Mathematics High School

Determine the intervals on which the function is increasing, decreasing, and constant.

A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)

Answers

Answer 1

Answer:

The answer is D

Step-by-step explanation:

Check to see when the graph is increasing and decreasing from left to right.

It is decreasing from x = -5 to x = -3 or (-5,-3) These look like a points but are not. They are intervals.

Then, it increases from x = -3 to x = 0 or (-3,0)

Then, it stays constant from x = 0 to x = 2 or (0,2)

Lastly, it decreases from x - 2 to x = 5 or (2,5)

To summarize, the graph is increasing from (-3,0). Decreasing on (-5,-3) and (2,5). and constant on (0,2)

The only option that fits these conditions is D.

Related Questions

25 lbs of potatoes cost $100. How much
would 15 lbs cost?

Round the answer to two decimal digit

Answers

The answer is $60 because each lbs of potatoes is worth $4.00 so $4.00 times 15 is 60

The diameter D of a sphere is 12.4 m. Calculate the sphere's surface area A.
Use the value 3.14 for , and round your answer to the nearest tenth.

Answers

The sphere has a surface area of 482.8064 square meters

How to determine the surface area of the sphere?

From the question, the given parameters are:

Diameter, D = 12.4 meters

π = 3.14

The surface area of the sphere is calculated using the following formula

S = 4π(D/2)²

Substitute the given parameters in the above formula

So, we have

S = 4 * 3.14 * (12.4/2)²

Evaluate the exponent

This is represented as

S = 4 * 3.14 * 38.44

Evaluate the product

This is represented as

S = 482.8064

Hence, the surface area of the sphere is 482.8064 square meters

Answers

Hello!

So, we are given the following to solve:

[tex]-m=9[/tex]

To solve this, simply divide both sides by -1.

[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]

Then, simplify the expression and you have your solution.

[tex]m=-9[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

Answer:

m= -9

Step-by-step explanation:

Divide both sides by -1

[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]

Simplify m = - 9

7
1
-5
35
-4 24
-3 15
-2 8
-1 3
0 0
1 -1
Match the average rates of change of f(x) to the corresponding intervals.
-7
-4
300
[-5, -1]
(-4,-1]
[-3, 1]
-2,1]

Answers

The rates of changes of the given function for the corresponding intervals are: [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.

What is function?

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The rate of change of a function can be calculate using the formula:

[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Putting the value from the question:

given [x₁, x₂] = [-5, -1]

f(-5) = 35 , f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-35}{-1 -(-5)}[/tex]

R = -32/4

R = -8

given [x₁, x₂] = [-4, -1]

f(-4) = 24, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-24}{-1 -(-4)}[/tex]

R = -21/3

R = -7

given [x₁, x₂] = [-3, -1]

f(-3) = 15, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-15}{-1 -(-3)}[/tex]

R = -12/2

R = -6

given [x₁, x₂] = [-2, -1]

f(-2) = 8, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-8}{-1 -(-2)}[/tex]

R = -5/1

R = -5

To know more about function, go to link

https://brainly.com/question/10439235

#SPJ13

Mr. Stewart wants to cut a board that is 34 inches long into four pieces that are the same length. How long will each
board be after he cuts them?
08.0 inches
8.2 inches
8.4 inches
O 8.5 inches

Answers

The pieces he cuts would be 8.5 inches

Identifying Variables and Writing Functions Practice . A function describes how a dependent variable changes with respect to one or more independent variables. When there are only two variables, they are often summarized as an ordered pair with the independent variable first: (independent variable, dependent variable) The dependent variable is a function of the independent variable. If x is the independent variable and y is the dependent variable, write the function as y = f(x) Related Quantities. Write a short statement that expresses a possible relationship between the variables. Example: (age, shoe size) Solution: As a child ages, shoe size increases. Once the child is full-grown, shoe size remains constant. 1. (volume of a gas tank, cost to fill the tank) 2. (time, price of a Ford sedan), where time represents years from 1975 to 2017

Answers

Let's begin with what we know:

For an ordered pair, we have (independent variable, dependent variable)

