For f(x)=3x-1 find the average rate of change on the interval [0,3]

Answers

Answer 1

For a linear function, the average rate of change is the same everywhere. It is the slope of the function, the x-coefficient.

The average rate of change is 3.

_____
(f(3) -f(0))/(3 -0) = (8 -(-1))/3 = 9/3 = 3

Answer 2

The average change is 3

Related Questions

A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
-When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84.
-When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A. (12, 20)
B. (15, 18)
C. (18, 15)
D. (20, 12)

Note: Please show work. My teacher checks it.

Answers

The answer is B. (15,18)

Solution:

First, let's set the variables first.

X = dollars per hour to clean the floor
Y = dollars per hour to clean the rest of the house

For the first statement, "2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84"
We can put it into an equation.
2X + 3Y = 84 ⇒ equation 1

For the first statement, "1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87'
X + 4Y = 87 ⇒ equation 2

Multiply first equation 2 by 2 to make the coefficient of both equations 1 and 2 the same.

Using elimination method in solving for x and y,

   (equation 1)   2X + 3Y = 84
   (equation 2)   2(X + 4Y) = 87
2X + 8Y = 174  ⇒ equation 3

Next, subtract equation 3 from equation 1.
  2X + 3Y = 84
- (2X + 8Y = 174)
-------------------------
- 5Y = -90
Y = 18

Find X when Y = 18
@ equation 1 : 2X + 3Y = 84
2X + 3(18) = 84
2X + 54 = 84
2X = 84 - 54
2X = 30
X = 15

The answer is in ordered pairs of cleaning the floors and to clean the rest of the house. So, in the form (X,Y).

Answer: (15,18)

The hourly charges to clean floors and to clean the rest of the house are $15 and $18, respectively. We determine this by setting up a system of equations from the provided scenarios and solving for x and y.

To solve for the hourly charges to clean floors (x) and to clean the rest of the house (y), we need to set up two equations based on the information provided:

2x + 3y = 84 (from the first scenario)1x + 4y = 87 (from the second scenario)

Let's solve this system of equations step by step.

Step 1: From the second equation, we can express x in terms of y:
x = 87 - 4y

Step 2: Substitute this expression for x in the first equation:
2(87 - 4y) + 3y = 84

Which simplifies to:
174 - 8y + 3y = 84

Combining like terms gives us:
-5y = -90

Step 3: Solve for y:
y = 18

Step 4: Now, plug the value of y back into the expression for x:
x = 87 - 4(18)
x = 15

Therefore, the hourly charges to clean floors and to clean the rest of the house are $15 and $18 respectively, which corresponds to option B. (15, 18).

what is the slope of the line through (6,9) and (7,1)

Answers

Slope of (6, 9) & (7, 1)

To find the slope, we use the equation : m = y₂-y₁ / x₂-x₁

**Remember : m = slope**

Let's say that (6, 9) is our first set of points, and (7, 1) is our second.

If those are our first and second points, then we now know this :

x₁ = 6, x₂ = 7, y₁ = 9, y₂ = 1

Now that we know that, we can simply plug those points into our slope equation.

m = y₂ - y₁ / x₂ - x₁

m = (1 - 9) / (7 - 6 )

Simplify.

m = -8 / 1

Simplify.

m = -8

So, our slope is -8.

~Hope I helped!~

the spaceship travels around the sun at a speed of 12.6 miles per second. How far will it travel in 45 seconds?

Answers

12.6/1 × m/45

12.6 x 12.6 = 567 miles

I REALLY NEED HELP ON THIS!!! HELP ASAP PLS!!! EXTRA POINTS TO THE FIRST PERSON WHO ANSWERS!!

adrian and rory start comic book collections at the same time. adrian started with 12 comic books and buys 4 more each month. rory started with 8 comic books and buys 4 more each month. will they ever have the same number of comic books? if so, how many months? use an equation to justify your answer

Answers

doing an X and Y table i do not see that they will have the same amount. Adrian will always have 4 more comic books than Roy

No.

4x + 12
4x + 8

Arian will always have 4 more comic books than Rory.

