Given various values of the linear functions f (x) and g(x in the table, determine the y-intercept of (f − g)(x).
x −6 −4 −1 3 4
f (x) -36 -26 -11 9 14
g(x) 15 11 5 -3 -5

Answers

Answer 1

A linear function has the following format

y=mx + b

In which:

m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.

Function f has two points, (-6,36) and (-4,26).

The slope is given by the change in y divided by the change in x, thus:

\(m= \frac{-26-(-36)}{-4-(-6)}=\frac{10}{2} = 5\)

therefore, f(x) =5x+ b

Point (-6, -36) means that when x= -6, y = -36, and this is used to find b.

-36 = 5*(-6) + b

b = -36 +30 = -6

so, f(x) = 5x - 6

Now, function g has two points, (-6, 15) and (-4, -11), and the slope is:

\(m= \frac{11-15}{-4-(-6)} = \frac{-4}{2} =-2\)

therefore, g(x)= -2x+b

Applying point (-6, 15):

15 = -2*(-6) + b

b = 15-12 = 3

so, g(x) = -2x + 3

The subtraction (f-g)(x) is:

(f-g)(x)= f(x)- g(x) = 5x - 6 -(-2x + 3)

5x - 6 + 2x - 3

7x - 9

Thus, the y-intercept is 7x-9

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Related Questions

i need help. i am confused.

i need help. i am confused.

Answers

Answer:

Step-by-step explanation:

2(4z+3+3z)=174

7z+3=174/2=87

7z=87-3=84

z=84/7=12

WX=3z=3×12=36 units

Answer:

36 units

Step-by-step explanation:

\(2(4z + 3 + 3z) = 174 \\ \\ (7z + 3) = \frac{174}{3} \\ \\ 7z + 3 = 87 \\ \\ 7z = 87 - 3 \\ \\ 7z = 84 \\ \\ z = \frac{84}{7} \\ \\ z = 12 \: \\ \\ WX = 3z \\ \\ WX \: 3 \times 12 \\ \\ WX = 36\: units\)

The local fighter fighters collect toys to distribute a various give-away events they have 4569 toys and will sponsor 129 giveaway events. how many toys can they each give away at each event? how many toys if any, will be left over?

Answers

the answer is 47 and also 773

No links pls answfast

No links pls answfast

Answers

Answer:

25

Step-by-step explanation:

Just put down the answer.

3/2 inches of snow fell in 3/4 of an hour. Which TWO statements are correct?
A) The unit rate is 2 inches of snow per hour.
B) The unit rate is 3 inches of snow per hour.
C) The unit rate is 9/8 inches of snow each hour.
D) At the same rate, 4 inches of snow will fall in 6 hours.
E) At the same rate, 12 inches of snow will fall in 6 hours.​

Answers

Answer:

A) The unit rate is 2 inches of snow per hour.

&

E) At the same rate 12 inches of snow will fall in 6 hours.

Step-by-step explanation:

Answer:

a and e

Step-by-step explanation:

did it on usatestprep

(06.02 MC)

Part A: Write an algebraic expression for 8 more than 5 times a number. (5 points)

Part B: Write a verbal expression for 4(n + 6). (5 points)

Answers

Answer:

5n+8

4 times the quantity of a number and six

Step-by-step explanation:

8 more than 5 times a number

more than comes after

5 time a number

5n

8 more than

5n+8

4(n + 6)

4 times the quantity of a number and six

Please help! Correct answers only please!

You roll a 6-sided die two times.

What is the probability of rolling an odd number and then rolling a 3?

Simplify your answer and write it as a fraction or whole number.

Please help! Correct answers only please!You roll a 6-sided die two times.What is the probability of

Answers

Answer:

The answer would be 2/3.

Step-by-step explanation:

There are 6 faces on a dice 3 of which are odd which would be 1/2. Then there is one face on a dice that has 3 dots on it which would 1/6. So 1/2+1/6= 4/6 which simplifies to 2/3.

Crystal's gym membership costs $48 a month. Which table shows the sum of the
amounts that Crystal will pay for her gym membership over the next 4 months?

