Mathematics College

Find the average rate of change on the interval [-3,3] for the given function

Answers

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so let's use those two points off the curve in order to get it, check the picture below.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{1}{3 +3}\implies {\LARGE \begin{array}{llll} \cfrac{1}{6} \end{array}}[/tex]

Related Questions

Which numbers are 4 units from −2 on this number line?

Drag and drop all the numbers that are 4 units from −2 to their correct position on the number line

Pls Show A Picture With The Number Line And Numbers

Answers

The numbers are 4 units from -2 on this number lines are -6, 2 and 6.

A number line is a horizontal line that has equally spread number increments.

The numbers included on the line will determine how the number on the line can be marked.

According to the question,

Firstly, we will add the two numbers.

4 + (-2) = 4 - 2 = 2

Then, we will subtract the two numbers.

4 - (-2) = 4 + 2 = 6

-2 - 4 = -6

The numbers 2, 6 and -6 are represented on the number line.

Therefore, the numbers are 4 units from -2 on this number lines are -6, 2 and 6.

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Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.

Answers

The pairs of equivalent expressions are:

(-14 + 3/2b) - (1 + 8/2b) --> -15 - 5/2b

(5 + 2b) + (2b + 3/2) --> 4b + 13/2

(7/2b - 3) - (8 + 6b) --> -5/2b - 11

(-10 + b) + (7b - 5) --> 8b - 15

How to Determine Equivalent Expressions?

Evaluate each of the given expressions in order to find out which expression is equivalent to each.

(-14 + 3/2b) - (1 + 8/2b) = (-14 + 3/2b) - (1 + 4b)

= -14 + 3/2b - 1 - 4b

= -15 - 5/2b

(5 + 2b) + (2b + 3/2) = 5 + 2b + 2b + 3/2

13/2 + 4b

4b + 13/2

(7/2b - 3) - (8 + 6b) = 7/2b - 3 - 8 - 6b

-5/2b - 11

(-10 + b) + (7b - 5) = -10 + b + 7b - 5

= -15 + 8b

= 8b - 15

Thus, the pairs of equivalent expressions are:

(-14 + 3/2b) - (1 + 8/2b) --> -15 - 5/2b

(5 + 2b) + (2b + 3/2) --> 4b + 13/2

(7/2b - 3) - (8 + 6b) --> -5/2b - 11

(-10 + b) + (7b - 5) --> 8b - 15

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Find the quadratic function (0,7)(2,15)(3,10)

Answers

The quadratic equation that contains (0, 7), (2, 15) and (3, 10) is y = - 3 · x² + 10 · x + 7.

What is the quadratic equation associated with a given set of points?

Quadratic functions are polynomials of the form y = a · x² + b · x + c, where a, b, c are real coefficients. To determine the coefficients, we need at least three distinct points on Cartesian plane. A solution that is algebraic exact only need three points, then we must resolve this system of linear equations:

c = 7 (1)

4 · a + 2 · b + c = 15 (2)

9 · a + 3 · b + c = 10 (3)

The solution to this system of linear equations is (a, b, c) = (- 3, 10, 7).

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PLEASE HELP ME!!! DUE TODAY, I WILL GIVE 20 POINTS!!!! NO EXPLAINATION NEEDED!!!! FIRST PERSON TO ANSWER GETS BRAINLIEST AWARD!!!!

Answers

Answer:

The weight of gold in the alloy is 32 g.

Answer:

The weight is 32 grams

Step-by-step explanation:

Emily has a spool of yarn that is. 12 1/8 yards in length Emily uses 2 2/3 from the spool there helppppp

Answers

Answer:

What do I solve for? If it's the length of spool not used, then the answer is

9 11/24 yards of spool.

Step-by-step explanation:

12 1/8 - 2 2/3=

12 - 2 + 1/8 - 2/3=

10 + (1/8 - 2/3)*24/24 = ==> multiply by 24 to get rid of denominator

10 + (24*1/8 - 24*2/3)/24 =

10 + (24/8 - 48/3)/24 =

10 + (3 - 16)/24 =

10*24/24+ (-13)/24 =

240/24 - 13/24=

(240-13)/24=

227/24=

(216+11)/24=

216/24 + 11/24=

9 + 11/24=9 11/24 yards of spool

you deposit $4800 in an account that earns simple interest . After 2 years, the account ears $537.60 in interest. What is the annual interest rate to the nearest tenth of a percent? use the formula i=prt

Answers

Annual interest rate on $4800 for 2 years is 5.6%.