What is x+2=-x+-2? Can you plz do it step by step!

Answers

To solve this equation, we are going to isolate the variable x. To do this, we are going to begin by adding x to both sides because this will cancel out the negative x on the right side of the equation.

x + 2 + x = -x + x - 2
When we combine like terms, we get:
2x + 2 = -2
Next, we will try to continue to isolate the variable by subtracting 2 from each side to get the 2x term on the left by itself.
2x + 2 -2 = -2 -2
When we combine like terms, we get:
2x = -4
Finally, to get x by itself we must divide by 2 to undo the multiplication of the coefficient of the term 2x.
2x/2 = -4/2
When we perform the division, we get:
x = -2
Therefore, x = -2.
We can check this answer by plugging it back into the original equation. Our answer is verified because 0=0.
Your answer is that x = -2.
Hope this helps!

1/4X^2 - 3/4X^2 =0
Solve each equation. Factor and use the zero product property to solve. Show all work algebraically.

Answers

1/4x^2 - 3/4x^2 = 0

-1/2x^2 = 0

x * x = 0

x = 0

One ounce is about the same as 0.06 pound. What is 0.06 written as a fraction?

Answers

Answer:

[tex].06 = \frac{6}{100} = \frac{3}{50} [/tex]

2 trifles cost 7 pounds how much does 6 cost

Answers

2/7=6/x
2x=42
x=21

6 TRIFLES WILL COST 21 pounds, since we can set up a proportion and cross multiply.

Cost of 6 trifles is 21 pound

Given that;

Cost of 2 trifles = 7 pound

Find:

Cost of 6 trifles

Computation:

Cost of 6 trifles = 6[7 / 2]

Cost of 6 trifles = [3][7]

Cost of 6 trifles = 21 pound

Learn more:

https://brainly.com/question/11763415?referrer=searchResults

A pitcher needs more than one pitch to be effective. Dizzy uses his changeup only half as much as his fastball, and to save his arm, he throws a slider a third as much as his fastball. In a 110-pitch game, how many sliders would he throw?

Answers

Answer: Dizzy will throw 20 sliders in his 110 pitch game.

To write an equation, let x be the number of fastballs that he throws.

Therefore, the number of change-ups will be x/2 and the number of sliders will be x/3.

Now, add the equations together to get:
x/2 + x + x/3 = 110

Multiply the equation and solve to get:
3x + 6x + 2x = 660
11x = 660
x = 60

The number of fastballs is 60, dividing that by 3 gives us 20 sliders.

Final answer:

In Dizzy's 110-pitch game, he threw 20 sliders. The answer was found by setting up and solving algebraic equations based on the information given in the question.

Explanation:

This question is about using algebra to solve word problems. Let's denote the number of fastballs Dizzy throws as F, the number of changeups as C, and the number of sliders as S.

According to the question, Dizzy throws his changeup half as much as his fastball (C = 0.5F) and his slider a third as much as his fastball (S = F/3). We also know the total number of pitches (110) is the sum of F, C, and S pitches (110 = F + C + S).

We then substitute the expressions for C and S from our first two equations into our third equation to get: 110 = F + 0.5F + F/3. Solving this equation gives us F = 60. We substitute F = 60 into S = F/3 to find that Dizzy threw 20 sliders in the game.

Learn more about Algebraic Equations here:

https://brainly.com/question/953809

#SPJ2

Lorena has two pieces of ribbons. One piece is 3 meter 14 centimeter long. The other piece is 8 meters 24 centimeters long. How many centimeters of ribbon does Lorena have in all

Answers

Lorena has
3 meters=300 cm
1st piece=314 cm
8 meters=800 cm
2nd piece=824 cm
together=824+314=1138 cm or 11 meters and 38 cm
1m=100 cm

A is 60% of B , B is 30% of C , what percentage of C is A? show working out and circle the correct answer: 18%, 28%, 30%, 90%

Answers

The percentage answer is 30%

please help I have 2 pages to do!

Answers

what do you need help with? it helps us to know the question!

