30% off the original price. You also have a coupon before you take the percent discount. If you have $150 to spend, which of the following equations will help you to determine how many shirts, x, you can buy

Answers

Answer:

125 shirts

Step-by-step explanation:

125 shirts. Sorry if it’s wrong:(

Find the distance between the two points rounding to the nearest tenth (if necessary). (-1,51 and (-7, -1) ​

Answers

Answer:

Given a straight line defined by the points (1,51) and (3,91),

x1 = 1, y1 = 51, x2 = 3 and y2 = 91

Slope of the line m = ∆y/∆x

m = y2-y1/x2-x1

m = 91-51/3-1

m = 40/2

m = 20

Hence the slope of the line is 20.

Given the equation of a line y = mx+c

To get the y intercept of the line c, we will substitute one of the give points and the slope into the equation as shown;

Using the point (1,51) and m = 20,

Substitute into the equation y = mx+c

51 = 20(1)+c

51 = 20+c

c = 51-20

c = 31

Hence the slope is 20 and the y intercept of the line is 31

Step-by-step explanation:

I hope this helps:)

in a video game clare
score 50 more points than Tyler if c is the number of points that clear score and tease the number of points that Tyler score which equations are correct select all that apply

C=1.5t C=t+0.5 C=t+0.5t C=(1+0.5)t C=t+50

Answers

Answer:  C=t+50

Step-by-step explanation: This equation means that Clare's score equals Tyler's score plus 50.

Only one choice is correct here.

Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200

Answers

Hello!

The distance, d, is less than 200 miles.

B. d > 200

If I have 90 crates of apples and I sell 72 what percent is left

Answers

The number of crates of apples left is 90 - 72 = 18

90 crates of apples represent 100%.

To find what percent represent 18 crates of apples, we can use the next proportion:

\(\frac{90\text{ crates of apples}}{18\text{ crates of apples}}=\frac{100\text{ \%}}{x\text{ \%}}\)

Solving for x:

\(\begin{gathered} 90\cdot x=100\cdot18 \\ x=\frac{1800}{90} \\ x=20 \end{gathered}\)

20 % is left

You use a tape measure to measure the dimensions of a canvas, as shown. Estimate the area of the
canvas.
50.8 cm
40.6 cm

Answers

2000 cm^2

Step-by-step explanation:

we simply round the dimensions of 50.8 cm to 50 cm and 40.6 cm to 40 cm, and we multiply 50*40 cm to get to 2000cm^2 (it is squared because this is area)

2. what is the correct r code to build a linear regression model with response variable y and explanatory variable x? a. lm(y~x) b. lr(y~x) c. lm(y

Answers

The correct r code to build a linear regression model with response variable y and explanatory variable x is option a. lm(y~x).

The code lm(y~x) will create a linear model with y as the response variable and x as the explanatory variable.

The lm() function in r is used for linear regression, and the formula y~x indicates that y is the response variable and x is the explanatory variable. The other options, lr(y~x) and lm(y, are not correct r code for building a linear regression model.

In summary, the correct r code for building a linear regression model with response variable y and explanatory variable x is lm(y~x).

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Need help ASAP

the value of each variable. If your answer is not
teger, express it in simplest radical form.
The length of a is
The length of b is
(Simplify your answer.)

Need help ASAPthe value of each variable. If your answer is notteger, express it in simplest radical

Answers

Answer:

me too (help)

Step-by-step explanation:

2nd time asking! I need answer please.

2nd time asking! I need answer please.

Answers

Answer:

33.49 cubic centimeters

Step-by-step explanation:

Equation for volume: 4/3*π*r^3

Substitute 2 for r and 3.14 for π

4/3*3.14*2^3

To the nearest hundredth is 33.49

to determine that a item is not in an unordered array of 100 items, how many values must linear search examine on average? a) 7 b) 10 c) 100

Answers

To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.

What is Linear Search?

Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.

Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.

Hence, in this case, since there are 100 items, then there will be 100 numbers of values.

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Which expression is equivalent to 2x4y3

Which expression is equivalent to 2x4y3

Answers

The answer is D. 2^3 is 8.

Helppp pls



Another one

Helppp pls Another one

Answers

20 percent hope it helps you

Answer:

25 percent

Step-by-step explanation:

There is 12 spots on the chart

3 of these spots are green or 3/12

3/12 is equivalent to 1/4

1/4 of 100 in 25 percent

Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of p. EP) .79 (to 2 decimals) op .0288 (to 4 decimals)

Answers

The sampling distribution of p is 0.0288 (to 4 decimals).