For example, when x is the independent variable & y is the dependent variable, we have (x, y)

y = f(x)

We are to write a short statement that expresses a possible relationship between the variables below:

1. (volume of a gas tank, cost to fill the tank)

Volume of gas is the independent variable & Cost to fill the tank is the independent variable. That means that:

As the volume of the gas tank increases. the cost of filling it increases. Once the volume of the gas tank is filled, the cost to fill the tank is at its maximum

2. (time, price of a Ford sedan), where time represents years from 1975 to 2017

Time is the independent variable & price of a Ford sedan is the independent variable. That means that:

As the time lapses from 1975 to 2017, the price of the Ford sedan depreciates/reduces.

6. Create a systems of inequalities to represent the graph below

Answers

System of inequalities

We are given the graph where two lines represent the solution of a system of inequalities.

The solution is the double-shaded region of the graph.

We need to find the equation of the blue line and the red line and then convert them to inequalities.

Let's start with the blue line. We need to find two clear points through which it passes. These are (0,6) and (2,0). Now we write the equation of the line when knowing two points (the point-point form):

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex][tex]\begin{gathered} \displaystyle y-6=\frac{0-6}{2-0}(x-0)=-3x \\ \text{Adding 6:} \\ y=-3x+6 \end{gathered}[/tex]

For the red line, the points are (0,0) and (2,2):

[tex]\begin{gathered} y-0=\frac{2-0}{2-0}(x-0)=x \\ y=x \end{gathered}[/tex]

Now we have the equations of the lines, we must convert the equation to inequality by inserting one of these symbols instead of the equal sign:

> ≥ < ≤

For the blue line, the equation of the line is:

y = -3x + 6

Testing the origin (0,0):

0 = 0 + 6

0 = 6

To convert this to a true inequality we must replace the = for < or ≤

Since the blue line is solid, the points on the line belong to the solution, thus the first inequality is:

y ≤ -3x + 6

Now for the red line. The equation is

y = x. Let's test the point (2,1)

1 = 2

We must use the sign ≤ to make the expression true, thus the second inequality is:

y ≤ x

Thus, the system of inequalities is:

y ≤ -3x + 6

y ≤ x

(10, 10) А (2, 4) Find point C so that that the ratio of length Ad to the length of CB is 3:1

Answers

ANSWER

[tex](8,8.5)[/tex]

EXPLANATION

When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:

[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+my_1}{m+n})[/tex]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.

Therefore, we have that:

[tex]\begin{gathered} m=3;n=1 \\ (x_1,y_1)=(2,4) \\ (x_2,y_2)=(10,10) \end{gathered}[/tex]

Therefore, the coordinates of point C are:

[tex]\begin{gathered} (\frac{3\cdot10+1\cdot2}{3+1},\frac{3\cdot10+1\cdot4}{3+1}) \\ (\frac{30+2}{4},\frac{30+4}{4}) \\ (\frac{32}{4},\frac{34}{4}) \\ (8,8.5) \end{gathered}[/tex]

Those are the coordinates of C.

Julia just let a new candle and then let it burn all the way down to nothing. The candle
burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an
equation for L, in terms of t, representing the length of the candle remaining
unburned, in inches, t hours after the candle was lit.
L=

Answers

Answer: L= 9-.75x

Step-by-step explanation: since it starts at 9 inches tall and is melting at .75 inches per hour, it's going to be the initial length, 9, minus the rate, .75, times the time/hours past, so x

Hi, can you help me to solve this problem, please !!!

Answers

Remember that

The y-intercept is the value of y when the value of x=0

In this problem

we have the equation

y=7x^2+4

For x=0

substitute

y=7(0)^2+4

y=4

the y-intercept is (0,4)

What is the value of the expression below when z=3?
10z^2 +7z+4

Answers

The value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115

The expression is

[tex]10z^2[/tex]+7z+4

The expression is defined as the statements that have a minimum of two terms containing numbers or variables , connected by an operator in between. The operator maybe addition, subtraction, division, multiplication etc..