Can somebody please help me, I’m stumped. Please explain easily to

Answers

You want to find the unit rate...how many miles in one hour. To do this we just divide the distance she walks by the time it takes her to walk that distance.

[tex]\sf 2\dfrac{1}{2}\div\dfrac{3}{4}[/tex]

Convert the mixed number into an improper fraction. We do this by multiplying the denominator to the whole number, adding it to the numerator, which becomes our new numerator, and we keep the denominator the same:

[tex]\sf \dfrac{5}{2}\div\dfrac{3}{4}[/tex]

When dividing fractions we flip(the reciprocal) the one we're dividing by and multiply:

[tex]\sf \dfrac{5}{2}\times\dfrac{4}{3}[/tex]

Multiply the numerators and denominators together:

[tex]\sf\dfrac{20}{6}[/tex]

Convert it back to a mixed number. Six goes into twenty three times. 6 * 3 = 18. 20 - 18 = 2. So we have 3 wholes and 2 left over, or:

[tex]\sf 3\dfrac{2}{6}[/tex]

We can simplify this further, divide 2 to the numerator and denominator of the fraction:

[tex]\boxed{\sf 3\dfrac{1}{3}}[/tex]

Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sides KL, LM, MN, and NK.

Answers

L(1, -4)=(xL, yL)→xL=1, yL=-4
M(3, -2)=(xM, yM)→xM=3, yM=-2

Slope of side LM: m LM = (yM-yL) / (xM-xL)
m LM = ( -2 - (-4) ) / (3-1)
m LM = ( -2+4) / (2)
m LM = (2) / (2)
m LM = 1

The quadrilateral is the rectangle KLMN
The oposite sides are: LM with NK, and KL with NK
In a rectangle the opposite sides are parallel, and parallel lines have the same slope, then:
Slope of side LM = m LM = 1 = m NK = Slope of side NK
Slope of side NK = m NK = 1

Slope of side KL = m KL = m MN = Slope of side MN

The sides KL and LM (consecutive sides) are perpendicular (form an angle of 90°), then the product of their slopes is equal to -1:
(m KL) (m LM) = -1
Replacing m LM = 1
(m KL) (1) = -1
m KL = -1 = m MN

Answer:
Slope of side LM =1
Slope of side NK =1
Slope of side KL = -1
Slope of side MN = -1

Answer: its A

Step-by-step explanation:

Robbie, Jennie, Willie, and Kylie played a numbers game. Jennie picked a number but did not tell her friends. Robbie and Willie both picked a number as well, and Jennie described their numbers like this to Kylie.

Robbie picked a number that is nine more than four times Jennie's number.
Willie picked a number that is two less than three times Robbie's number.

Deciding to call her number, n, Jennie asked Kylie to write an expression that describes Willie's number.

Kylie came up with two expressions that equal Willie's number.

What are the equations?

Answers

Answer:

1. 3(4n+9)-2

2. 3*13n-2

Step-by-step explanation:(*)This symbol that looks like a little star means multiplication.

The two equations that describe Willie's number are W = 12J + 25 and W = 12J + 34

What is Expression?

An expression is combination of variables, numbers and operators.

Robbie's number = 4J + 9, where J is Jennie's number.

Now we can use this expression to find Willie's number:

Willie's number = 3(4J + 9) - 2 = 12J + 25

So one equation that describes Willie's number is:

W = 12J + 25

Kylie found another expression that equals Willie's number, so we can find it by solving for J in Robbie's expression and substituting it into Willie's expression:

Robbie's number = 4J + 9

4J = Robbie's number - 9

J = (Robbie's number - 9)/4

Substitute this expression for J into Willie's expression:

W = 12J + 25

W = 12[(Robbie's number - 9)/4] + 25

W = 3(Robbie's number - 9) + 25

W = 3(4J + 9 - 9) + 25 (substituting 4J + 9 for Robbie's number)

W = 12J + 34

So another equation that describes Willie's number is:

W = 12J + 34

Therefore, the two equations that describe Willie's number are W = 12J + 25 and W = 12J + 34

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ3

What is the area of a circle that has a circumference of 48 feet?