The sampling distribution of p is a theoretical distribution of the proportion of successes (p) in a sample of a given size, drawn from a population with a known proportion of successes (p). In this case, the proportion of successes is the proportion of complaints involving new car dealers that are resolved, which is given as 0.79 (to 2 decimals).

The standard error of the proportion is given by the formula:

\(SE = \sqrt{(p * (1 - p) / n)}\)

where n is the sample size. Plugging in the values, we get:

\(SE = \sqrt{(0.79 * (1 - 0.79) / 200)}\) = 0.0288 (to 4 decimals).

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Ken owns 500 shares of LaceNBrace, which makes hockey equipment. He receives a notice stating the company will be paying $0.15 dividend per share. What is the total dividend payment he receives for that quarter? O $750 O $8.50 O $7.55 O $75​

Answers

Ken will receive a total dividend payment of $75 for that quarter.

We have to given that,

Ken owns 500 shares of LaceNBrace, which makes hockey equipment.

And, He receives a notice stating the company will be paying $0.15 dividend per share.

Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:

= $0.15 per share x 500 shares

= $75

Therefore, Ken will receive a total dividend payment of $75 for that quarter.

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Using the digits 3,4 and 9.write the least to greatest decimal number less than 1.

Answers

0.3, 0.4, and 0.9 (not sure if this is the answer tho)‍♂️

Tyler says there are indefinitely many additional numbers between 0 and 1 do you agree

Answers

Answer:

Yes

Step-by-step explanation:

There are infinite numbers between  0 and 1. Think of decimals. E.g.

1.1 , 1.2 , 1.3 , 1.31 , 1.32 , 1.30000000000000009

It goes on forever and never ends. So yes, Tyler is correct.

Write your answer as an integer or as a decimal rounded to the nearest tenth.

Write your answer as an integer or as a decimal rounded to the nearest tenth.

Answers

Applying the sine rule the value of side w is calculated to be 6.2

How to find the size of w

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Giving F (x) =-3x +4,find f (-6).

Answers

Answer:

22

Step-by-step explanation:

we plug -6 to x which would get us -3(-6) + 4

-3(-6) = 18 + 4 = 22

PLZ mark brainliest :DD

Answer:

22

Step-by-step explanation:

1. -3 times -6 would be +18.

2. 18+4=22

4) A box has dimensions of 14 inches long, 1.4 feet wide,
and 9 inches high. What is the volume of the box?
The formula for the volume is V=1.w.h.

Answers

Answer:

2116.8 in^3

Step-by-step explanation:

V = l*w*h

All the units need to be the same

Convert 1.4 ft to inches

1.4 ft * 12 inches/ ft = 16.8 inches

V = 14 * 16.8  * 9

   = 2116.8 in^3

Consider a medium with parameters € = 1.2 (10^-10 )F/m , n= 3(10^-3) H/m and sigma=0. Magnetic field intensity in the medium is given as R = 2cos (10^10t- 600x)äz Am.
Use Maxwell's equations to obtain the followings:
1) Magnetic flux density
These questions is circuit theory

Answers

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

The average distance from Earth to everyone's favorite dwarf planet, Pluto, is 3.27 billion miles.  At the speed of 24,500 miles per hour, how long would it take to reach Pluto?  Give your answer in years.

Answers

Given:

The distance is 3.27 billion miles.

The speed is 24500 miles per hour.

Required:

We need to find the time to reach Pluto.

Explanation:

We know that

\(billion=1,000,000,000\)

Multiply 3.27 on both sides.

\(3.27\text{ }billion=3.27\times1,000,000,000\)\(3.27\text{ }billion=3,270,000,000\)

Co

how do i refund and stop my subscription for brainly

Answers

To refund and stop your subscription for Brainly.

Visit the Brainly website and log into your account using your credentials.Navigate to your account settings or profile page.Look for the "Subscription" or "Billing" section and click on it.In the subscription settings, locate the option to cancel or stop your subscription.Follow the provided instructions to cancel your subscription. This may involve confirming your cancellation or providing a reason.Once your subscription is canceled, check the terms and conditions for refund eligibility. If you are eligible for a refund, follow the refund process specified.If there is no refund available or if you encounter any issues, contact Brainly's customer support through their website or via email.Explain your situation and request assistance with the refund process.Be sure to monitor your bank or credit card statements to confirm that the subscription charges have been stopped.

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What three consecutive integers have a sum of 12?; What is the sum of 3 consecutive integers?; What is the formula for 3 consecutive integers?; What are the consecutive numbers of 12?