What is Interest rate?

An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.

Given,

The principal amount = $4800

Time period = 2 years

Interest rate = $537.60

I = P × R × T / 100

where P = principal amount,

R = rate of interest,

T = Time period

537.60 = 4800 × R ×2 / 100

⇒ R = 537.60 ×100 / 4800 × 2

⇒ R = 5.6%

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can someone help me with this question? :)

Thank you so much for the help

Answers

For the given function, we have that:

The domain is [-4,4].The function has no zeros.The function is positive for x ≤ 0.The function is negative for x > 0.

What is the domain of a function?

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.

Hence, the domain is [-4,4] for the given function.

What are the zeros of a function?

The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.

For this problem, the function does not cross the x-axis, hence it has no zeros.

When a function is negative and when it is positive?

Looking at the graph of the function, we have that:

It is positive if it is above the x-axis.It is negative if it is below the x-axis.

Hence, for the function in the given graph:

The function is positive for x ≤ 0.The function is negative for x > 0.

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Jonah measured a picnic area near the river and made a scale drawing. The picnic area,
which is 70 yards wide in real life, is 10 inches wide in the drawing. What scale did Jonah
use?

Answers

The scale used by Johan is 1: 252.

Here, we are given that Jonah made a scale drawing of the picnic area in which the 70 yards wide picnic area in real life, was 10 inches wide in the drawing.

As per mathematical measurements-

1 yard = 3 feet

and 1 feet = 12 inches

Thus, 3 feet = 12 x 3 inches

= 36 inches

Therefore, we get that 1 yard = 36 inches

Now, the picnic area is 70 yards

the picnic area in inches is = 70 x 36 inches wide

= 2520 inches

Thus the scale used by Johan will be-

10 : 2520

= 1 : 252

Thus, the scale used by Johan is 1 : 252.

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1. Airline A and Airline B both have earnings before interest and taxes (EBIT) of $100 million. Airline B has no debt, while Airline A has interest expenses of $20 million. Assume a tax rate of 35% applies to both airlines.
How many dollars will Airline A pay in taxes? Type your answer into the textbox.

2. Discuss in a the importance of understanding taxes and what financial choices will have an impact on taxable income. Would Airline A have been willing to take on a debt that would cost $20 million in interest if they had not considered the tax break it would afford

Answers

Airline A will pay $28 million in taxes based on the EBIT of $100 million

The increase in interest expenses by $20 million means that the income tax expense decreases by $7 million.

What is the taxable earnings for company A?

The fact that company A has debt and would pay interest expenses of $20 million means that its taxable income is the earnings before interest and tax minus the interest expense

taxable income=$100 million-$20 million

taxable income=$80 million

taxes=taxable income*tax rate

tax rate=35%

company A's taxes=$80 million*35%

company A's taxes=$28 million

It should be noted that the higher the increase in interest expenses, the higher the tax savings that Airline A would achieve, hence, adding an additional borrowing which costs an extra $20 million in interest means that the company's taxes can be computed as shown below:

taxable income=$100 million-$20 million-$20 million

taxable income=$60 million

taxes=taxable income*tax rate

tax rate=35%

company A's taxes=$60 million*35%

company A's taxes=$21 million

In other words, Airline A would achieve a $7 million savings in taxes since the increase in interest expenses means that taxes decrease from $28 million to $21 million

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Misses Ali owns a business. She assigns two of her employees their shifts. She assigns the first employee 6 hour shift and the second employee 15 hours shift. If both workers recieved same number of hours what is the mininum number of hours each employee will be assigned.

Answers

Based on the fact that both workers received the same number of hours, the minimum number of hours that each employee will be assigned is 60 hours.

What is the minimum assigned hours?

One worker gets 15 hours shifts and the other gets 6 hour shifts.

If they will have the same number of working hours, the minimum number of hours for these workers will be the lowest common multiple of 6 and 15.

Multiples of 15:

15, 30, 45, 60, 75

Multiples of 6:

6, 18, 30, 42, 60, 72

The minimum number of hours is therefore 60 hours.