Answers

The area formula for a circle is
[tex]a = \pi(r)^{2} [/tex]
when r is radius.

The circumference formula is
[tex]c = 2(\pi)r[/tex]
Since you have the circumference, you can plug it in and solve for the circle's radius.
[tex]48 = 2(\pi)r[/tex]
[tex]24 = \pi(r)[/tex]
[tex] \frac{24}{\pi} = r [/tex]
Now that you have r, you can plug it into the area formula and find the area.
[tex]a = \pi( \frac{24}{\pi} )^{2} [/tex]
[tex]a = (24)^{2} [/tex]
[tex]a = 576[/tex]

A car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. What was the mean for the profits of the sales? A. $8,906.00 B. $9,819.40 C. $12,398.00 D. $10,375.00

Answers

The mean is the average
to find the average, first you add all the numbers together
10,126 + 9 999 + 12,398 + 12,007 + 4,567= 49,097
since you added five numbers together, you will divide by five
49,097 ÷ 5 = 9,189.40, so the answer is B

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by _______________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?

Answers

Final answer:

The triangles ABD and CDB are congruent by the Side-Angle-Side (SAS) postulate, leading to the conclusion that quadrilateral ABCD is a parallelogram.

Explanation:

The triangles ABD and CDB can be proved congruent by the Side-Angle-Side (SAS) postulate. Since side AB is parallel to side DC, the alternate interior angles angle ABD and angle BDC are congruent. With both triangles sharing side DB and having equal sides AB and DC, the two triangles satisfy the conditions of the SAS postulate.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) principle, angles DBC and ADB are congruent as well as sides AD and BC. Since angle DBC and angle ADB form a pair of alternate interior angles, this implies that AD is congruent and parallel to BC. This leads to the conclusion that quadrilateral ABCD is a parallelogram, characterized by its opposite sides being equal and parallel.

Please helpp!! Due soon

Answers

Answer:
The area of triangle QUV is 24 square feet

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

Explanation:

Segment TV is the base of the green parallelogram PRTV
The height is segment RS which is 8 ft. This is marked as the perpendicular dashed segment line (note the right angle marker). RS is perpendicular to SV, which in turn means RS is perpendicular to TV as well.

Area of Parallelogram = Base*Height
96 = TV*RS
96 = TV*8
96/8 = TV
12 = TV
TV = 12

Segment TV is composed of TU and UV, both of which are congruent segments. The single tickmarks show this. The instructions also state "the lengths of segment TU an segment UV are equal"
So TU = UV
TU + UV = TV
UV + UV = TV
2*UV = TV
2*UV = 12
UV = 12/2
UV = 6

The height of triangle QUV is also RS = 8 because triangle QUV is completely enclosed inside the parallelogram, and because RS is perpendicular to UV. The base of triangle QUV is the segment UV = 6

Area of triangle QUV = (base)*(height)/2
Area of triangle QUV = UV*RS/2
Area of triangle QUV = 6*8/2
Area of triangle QUV = 48/2
Area of triangle QUV = 24 square feet

The opening in a rectangular door frame measures 9 feet by 3 feet. Each of the four doors described in the table measures 9 feet by 3 feet, but have different diagonal lengths. Which door will fit in the rectangular opening?

Door 1: 10 ft
Door 2: 3 square root 10ft
Door 3: 6 square root 2ft
Door 4: 12ft

Answers

Answer: Door 2 will fit through the rectangular door.

To do this problem, we need to use the Pythagorean Theorem. The door is a rectangle and if we draw a line from corner to corner, we have right triangles.

To find the diagonal distance, we have to write and solve the equation below.

3^2 + 9^2 = c^2
9 + 81 = c^2
90 = c^2
c = the square root of 90

The square root of 90 can be simplified to 3 square roots of 10.

Answer:B

Step-by-step explanation:

MATH HELP PLEASE WILL GIVE BRAINLIEST!!!
Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle C

Answers

Hello,

When we have a quadrilateral inscribed in a circle, the opposite angles add up to 180 degrees (supplementary).