The expression is

[tex]10z^2[/tex]+7z+4

The value of z = 3

Substitute the value of z in the given expression

= [tex]10(3)^2[/tex]+ 7×3 + 4

= 10×9 + 21 + 4

Multiply the terms first

= 90 + 21 + 4

Add them together

= 115

Hence, the value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115

Learn more about expression here

brainly.com/question/1619296

#SPJ1

Fighting fires is a profession that is really heating up. The average firefighter works 160 hours a month and make $4,090 for the month. If you only work 32 hours in a week, how much will you make?

Answers

Working 32 hours a week will fetch you $818

How to calculate the amount you will make?

From the question, the given parameters are:

Number of hours = 160

Earnings in a month = $4090

Start by calculating the unit rate

This is calculated using the following unit rate formula

So, we have

Unit rate = Earnings in a month/Number of hours

Substitute the known values in the above equation

So, we have

Unit rate = 4090/160

Evaluate the quotient

Unit rate = 25.5625

For 32 hours, the total earnings is

Total = Unit rate x Number of houts

So, we have

Total = 25.5625 x 32

Evaluate

Total = 818

Hence, you will earn $818 weekly

Answers

Answer:

1.2

Step-by-step explanation:

2x-5y = 16 solve for y

Answers

[tex]\frac{2(x-8)}{5}[/tex] = y

To Solve: value of y

Given: 2x-5y=16

Solution: The solution to this problem involves the following steps:

2x-5y-16=0

2x-16=5y

[tex]\frac{2x-16}{5}[/tex] = y

[tex]\frac{2(x-8)}{5}[/tex] = y

Answer: The final answer is : [tex]\frac{2(x-8)}{5}[/tex] = y

Learn more about equations here: https://brainly.com/question/2030026

Pls help solve all 3 questions

Thank you :)

Answers

Answer:

Q18: x = 21, y = 15

Q19: x = 16, y = 10

Q20: x = 24, y = 19

Step-by-step explanation:

Q18:

(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)

9x - 9 = 180

9x = 189

x = 21

11y - 32 = 6x + 7 (vertically opposite angles)

11y - 32 = 6(21) + 7

11y - 32 = 133

11y = 165

y = 15

Q19:

8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)

3x = 48

x = 16

(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)

8(16)-14 + (5y + 16) = 180

114 + 5y + 16 = 180

5y + 130 = 180

5y = 50

y = 10

Q20:

47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)

5x + 60 = 180

5x = 120

x = 24

5y - 23 = 3x (corresponding angles)

5y - 23 = 3(24)

5y - 23 = 72

5y = 95

y = 19

XYZ has coordinates X(2, 3), Y(1, 4), and Z(8, 9). A translation maps X to X′(4, 8). What are the coordinates for Z′? *

Answers

Answer:

Z'(10, 14)

Explanation:

Taking into accoun that the vertex point X(2, 3) is mapped to X'(4, 8), we can say that the translation rule is:

(a, b) ----> (a + 2, b + 5)

Because

X(2, 3) ----> (2 + 2, 3 + 5)

----> X'(4, 8)

So, using this rule, we can find the coordinates for Z' as:

Z(8, 9) ----> (8 + 2, 9 + 5)

----> Z'(10, 14)

Therefore, the answer is Z'(10, 14)

The sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, write and solve a compound inequality to show the possible heights of the third tree.

Answers

The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.

How to calculate the value?

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤

Let the height of the third tree be x.

By the given condition, this will be:

8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42

The first relation will give x ≥ 32 - 24 = x ≥ 8

The second relation will give:

8 + 16 + x ≤ 42

24 + x ≤ 42

x ≤ 42 - 24

x ≤ 18

The inequality is 8 ≤ x ≤ 18.

Learn more about inequalities on:

brainly.com/question/24372553

#SPJ1

If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.

What is Inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let height of the third tree be x.

By the given condition

The sum of three palm tree heights range from 32 to 42 feet

8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42

Solve these inequalities

8 + 16 + x ≥ 32

24+x ≥ 32

x≥ 32-24

x≥ 8

and 8 + 16 + x ≤ 42

24+ x ≤ 42

x≤ 42-24

x ≤ 18

Hence the inequality is 8 ≤ x ≤ 18.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

What number is five times the first number. The third number is 100 more than the first number. Of the sound of three numbers is 490, find the numbers

Answers

Answer:

The three numbers are:

4.62,

23.1, and

462.2

Step-by-step explanation:

Let X be the "first number."