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Answer: 60

Step-by-step explanation:

LCM of 6 & 15

-------------

105

---------

LCM of 6 & 15 is 60

Teresa borrowed $8,000 at a rate of 15.5% , compounded semiannually. Assuming she makes no payments, how much will she owe after 3 years?
Do not round any intermediate computations, and round your answer to the nearest cent.

Answers

Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.

What is compound interest?The interest you earn on interest is known as compound interest. This can be demonstrated with simple math: if you have $100 and it earns 5% interest per year, you will have $105 at the end of the first year. You'll have $110.25 at the end of the second year. Compound interest accelerates the growth of your money because interest is calculated on both the accumulated interest over time and the original principal. Compounding can cause a snowball effect, in which the initial investments and the income earned from those investments grow in tandem.

So, Teresa borrowed $8,000 at a rate of 15.5%:

(Refer to the table given below)

Owe in 3 years: $12.519.69Rounding off: 12.520Teresa will owe $12.520 in 3 years.

Therefore, Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.

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Please hurry i need an answer

Answers

Answer:

sum = addition. p+157=171

Step-by-step explanation:

Answer: P + 157 = 171

Step-by-step explanation:

To mail a letter to Vienna, Austria the post office charges a flat rate of $8.00 and an additional $0.75 for every ounce the letter weighs. The cost of mailing a letter is
determined by the equation y = 0.75x+8.00, where y is the cost of the postage and x is the weight of the letter in ounces.
Step 2 of 2: Use the graph to estimate to the nearest quarter of a dollar ($0.25) the cost to send a letter that weighs 5 ounces.
Enable Zoom/Pan
Price for Postage
15
10
S
5
10
Weight (oz)
15

Answers

The cost to send a letter that weighs 5 ounces is $11.75.

Flat rate = $8.00

Charges on every ounce = $0.75

Given equation :

y = 0.75x + 8.00

'y' = Cost of the postage

'x' = Weight of the letter in ounces

According to the question we can determine the cost of mailing a letter with the help of given equation (y = 0.75x + 8.00).

We have given that the weight of letter that need to send is 5 ounces.

So, x = 5

Lets find the cost of postage,

y = 0.75x + 8.00

y = (0.75 × 5) + 8.00

y = 3.75 + 8.00

y = $11.75

Hence, it will take $11.75 to mail a letter or we can say cost of postage.

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How is the product of 3 and -2 shown using integer tiles?

Answers

Answer:

C) 3 sets of -2 tiles

Step-by-step explanation:

Its -2 three times, making it -6

If you multiply a positive and negative it is always negative

1. What is the sum of three thousand two hundred and forty seven hundredths, and thirteen and seven
hundred ninety-nine thousandths?
A. 3,247
B. 13,790
C. 213.790
D. 3,214.269

Answers

Answer: i think it is d but im not sure

Step-by-step explanation:

3rd grade math
A grocer puts cans
in 5 rows. Each
row has 3 cans.
The next day, 2 of
the cans are sold.
How many cans
are left?
A. 3
B. 6
C. 9
D. 13

Answers

the answer to this question is D. 13!

The answer is D

5x3-2= 13

At Acme Supermarket there are 12 full-time employees; 10 of them earn $12 per hour each, and the assistant manager and manager make $18 and $20 per hour respectively. What is the average rate of pay for the 12 employees? What is the median rate of pay? Which do you think is the better summary model to represent the pay rate of Acme’s employees?

Answers

Answer:

Average salary 13.16 120 + 18 + 20/12

At the end of a snow storm, Emily saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 15 inches of snow on the lawn when the storm ended and after 4 hours, the depth of snow was down to 12 inches. Write an equation for S,S, in terms of t,t, representing the depth of snow on Emily's lawn, in inches, tt hours after the snow stopped falling.

Answers

The equation that represents the depth of snow on Emily's lawn t hours after the snow stopped falling is

S = 15 - 0.75t

Writing an equation

From the question, we are to write an equation for S, in terms of t, that represents the depth of the snow on Emily's lawn, t hours after the snow stopped falling

From the given information,

"There was a depth of 15 inches of snow on the lawn when the storm ended"

and

"after 4 hours, the depth of snow was down to 12 inches"

That is,

The snow has reduced by 15 - 12 inches after 4 hours

15 - 12 = 3

Thus,

The snow has reduced by 3 inches after 4 hours

Now,

If the snow reduced by 3 inches after 4 hours,

Then,

The snow will reduce by x inches after 1 hour

x = (3×1)/4

x = 3/4 inches

x = 0.75 inches

This means the snow reduces by 0.75 inches every hour.