Therefore, we can write and solve the following equation first with angles B and D.
3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x =175
x = 35

Then, sub 35 in the expression for angle A and you will get:
2(35) + 3
70 + 3
73

Angle A is 73, that would make angle C equal to 107 degrees, because 180 - 73 = 107.

Good luck,
MrEQ

8x+12=10x-8 help me out bruh

Answers

The answer would be x = 10.
This can be found subtracting 8x from 10x and getting 2x and adding 8 to 12. This would give you 2x = 20 which you need to divide by 2 to get "x" by itself. The final answer would be x = 10.

For what value of c is the relation a function? [(2,8) (12,3) (c,4) (-1,8) (0,3)]
a -1
b 1
c 2
d 12

Answers

1 is the only number that won't duplicate a value.

Answer: The correct option is

(b) 1.

Step-by-step explanation: We are given to find the value of c for which the following relation is a function :

R = {(2,8) (12,3) (c,4) (-1,8) (0,3)}.

We know that

a relation is a function if each first element is associated with only one second element.

Since the first elements in R are 2, 12, -1 and 0, so, the value of c cannot be equal to these four values.

Therefore, the only option for c is 1.

Thus, c = 1.

Option (b) is CORRECT.

Explain how to write an inequality to model the problem.

The winning baseball team scored more than 5 runs. as in 5 < P

Answers

Answer:

Identify the variable as the number of runs. Identify the inequality symbol needed as greater than. Identify the constant as 5 runs. Write the inequality as r > 5.

Step-by-step explanation:

The inequality that represents the situation "The winning baseball team scored more than 5 runs" is (r > 5) where r represents the total runs scored by the team and this can be determined by using the given data.

Given :

The winning baseball team scored more than 5 runs.

The following steps can be used to determine the inequality that represents the given situation:

Step 1 - Let the total runs scored by the baseball team be 'r'.

Step 2 - Now, it is given that the winning baseball team scored more than 5 runs, the inequality that represents this situation is:

[tex]r > 5[/tex]

Greater than sign represents that the team scores more than 5 runs.

For more information, refer to the link given below:

https://brainly.com/question/15137133

Question 5 of 5 At 7:00 a.m., the temperature was 8°C. What was the temperature at midnight if the temperature was 10° lower? A. −18° C B. −2° C C. 2° C D. 18° C

Answers

The answer that's displayed above is B. -2 degrees

Josie has /60 cubic centimeter of candle wax. She wants to make a hexagonal prism candle with a vase area of 21 square centimeters and height of 8 centimeters. She also wants to make a triangular prism candle with a height of 14 centimeters. Can the bass area of the triangular prism candle be 7 square centimeters

Answers

If Josie only has 60 cm^3 of wax, she doesn't have enough for either model candle.

The candle volume (V) is the product of base area (B) and height (h).

V = Bh
For the hex candle,
.. V = (21 cm^2)*(8 cm) = 168 cm^3

For the triangular candle,
.. V = (7 cm^2)*(14 cm) = 98 cm^3

Both candles are more than 60 cm^3.

The triangular candle is less than 160 cm^3. If that is the volume of wax Josie has, then she could make one of those.

Ella surveyed the students at her school to find out if they like math and/or science. The table below shows the results of the survey:

Like Math Do Not Like Math Total
Like Science 41 22 63
Do Not Like Science 7 31 38
Total 48 53 101

If a student likes science, what is the probability that student does not like math?
14.5%
18.4%
34.9%
65.1%

Answers

The answer is 34.9%.
Divide the number of answers in "do not like math" by the total of the "Like Math" plus "Do not like math"
Wherein, 22 divide by 63 will give you 0.3492. Then, multiply it to 100 to become a percentage, and it will give us an answer of 34.92% or 34.9%.

Answer:

34.9

Step-by-step explanation:

can someone please help me i got stuck in this question

Answers

You could set up a ratio given that it is a 5% solution (5% of the total, not 5% of water.