B = What number is five times the first number: 5X

C = third number is 100 more than the first number: 100X

The sum of all three is 490: X + B + C = 490

----

X + B + C = 490

X + 5X + 100X = 490

106X = 490

X = 4.622

Check:

X = 4.622

B = 5X = 23.11

C = 100X = 462.2

Check:

Sum (4.622 + 23.11 + 462.2) = 490

Graph the equation after rewriting it in slope-intercept form. 9x+3y=18

Answers

The equation of a line in the slope intercept form is expressed as

y = mx + c

The given equation is

9x + 3y = 18

We would rearrange it so that it takes the form of the slope intercept equation shown above.

We would divide both sides of the equation by 3, we have

9x/3 + 3y/3 = 18/3

3x + y = 6

Subtracting 3x from both sides of the equation, we have

3x - 3x + y = 6 - 3x

y = 6 - 3x

The slope intercept form is

y = - 3x + 6

To plot the graph, we would substitute values of x into the equation to get corresponding y values. These x and y values would be plotted on the x and y coordinates of the graph. We have

For x = - 2, y = 6 - 3(- 2) = 6 + 6 = 12

For x = - 1, y = 6 - 3(-1) = 6 + 3 = 9

For x = 0, y = 6 - 3(0) = 6 - 0 = 6

For x = 1, y = 6 - 3(1) = 6 - 3 = 3

For x = 2, y = 6 - 3(2) = 6 -6 = 0

The graph is shown below

For each of the following quadrilaterals, select all the properties that must be true.

Answers

Rhombus have right angle all sides are congruent parallelogram have right angle and two pairs of parallel sides
Rectangle four right angle two pair of parallel sides

Answer:

Rhombus: All sides congruent, two pairs of parallel sides

Parallelogram: Two pairs of parallel lines

Rectangle: 4 right angles, Two pairs of parallel sides

Step-by-step explanation:

What is the solution to 4x-5(2x-1) <= 7(2x+3)

Answers

[tex]4x-5(2x-1)\le7\mleft(2x+3\mright)[/tex][tex]\begin{gathered} 4x-10x+5\le14x+21 \\ -6x+5\le14x+21 \\ -6x-14x\le21-5 \\ -20x\le16 \\ x\ge\frac{16}{-20} \\ x\ge-\frac{4}{5} \end{gathered}[/tex]

6) Bill found a pair of jeans that cost $35.00. If he had a 20%-off coupon, how much would the
jeans cost?

Answers

20% of 35 is 7, so you would be getting the jeans for 28, not including tax

Solve the compound inequality. 2x-4 > 8 or 3x-1 < -10
-3 < x < 6

x > 6 or x < -3

x > 2 or x < -3

x < 6 or x < -3

Answers

The solution to the compound inequality is x > 6 or x < -3

How to solve compound inequality?

An inequality is a mathematical expression that has <, >, ≤ and ≥.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality as follows:

2x - 4 > 8 or 3x - 1 < - 10

2x - 4 > 8

add 4 to both sides of the inequality

2x - 4 + 4 > 8 + 4

2x > 12

divide both sides by 2

x > 12 / 2

x > 6

3x - 1 < - 10

add 1 to both sides of the inequality

3x - 1 + 1 < - 10 + 1

3x < - 9

divide both sides by 3

x < -9 / 3

x < -3

Therefore, x > 6 or x < -3

learn more on inequality here: https://brainly.com/question/23012774

#SPJ1

The solution to the compound inequality will be; x > 6 or x < -3

What is inequality?

Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.

A compound inequality is defined as an inequality that combines two simple inequalities.