Now,

After t hours, the snow would have reduced by 0.75t

Thus, the depth of the snow, S, after t hours will be

S = 15 - 0.75t

Hence, the equation that represents the depth of snow on Emily's lawn t hours after the snow stopped falling is

S = 15 - 0.75t

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Henry bought a bag of 5 onions for a total cost of $4.75. At that rate, how
much would Henry pay for 12 onions?
A. $ 9.75
B. $11.40
C. $11.75
D. $16.75

Answers

B. Henry would pay $11.40 for 12 onions. To find out how much 1 onion is, divide $4.75 by 5 and you will get $0.95. Then times $0.95 by 12. So in the end, Henry would pay $11.40 for 12 onions.

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $20. For one performance, there were 45 tickets sold in all, and the total amount paid for them was $1125. How many tickets of each type were sold?

Answers

By solving a system of equations, we conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.

How many tickets of each type were sold?

Let's define the variables that we will be using:

x = number of advance tickets sold.y = number of same-day tickets sold.

We can write the system of equations:

x + y = 45

x*35 + y*20 = 1125

Isolating x on the first equation we get:

x = 45 - y

Repacing that in the other equation we get:

(45 - y)*35 + y*20 = 1125

1,575 - y*15 = 1125

1,575 - 1125 = y*15

(1,575 - 1125)/15 = y = 30

Then:

x = 45 - y = 45 - 30 = 15

We conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.

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Which type of compound inequality is 3|y+7|-16>5

-union
-hole
-disjunction
-intersection

Answers

The type of the compound inequality 3|y+7| - 16 > 5 is an intersection

How to determine the type of the compound inequality?

The compound inequality is given as

3|y+7| - 16 > 5

Add 16 to both sides of the inequality

So, we have

3|y+7| > 21

Divides both sides by 3

So, we have

|y+7| > 3

When the above inequality is solved, the region between the boundaries are shaded

This represents an intersection

Hence, the type of the compound inequality 3|y+7| - 16 > 5 is an intersection

Answers

Mars is half as big as Earth and that they each have an equal amount of dry land surface to determine by how much the circumference of the Earth is larger than that of Mars.

we need D(Earth) / D(Mars).

D(Earth) / D(Mars) = 1.2763 x 10⁴km/6.8 x 10³ km ≈ 1.9

D(Earth) / D(Mars) ≈ 1.9

The fifth-largest planet in our solar system by radius, the Earth has a circumference of 3,959 miles.

The other seven planets are joined by Earth and Mars. These two planets in our solar system share some geological characteristics, such as the fact that Mars, the seventh-largest planet in our solar system, has a radius of 2,106 miles. There are a few distinctions between Mars and Earth, though.

Hence, these planets differ in terms of their sizes, atmospheres, and temperatures.

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Solve for g.
9g - 8g - 1 = 16
g=

Answers

9g-8g-1=16

g-1=16

g=17

Margaret uses 1 3/4 teaspoons of key lime zest to make 12 like cupcakes. She wants to make 30 cupcakes. How much key lime zest will margaret use?

Answers

The number of teaspoons of key lime zest to make 30 cupcakes is

35/8 or 4 3/8

Given,

Margaret uses 1 3/4 teaspoon of key lime zest to make 12 cupcakes.

She wants to make 30 cupcakes.

We need to find how much key lime zest will Margaret use.

How to compare given two units?

Example:

1 bag = N mango

Then to find the number of mangoes in 5 bags we need to multiply 5 on both sides.

5 bags = 5 x N mangoes.

We have,

1 3/4 teaspoons of key lime zest = 12 cupcakes

7/4 teaspoons of key lime zest = 12 cupcakes

7/4 = 12 cupcakes

Multiply 30 on both sides.

7/4 x 30 = 30 x 12 cupcakes

Divide both sides by 12.

7/4 x 30/12 = 30 cupcakes

35 / 8 = 30 cupcakes

4 3/8 = 30 cupcakes

This means,

35/8 or 4 3/8 teaspoons of key lime zest to make 30 cupcakes.