Answers

The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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Find the equation of the line that contains the point (4, - 2) and is perpendicular to the line y = - 2x + 5. ​

Answers

Answer:

y=1/2x

Solution:The slopes of perpendicular lines are opposite reciprocals of each other.The simplest way to determine a number's reciprocal is to flip it over, like so:\(-2 ~ - > -\displaystyle\frac{1}{2}\)Now, change the sign:\(\displaystyle\frac{1}{2}\)So we have the slope of the line that's perpendicular to the given line.Now, let's find the line's equation.First, let's write it in Point-Slope Form:y-y1=m(x-x1)y-(-2)=1/2(x-4) y+2=1/2x-2 (Point slope)Now, convert to slope-intercept:y=1/2x+2-2y=1/2x

Hope it helps.

Do comment if you have any query.

Answer:

y=1/2x

Step-by-step explanation:

PLEASE HELP IM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100PTS!!!

Adding two functions results in h(x) = –x + 9, while multiplying the same functions results in j(x) = –9x.

Which statements describe f(x) and g(x), the original functions? Select two options.
A. Both functions must be quadratic.
B. Both functions must have a constant rate of change.
C. Both functions must have a y-intercept of 0.
D. The rate of change of either f(x) or g(x) must be 0.
E. The y-intercepts of f(x) and g(x) must be opposites.

PLEASE HELP IM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100PTS!!!Adding two functions

Answers

Answer:

Both functions must have a constant rate of change.

The rate of change of either f(x) or g(x) must be 0.

From the first equation we know that both f (x) and g (x) must be of order 1 or of order 0, since the maximum exponent of X is 1. This indicates that both functions must have a constant rate of change , since the derivative of a function of order 0 or of order 1 is a constant.

From equation 2 we know that both f (x) and g (x) are composed of a single term, since the multiplication of both results in a single term (-9x). In addition, we verify that one of the functions is of order 0 and the other is of order 1, since the result of the product is of order 1.

If f (x) or g (x) are of order 0, which means that they are composed of only one constant, the rate of change of any of the 2  functions is 0.

Step-by-step explanation:

Answer:

B and D.

Step-by-step explanation:

We know that when we added the two functions together, we get:

\(h(x)=-x+9\)

However, when we multiplied them together, we get:

\(j(x)=-9x\)

Let's first consider what we can determine from this.

If we add them together, we get a linear equation. However, this doesn't mean that our two original functions are linear since if we have, say, -x^2 and x^2-x+9, they will cancel and form a linear equation if we add them together.

However, since we know that if we multiply the two functions together, we get a linear equation, this means that both our original functions must be linear.

But, if we multiplied two linear functions, then we should get a quadratic, since x times x will yield x².

Therefore, this means that one of our linear functions is a horizontal line with no x variable. This is the only way to have a linear equation when multiplied.

Therefore, we have determined that both of our original functions are linear functions, and one (only one of them) is a horizontal line.

Let's go through each of the answer choices.

A) Both functions must be quadratic.

This is false as we determined earlier. If this was true, then the resulting function should be a quartic and not a line. A is false.

B) Both functions must have a constant rate of change.

Remember that all linear equations have a constant rate of change.

Since we determined that both our original functions are linear equation, this means that both our functions will have a constant rate of change.

So, B is true.

C) Both functions must have a y-intercept of 0.

Remember that one of our functions is a horizontal line.

If the y-intercept was 0, then the equation of our horizontal line will be:

\(y=0\)

And we know that anything multiplied by 0 will give us 0. However, the product of our function is -9x.

So, C cannot be true.

Rather, only our linear equation (not the horizontal line) may have a y-intercept of 0.

D) The rate of change of either f(x) or g(x) must be 0.

Remember that we determined that one of our lines must a horizontal.

Remember that horizontal lines have a slope of 0. In other words, the rate of change is 0.

So, D is true.

E) The y-intercepts of f(x) and g(x) must be opposites.

Well, since B and D is are true, this must be false since we can only select two options ;D

But, we can think about this. Note that if we multiply the two functions, we have a function without a y-intercept.

Remember that our horizontal line is not 0. So, the y-intercept of the horizontal line is a number.

So, the opposite of a number is another number.

So, if we multiply two non-zero numbers, we must get another number.

However, from our product, j(x)=-9x, we don't have another number. The y-intercept from this is 0.

Therefore, the two y-intercepts cannot be opposites of each other. If it was so, then we should have a y-intercept. So, E must be false.

In fact, this means that the y-intercept of our line (not the horizontal one) must be 0.

So, our answers are B and D.

And we're done!

Edit: Some (minor) errors in reasoning. Sorry!

Other Questions
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