Therefore, solve the compound inequality that will be;

2x - 4 > 8 or 3x - 1 < - 10

2x - 4 > 8

Then add 4 to both sides of the inequality so,

2x - 4 + 4 > 8 + 4

2x > 12

Now, divide both sides by 2

x > 12 / 2

x > 6

3x - 1 < - 10

Again, add 1 to both sides;

3x - 1 + 1 < - 10 + 1

3x < - 9

Then divide both sides by 3;

x < -9 / 3

x < -3

Therefore, solution to the compound inequality is; x > 6 or x < -3

learn more on inequality here:

brainly.com/question/23012774

#SPJ1

Complete the table and use the results to find the indicated limit.

Answers

Given the function:

[tex]k(x)=\frac{x^3-x-6}{x-2}[/tex]

when x = 1.9

[tex]k(x)=\frac{1.9^3-1.9-6}{1.9-2}=\frac{-1.041}{-0.1}=10.41[/tex]

when x = 1.999

[tex]k(x)=\frac{1.999^3-1.999-6}{1.999-2}=\frac{-0.0109944}{-0.001}=10.994001[/tex]

When x = 2.001

[tex]k(x)=\frac{2.001^3-2.001-6}{2.001-2}=\frac{0.011006}{0.001}=11.006[/tex]

When x = 2.1

[tex]k(x)=\frac{2.1^3-2.1-6}{2.1-2}=\frac{1.161}{0.1}=11.61[/tex]

so, the limit of the function k(x) = 11

The answer is option A. 11

Can someone help me out (I will give branliest)

Answers

Answer: Emma > Amelia > Brandon > Celesle > Damian

Step-by-step explanation:

We convert all the fractions to decimals (2 decimals).

Amelia 4.35 lbs

Brandon [tex]4\frac{1}{3}= \frac{12}{3} +\frac{1}{3} =\frac{13}{3}[/tex] ≈ 4.33 lbs

Celesle 4.2 lbs

Damian √15 ≈ 3.87 lbs

Emma [tex]4\frac{2}{3} =\frac{12}{3} +\frac{2}{3} =\frac{14}{3}[/tex] ≈ 4.67 lbs

4.47 lbs > 4.35 lbs > 4.33 lbs > 4.2 lbs > 3.87 lbs

Emma > Amelia > Brandon > Celesle > Damian

Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.

Answers

Answer:

Step-by-step explanation:

5) Naomi painted 16.5 square feet of a mural at a rate of 2 square feet per hour. Calire painted 7.5 square
feet of the mural at a rate of 4 square feet per hour. If they continue to paint at the same rates, how many
more hours will it take until Naomi and Claire have painted equal areas of the mural?

Answers

Answer: 4.5

Step-by-step explanation:

We need to find the amount of time until Calire paints a total of 9 more square feet.

Since the difference in their rates is 2 square feet per hour, it will take 9/2 = 4.5 more hours.

The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy. The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
Which equation could you use to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet?

Answers

The equation which can be used to find the area of the place where guests wait for the ride if the area of the canopy is 7600 square feet is:

2a+100=7600.

Given, The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy.

The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.

let the area of the place where guests wait be represented by 'a'.

the canopy covers the area = 2a + 100

total area of the canopy = 7600

equation used to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet = ?

⇒ 2a + 100 = 7600

arrange the like terms.

⇒ 2a = 7600 - 100

calculate the difference.

⇒ 2a = 7500

⇒ a = 7500/2

⇒ a = 3750

Hence the area of the place where guests wait is 3750 square feet.

Learn more about Linear equations here:

brainly.com/question/26310043

#SPJ1

Which two county libraries charge the same penalty per week

Answers

Cumberland and Lincoln

An economy size car can travel 32 miles for each gallon of gasoline. The function d(g) = 32g represents the distance traveled in miles, d(g), that the car can travel with g gallons of gasoline. Find d(30).

*Type in your answer.

d(30) = miles

Answers

The number of miles to drive for 30 gallons is 960 miles

How to determine the function value?

From the question, the function definition is given as

d(g) = 32g

Where g represents the number of gallons and d represents the distance

The function value to calculate is given as

d(30)

This means that we calculate the number of miles to drive for 30 gallons

So, we have

d(30) = 32(30)

This gives

d(30) = 32 x 30

Evaluate the product

d(30) = 960

Hence, the function value is d(30) = 960