Thus the number of teaspoons of key lime zest to make 30 cupcakes is

35/8 or 4 3/8.

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Write an inequality that represents the statement “x is greater than -2 and less than 8.”

Answers

The inequality which represents the statement given in the task content; x is greater than -2 and less than 8 is; -2 < x < 8.

Which inequality correctly represents the statement as given in the task content?

It follows from the task content that the inequality which represents the statement given in the task content is to be determined.

First each section of the statement must be highlighted as follows;

x is greater than -2 can be written as;

x > -2 or -2 < x

x is less than 8 can be written as:

x < 8.

Therefore, the compound inequality which represents the word phrase is; -2 < x < 8.

Ultimately, The inequality which represents the statement given in the task content; x is greater than -2 and less than 8 is; -2 < x < 8.

Answers

The value of y in the given equation is 19/20

Solving linear equations

From the question, we are to determine the value of y in the given equation

The given equation is

3 1/3(y + 1 1/8) = 6 11/12

First, convert the the fractions into improper fractions

10/3(y + 9/8) = 83/12

Multiply both sides of the equation by 3/10

3/10× 10/3(y + 9/8) = 3/10× 83/12

y + 9/8 = 3/10× 83/12

y + 9/8 = 83/40

y = 83/40 - 9/8

y = (83 - 45)/40

y = 38/40

y = 19/20

Hence, the value of y in the given equation is 19/20

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You play a board game with your little brother. You pick a card that sends you back five spaces. On your next turn, you must move back three more spaces. On your third turn, you get to move forward three spaces. Which expression best shows how you could find your new spot on the game board? CLEAR CHECK -5 + (-3) + (-3) -5 + 3 + 3 -5 + (-3) + 3 5 + (-3) + (-3)

Answers

Expression best shows above condition is -5-3+3

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that while playing board game we pick a card that sends us back five spaces. On our next turn, we must move back three more spaces. On our third turn, we get to move forward three spaces.

and, expression best shows how we could find our new spot on the game board will be :

for first move, five spaces back means = -5

for second move, three spaces back means = -3

and for third move, three spaces move forward = +3

combining all the three terms we get : -5-3+3

Therefore, expression best shows above condition is -5-3+3

Answers

Answer:

this makes no sense but I think the answer is 38 inches

Step-by-step explanation:

Yolanda opened a retirement account earning 5.5% interest per year, compounded monthly. She deposited $100 each month. Assume that no other deposits or withdrawals were made. Answer the following, writing your answers to the nearest dollar.

Answers

The balance in dollars and cents in Yolanda's account at the end of 4 years is $5,355.29

What is the future value of an ordinary?

An ordinary annuity is the one where the monthly deposit occurs at the end of each month rather than at the beginning of the months such its future value based on 5.5% annual interest rate can be determined thus:

FV=PMT*(1+r)^N-1/r

FV=balance in dollars and cents in Yolanda's account at the end of 4 years=unknown

PMT=monthly deposit=$100

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly deposits in 4 years=4*12=48

FV=$100*(1+0.00458333333333333)^48-1/0.00458333333333333

FV=$5,355.29

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Missing question:

What was the balance in dollars and cents in Yolanda's account at the end of 4 years?

Solve w(2v + 9) = 3w(v - 1) given that w(v) = 3v + 2.
Enter the exact answer.
V=

Answers

After solving the given equation the two values of V are (v = 12) and

(v = -2/3).

What exactly are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

So, substitute 'w = 3v + 2' in w(2v + 9) = 3w(v - 1):

w(2v + 9) = 3w(v - 1)3v + 2(2v + 9) = 3(3v + 2)(v - 1)3v(2v + 9) + 2(2v + 9) = 3[3v(v - 1) + 2(v - 1)]6v² + 27v + 4v + 18 = 3(3v² - 3v + 2v - 2)6v² + 31v + 18 = 3(3v² -1v - 2)6v² + 31v + 18 = 9v² -3v -69v² - 6v² -3v - 31v - 6 - 18 = 03v² - 34v - 24 = 03v² - v ( 36 - 2 ) - 243v² - 36v + 2v - 243v (v - 12) + 2 (v - 12)(v - 12) and (3v + 2)Values: (v = 12) and (v = -2/3)

Therefore, two values of v are (v = 12) and (v = -2/3)

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