Consider the graph of f(x) = 5x + 1. Explain how to find the average rate of change between x = 0 and x = 4.

What is the average rate of change?

Answers

Answer 1

Given:

Consider the given function is:

[tex]f(x)=5^x+1[/tex]

To find:

The average rate of change between x = 0 and x = 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

We have,

[tex]f(x)=5^x+1[/tex]

At [tex]x=0[/tex],

[tex]f(0)=5^0+1[/tex]

[tex]f(0)=1+1[/tex]

[tex]f(0)=2[/tex]

At [tex]x=0[/tex],

[tex]f(4)=5^4+1[/tex]

[tex]f(4)=625+1[/tex]

[tex]f(4)=626[/tex]

Now, the average rate of change between x = 0 and x = 4 is:

[tex]m=\dfrac{f(4)-f(0)}{4-0}[/tex]

[tex]m=\dfrac{626-2}{4}[/tex]

[tex]m=\dfrac{624}{4}[/tex]

[tex]m=156[/tex]

Hence, the average rate of change between x = 0 and x = 4 is 156.


Related Questions

Which statement about a right triangle is true?

A: The length of each leg equals 1/2 of the hypotenuse.

B: The square of the hypotenuse is equal to the sum of the squares of the legs.

C: One leg is always longer than the hypotenuse.

D: A right triangle can have only one obtuse angle.

Answers

Answer:

the square of hypotenuse rs eqaul to the sum of the square of the legs

someone help me please with this algebra problem

Answers

Answer:

60

Step-by-step explanation:

5x + 10y = 800

y = 50

5x + 10(50) = 800

5x + 500 = 800

5x = 300

x = 60

Answer: 60

Step-by-step explanation:

If x = small vehicles and if y = large vehicles and y = 50, then substitute and solve for x. So,

5x + 10(50) = 800

5x + 500 = 800

5x = 300

x = 60

So, the number of small vehicles is 60.

The area of the rectangular sandbox at Dave's school is 117 square feet. The sandbox has a width of 9 feet as shown in the diagram. What is the perimeter of the sandbox?

Answers

Answer:

ay bru ima tell yu dhis rn is c

Step-by-step explanation:

Please help me with this one.. it's due today!!!

Answers

Answer:

75 in^2

Step-by-step explanation:

The surface area is the sum of the areas

Area of the square:

A = s^2 = 5^2 =25

Area of one triangle

A = 1/2 bh = 1/2 (5)(5) = 25/2

There are 4 triangles

4* (26)/2 = 50

The sum is 25+50 = 75

Hi!

[tex]P_{\square}=5^2=25 \ in.^2\\\\P_{\triangle}=\frac{1}{2}\cdot5\cdot5=\frac{1}{2}\cdot25=12,5 \ in.^2\\\\P_c=25+4\cdot12,5=25+50=\boxed{75 \ in.^2}[/tex]

What is the value of x?


[tex] \frac{4}{5} x - \frac{1}{10} = \frac{3}{10} [/tex]

Answers

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{5}[/tex] x - [tex]\frac{1}{10}[/tex] = [tex]\frac{3}{10}[/tex]

Multiply through by 10 ( the LCM of 5 and 10 ) to clear the fractions

8x - 1 = 3 ( add 1 to both sides )

8x = 4 ( divide both sides by 8 )

x = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]

A microwave oven has a capacity of 1.75 ft³. The interior of the microwave is 18in wide and 14in deep. What is the height of the interior of the microwave, to the nearest tenth of a foot?

Answers

Answer:

Step-by-step explanation:

This is a volume problem as indicated by the exponent on the unit feet. Cubed is a volume thing, whereas squared is an area thing, etc.

The volume for a box-shaped microwave is

V = l x w x h and we are given the length and the width, but those are in inches and they need to be in feet. That's the tricky part here...catching the inconsistency in the units!

18 inches = 1.5 ft and

14 inches = 7/6 feet

Filling in:

1.75 = 1.5 x 7/6 x h and

1.75 = 1.75h so

h = 1 foot

Someone help?????????????