5/100 = x/473 You need to find out how much is vinegar. Cross multiply
5 * 473 = 100 x Find the number on the left.
2365 = 100 x Divide by 100
2365 / 100 = x
x = 23.65 mL of vinegar.
The water is found by subtraction
473 - 23.65 = 449.35 mL of water.

First 5 multiples of 6: 6, 12, 18, 24, 30 First 5 multiples of 9: 9, 18, 27, 36, 45 What is the least common multiple (LCM) of 6 and 9?

Answers

Solution:

We are given the first five multiples of 6 and 9.

First 5 multiples of 6: 6, 12, 18, 24, 30 First 5 multiples of 9: 9, 18, 27, 36, 45

If we look carefully, we can see that the smallest number that is common in both multiples is 18.

First 5 multiples of six: 6, 12, 18, 24, 30 First 5 multiples of nine: 9, 18, 27, 36, 45

Thus, the LCM of 6 and 9 is 18.

LCM is lowest common multiple

Let's check

2|6,9

3|3,9

3|1,3

LCM=2(3)(3)=18

Anthony brings 4 bags of popcorn to a meeting. The bags of popcorn are all the same size. There are 14 people at the meeting. Each person eats the same amount of popcorn, and all of the popcorn is eaten. What fraction of a bag of popcorn did each person eat?

Answers

each person ate 2/7 of the popcorn

Other Questions

What momentum of a 50kilogram ice skater gliding across the ice at a speed of 5m/s? The restoration of which monarch to the throne initiated the era known as the restoration Emily forge a relationship with Daniel and his dog dies During his summer vacation, Alex spent 6 minutes riding his bike for every minute he spent watching television. If he rode his bike for 780 minutes, how many minutes did he spend watching television? Use an equation to solve. [Type your answer as a number.] Can someone please help me with a few questions in math? I'll be eternally grateful and mark brainliest. 5n^3-230=90 San Domingo shares the island of Hispaniola with which country? 5 - 5x > 20. Solve the inequality You're most to . The tone of narrative writing A.doesn't matter very much.B.is always informal.C.is always formal.D.varies by the message. your county or town taxes in the form of a/an _______ tax. identify the sentence in which the underlined clause is a noun clause that functions as the subject of the sentence DNA exists in chromatin form in the nucleus: letter A in the illustration. During mitosis and meiosis, chromatin undergoes a change. What is that change? ________ refers to the heterogeneity of organizations in terms of gender, age, race, ethnicity, sexual orientation, and inclusion of other diverse groups.a. organizational congruityb. workforce associabilityc. operational homogeneityd. workforce diversitye. cultural similarity The ________ is responsible for the initiation of wind Nick gets out of school at 2:25 p.m he gas a 15-minute ride home on the bus. Next he goes on a 30-minute bikr ride. Then he spens 55 minutes doing homework. At what time does nick finsh his homework? How do temperatures above the range of maximum growth effect bacterial cells?a.high temperatures cause water to exit bacterial cells.b.high temperatures denature essential enzymes and other proteins.c.high temperatures slow down bacterial metabolism.d.high temperatures rupture bacterial cell walls. submit for grading save and finish later? Which natural hazard would California be more likely to experience than Florida?tsunamisdroughtswildfiresfloods 1500 people to part in a walkathon. 450 of them were school children. The rest are adults. What percentage of the participants were adults? If you wanted to collect the number of comments users posted to a webpage on your site, which of these would you set up? A survey of patients at a hospital classified them by sex and blood type, as shown in the table. What percent of all patients are male? [Round answer to the nearest tenth of a percent.] A blood type: 105 male, 93 female. B blood type: 99 male, 84 female. O blood type: 160 male, 140 female. AB blood type: 15 male, 18 female.A.) 47.0%B.) 47.8%C.) 53.1%D.) 54.1% Brainliest! Explain whether these situations violated the First - Fourth Amendments - which one, and why or why not: HIGH SCHOOL STUDENTS NOT ALLOWED TO ATTEND A PUBLIC MEETING ON ENVIRONMENTAL ISSUES Which expressions are equivalent to the one below?check all that apply.