Answers

Answer:

it will cost 240$ dollars to pay for 5 month

Step-by-step explanation:

PLZ GIVE ME BRAINLEST

Simplify the expression:

-3.5i -4h +22 -0.3h +4.6i

Answers

Answer:

\(22 + 1.1 \times i - 4.3h\)

Step-by-step explanation:

1) Collect like terms.

\(22 + ( - 3.5i + 4.6i) + ( - 4h - 0.3h)\)

2) Simplify.

\(22 + 1.1 \times i - 4.3h\)

hence, the answer is 22 + 1.1 × i - 4.3h.

Can someone help me with number 4?

Can someone help me with number 4?

Answers

The US: 300m World: 9b Most accurate: B

300m•20=6b population

B is the most accurate

Can someone please help me with 1,4,3

Can someone please help me with 1,4,3

Answers

Answer:

Answer 4 = 4 / 11

Answer of 1 is  ± 25

Answer of 3 is - 56

Step-by-step answer

Just take square roots

is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is divisible by 12.

Answers

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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How to do these questions step by step

How to do these questions step by step

Answers

Answer:

Only for question 1

Step-by-step explanation:

The answer is

When numbers with indices are being multiplied together, the indices act as if its being added together whereas if you multiply the indices together then it would multiply them all

some iq tests are standardized to a normal model with a mean of 100 and standard deviation of 16. what percent of iqs would be over 80?

Answers

Answer:

The percentage of IQs that would be over 80 is 68%.

Step-by-step explanation:

The percentage of IQs that would be over 80 is 68%.

This is because 68% of the population falls within one standard deviation of the mean on a normal distribution. In this case, the mean is 100 and the standard deviation is 16, so 68% of the population has an IQ between 84 and 116.

The remaining 32% of the population falls outside of one standard deviation of the mean. 16% of the population has an IQ below 84 and 16% of the population has an IQ above 116.

The mean is represented by the dotted line in the center of the graph. The standard deviation is represented by the two dotted lines on either side of the mean. The shaded area represents the 68% of the population that has an IQ between 84 and 116.

Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house

Can you show the math as far as formulas go?

Answers

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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PLEASE HELP ME GUYS THERE IS 60POINTS FOR THIS IM BEGGING U GUYS❤️

PLEASE HELP ME GUYS THERE IS 60POINTS FOR THIS IM BEGGING U GUYS

Answers

Answer:

the second one.... ( 8,9 )

Step-by-step explanation:

the zero-product system is rlly easy to use....

it basically means to take each term and equal it to zero....

so for your equation it is....

( x - 9 ) ( x - 8 ) = 0

so you would write it as....

( x - 9 ) = 0

and

( x - 8 ) = 0

and then you solve them like this...

( x - 9 ) = 0

add 9 to both sides to get the variable by itself...

x= 9

( x - 8 ) = 0

add 8 to both sides to get the variable by itself....

x = 8

in a certain company 120 of the employees are men. what is the total number of employees if 5 out of every 8 employees are men?

Answers

Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)

x = 192

what is a necessary step for consturcting perpendicular lines through a point off the line?

Answers

Answer:

Step-by-step explanation:

O Draw a line that intersects the first line at an acute angle using a straightedge.

O Draw a ray that intersects the first line at an acute angle using a straightedge.

Draw arcs on either side of a given point on the line,

Draw ares on either sig, of a given point of the lin

the owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. she randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. what are the null and alternative hypotheses for this hypothesis test?

Answers

The null and different hypotheses for hypothesis test are

\(H_{0}\) : P =0.63 against \(H_{1}\) p \(\neq\) 0.63

Null hypotheses

Null hypothesis is usually what researchers or scientists try and confute, and if the null hypothesis is accepted, we have a tendency should modification our opinion, i.e., we have a tendency should modification our original opinion or statement so as to match the null hypothesis. H0 denotes the null hypothesis.

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

\(H_{0}\) : P =0.63 against \(H_{1}\) p \(\neq\) 0.63

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What is the slope of the line shown?

What is the slope of the line shown?

Answers

the slope would be -1/3
I think the answer is -1/3

i’m being timed !!!
Given the function f(x) = -x^2 + 4x + 6, determine the average rate of change of
the function over the interval -4 < x < 7.

im being timed !!!Given the function f(x) = -x^2 + 4x + 6, determine the average rate of change ofthe

Answers

Step-by-step explanation:

I dont know the answer but I know you should make a graph for it and it will tell u the answer I will try and take a photo

Mr. Johnston supports a young tree by using a stake and a string forming a right angle with the ground. View the di
33 in.
60 in.
What is the length of the string? Round to the nearest tenth.
Enter the correct answer in the box.
Please help I am sooo confused!!!! Asapppp!!!

