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3 years ago

What is the average rate of change of f(x), represented by the graph, over the interval [-1, 1]? and my answers are

Mathematics

1 answer:

Alina [70]3 years ago

8 0

Answer: Choice C) 5

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Explanation:

Step 1) Draw a vertical line through -1 on the x axis. This vertical line crosses through the point (-1,-5) which is a point on the hyperbola.

Step 2) Draw a vertical line through 1 on the x axis. This line crosses the hyperbola at (1,5).

Step 3) Find the slope of the line through the two points (-1,-5) and (1,5) using the slope formula

m = (y2 - y1)/(x2 - x1)
m = (5 - (-5))/(1 - (-1))
m = (5 + 5)/(1 + 1)
m = 10/2
m = 5

The slope of the line is 5. This is the same as saying the average rate of change is 5. The average rate of change is over the interval [-1,1] which is the same as the interval -1 <= x <= 1

Note: writing "<=" without quotes means "less than or equal to".

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8090 [49]

The relation {(-1 , 3), (4 , 2), (-1 , 5)} is not a function ⇒ 2nd

Step-by-step explanation:

Let us revise the meaning of relation and function

The relation is a set of inputs and outputs
A function is a relation with one output for each input, that means every x has only one y
Ex: {(2 , 3) , (-1 , -2) , (3 , 2)} is a function because 2 has only 3 , -1 has only -2 and 3 has only 2, {(1 , 7) , (2 , -4) , (1 , -3)} is not a function because 1 has 7 and -3

The relation is a function if and only if every x has only one y

In {(0 , 0), (1 , 0), (2 , 0)}

∵ x = 0 has y = 0

∵ x = 1 has y = 0

∵ x = 2 has y = 0

∴ Every x has only one y

∴ {(0 , 0), (1 , 0), (2 , 0)} is a function

In {(-1 , 3), (4 , 2), (-1 , 5)}

∵ x = -1 has y = 3

∵ x = 4 has y = 2

∵ x = -1 has y = 5

∴ x = -1 has y = 3 and 5

∴ Not every x has only one y

∴ {(-1 , 3), (4 , 2), (-1 , 5)} is not a function

In {(1 , 2), (3 , -5), (-1 , 7)}

∵ x = 1 has y = 2

∵ x = 3 has y = -5

∵ x = -1 has y = 7

∴ Every x has only one y

∴ {(1 , 2), (3 , -5), (-1 , 7)} is a function

In {(7 , -1), (3 , -2), (5 , -2)}

∵ x = 7 has y = -1

∵ x = 3 has y = -2

∵ x = 5 has y = -2

∴ Every x has only one y

∴ {(7 , -1), (3 , -2), (5 , -2)} is a function

The relation {(-1 , 3), (4 , 2), (-1 , 5)} is not a function

Learn more:

You can learn more about the relations and functions in brainly.com/question/10570041

#LearnwithBrainly

6 0

2 years ago

Your school is sponsoring a pancake dinner to raise money for a field trip. You estimate that 200 adults will attend. You are tr

AfilCa [17]

Answer:

Some of the possible combinations are;

1) $19 per adult, $0 per child

2) $10 peer adult, $9 per child

3) $14 peer adult, $5 per child

Step-by-step explanation:

The given information are;

The estimated number of adults to attend the fund raising dinner = 200 adults

The amount the fund raiser is trying to realize = 3800

Therefore, some of the possible combinations are;

1) 3800/200 = 19 per adult to give;

$19 per adult, $0 per child

2) Given that each adult is charged $10, we have;

Total amount from adults = $10 × 200 = $2000

The total amount to be raised from the children = The amount the fund raiser is to realize - (Total amount from adults)

∴ The total amount to be raised from the children = 3800 - 2000 = 1800

The total amount to be raised from the children = $1,800

If there are 200 children we have;

The amount charged per child = (The total amount to be raised from the children)/(The total number of children)

The amount charged per child = $1,800/200 = $9 per child

Therefore, we have;

$10 peer adult, $9 per child

3) If each of the 200 children are charged $5 each, we have;

The total amount to be raised from the children = $5 × 200 = $1,000

∴ The amount to be raised from adults = $3800 - $1000 = $2800

The amount to each adult is to be charged = $2800/200 = $14

Therefore, we have;

$14 peer adult, $5 per child.

7 0

2 years ago

Provide reasons for the proof. Given line h is parallel to line k. line j is perpendicular to line h. Prove line j is perpendicu

dusya [7]

Answer: Provided.

Step-by-step explanation: We are given two lines 'h' and 'k' which are parallel to each other. Also, there is another line 'j' that is perpendicular to line 'h'.

We are to prove that line 'j' is perpendicular to line 'k'.

Let, m, n and p be the slopes of lines 'h', 'k' and 'j' respectively.

Now, since line 'h' and 'k' are parallel, so their slopes will be equal. i.e., m = n.

Also, lines 'h' and 'j' are perpendicular, so the product of their slopes is -1. i.e.,

m×p = -1.

Hence, we can write from the above two relations

n×p = -1.

Thus, the line 'j' is perpendicular to line 'k'.

Proved.

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3 years ago

a petting zoo has 5 lambs 11 rabbits 4 goats and 4 piglets. find the ratio of goats to the total number of animals. write the ra

azamat

Ratio of:
Lambs 5:24
Rabbits 11:24
Goats 4:24
Piglets 4:24

8 0

2 years ago

Read 2 more answers

What is the quotient. Of 25)9250

saul85 [17]

Answer:

370

Step-by-step explanation:

Isolate the numbers so that you are only dividing sections at a time.

So 25 goes in to 92 three times. so we multiply 25 by three and subtract that from 92. Put the three at the top and repeat throughout.

92-75=17

Bring the next number down and repeat.

6 0

2 years ago

Read 2 more answers