Mr. Johnston supports a young tree by using a stake and a string forming a right angle with the ground.

Answers

Answer: Hey! The answer is 68.48 (rounded)

Step-by-step explanation:

These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=

These figures are similar. The perimeter and area of one are given. The perimeter of the other is also

Answers

The area of the larger figure that is similar to the smaller one is: 28.2 m².

How to Find the Area of Similar Figures?

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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Can someone help me with this picture? (Ignore 45,15)

Can someone help me with this picture? (Ignore 45,15)

Answers

Answer:

h = 5 (3+p)

Step-by-step explanation:

3 hrs = $45 + $15p

h = 45+15p / 3 (This was supposed to be a fraction)

h = 15 (3+p)/ 3 (This was supposed to be a fraction)

h = 5 (3+p) (You might use different variables from me)

hrs = hours

p = per person

Brainlist pls!

You thought i was filli n you ?

Answers

F EWfysefjc skcfhse hcfh

np

Which rule describes the relationship between the input and output pairs in the following table?
Input
Output
10
5
8
3
6
1
Choose 1 answer:
اے
Subtract 5 from the input to get the output.
в)
Multiply the input by 0. Then add 5 to the result to get the output.
Divide the input by 2. Then subtract 1 from the result to get the output.

Which rule describes the relationship between the input and output pairs in the following table?InputOutput1058361Choose

Answers

Answer:

Subtract 5 from input.

Step-by-step explanation:

10-5=5

8-5=3

6-5=1

Note:if you need to ask question let me know about it.

the lengh of a rectangular prism is 16 inches and the height is 8 inches. If the volume is 640 in ³, what is the width

Answers

Answer:

The width is 5 because if you multiply 16 by 8 by 5 you will get 640 cubed.

cyril is addressing 200 invitations to a reunion. He completes 20% of the invitations on wednesday and 40% of the invintations on thursday. Cyril says he has adressed 60 invitations. Why is cyrils statement not reasonable

Answers

Because he's finished 60% of the invitations at that point.

60% of 200 is 120, so Cyril is wrong.

Dan is Civil Engineer. He wants to create a small scale drawing of a city block. The block is a square with sides of length 100 m,

What would the dimensions of the scale drawing be if 1 unit represented 10 meters?

Answers

Is square with sides of length 100m, what would the the dimensions of the scale drawing be if 1 unit represented 10 meters

If troy says that 0. 9 is greater than 0. 90 because tenths are greater than hundreds and Kieth says 0. 9 is less than 0. 90 because 90 is greater than 9. Is either troy or Kieth correct?
How would you compare 0. 9 and 0. 90?

Answers

Neither are correct. 0.9 and 0.90 are equal

Answer: troy is correct

Step-by-step explanation:

m

the approximate z-score that corresponds to a right tail area of is

Answers

The approximate z-score that corresponds to a right tail area of is standard normal distribution

In a right-tailed scenario, we are interested in finding the z-score that corresponds to a specific area or probability in the right tail of the standard normal distribution. This area represents the probability of obtaining a z-score greater than a certain value.

To determine the z-score corresponding to a right tail area, we can use either a z-table or statistical software. A z-table lists the cumulative probabilities or areas under the standard normal distribution curve. These tables provide the area to the left of a given z-score. However, since we are interested in the right tail, we need to find the complementary area or subtract the given area from 1.

For example, if the right tail area is 0.05, we need to find the z-score that corresponds to an area of 0.95 (1 - 0.05). We can use a z-table to find the z-score that has an area of 0.95 to its left. By looking up this area in the z-table, we can find the corresponding z-score.

Alternatively, statistical software or online calculators can also provide us with the z-score for a given right tail area. These tools allow you to input the area or probability directly and retrieve the corresponding z-score.

It's important to note that finding the exact z-score can be challenging because z-tables usually provide values rounded to two decimal places. However, these approximations are typically sufficient for most practical purposes.

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