Answers

Answer:

D

Step-by-step explanation:

f(x)=x²+3x+5

put x=a+h

f(a+h)=(a+h)²+3(a+h)+5

=a²+2ah+h²+3a+3h+5

A 4 metre ladder is placed against a vertical wall.
The base of the ladder is 1.5 metres from the base of the wall.

Answers

Answer:

Original position: base is 1.5 meters away from the wall and the vertical distance from the top end to the ground let it be y and length of the ladder be L.

Step-by-step explanation:

By pythagorean theorem, L^2=y^2+(1.5)^2=y^2+2.25 Eq1.

Final position: base is 2 meters away, and the vertical distance from top end to the ground is y - 0.25 because it falls down the wall 0.25 meters and length of the ladder is also L.

By pythagorean theorem, L^2=(y -0.25)^2+(2)^2=y^2–0.5y+ 0.0625+4=y^2–0.5y+4.0625 Eq 2.

Equating both Eq 1 and Eq 2: y^2+2.25=y^2–0.5y+4.0625

y^2-y^2+0.5y+2.25–4.0625=0

0.5y- 1.8125=0

0.5y=1.8125

y=1.8125/0.5= 3.625

Using Eq 1: L^2=(3.625)^2+2.25=15.390625, L=(15.390625)^1/2= 3.92 meters length of ladder

Using Eq 2: L^2=(3.625)^2–0.5(3.625)+4.0625

L^2=13.140625–0.90625+4.0615=15.390625

L= (15.390625)^1/2= 3.92 meters length of ladder

hope it helps...

correct me if I'm wrong...

PLEASE HELP ME ILL MARK YOU BRAINLIEST !!!!!!!!!!

Answers

Step-by-step explanation:

(1/2) / (1/3) = (1/2)(3/1) = 3/2 miles per hour = 1.5 miles per hour

Answer:

Step-by-step explanation:

to find the unit rate, which is what we are looking for, we have to divide the number of miles by the number of hours. Specifically:

[tex]\frac{\frac{1}{2} }{\frac{1}{3} }[/tex] and to work this out, we bring up the bottom fraction and flip it to multiply, giving us:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] which is [tex]\frac{3}{2}[/tex] miles per hour (which is the same thing as walking a mile and a half every hour). The choice you're looking for is the one that reflects 3/2 miles per hour. (I can't see which choice it is; they're too small!)

What is the phase shift of F(x) = 3 sin(2x - 4)?

Answers

Answer:

2

Step-by-step explanation:

Use the form asin(bx−c)+d

a=3

b=2

c=4

d=0

Phase Shift: c/b

Phase Shift: 4/2 = 2

i really need someone’s help on this one asap.

Answers

Answer:

(3,-19)

Step-by-step explanation:

To find the approximation where both functions equal, find where both lines intersect at. Both lines intersect in the Fourth Quadrant so The first 2 are wrong.

The y coordinate is lesser than -10 so the 4th one is wrong.

The answer is (3,-19)

Answer:   Choice C.  (3, -19)

Explanation:

The solution to f(x) = g(x) is where the f(x) and g(x) curves cross, aka the intersection point.

Based on the graph alone, it's a bit tricky to tell where they cross. Luckily, your teacher gave you multiple choices to pick from. We can rule out choices A and B since x < 0 here, but the x coordinate of the intersection is positive.

Choice D can be ruled out because the intersection point has a y coordinate such that -20 < y < -15. It looks like y is much closer to -20 than it is to -10. So there's no way to have y = -8 happen.

The only thing left is choice C. It appears that the intersection point could be (3,-19).

Find the scale factor and the value of x. HELP !

Answers

Answer:

k = 5/3

x = 21

Step-by-step explanation:

Here, we have two similar shapes

The scale factor here would be the ratio of the corresponding similar sides

so we have k as 15/9 = 5/3

To find the value of x

When two shapes are similar, the ratio of the sides corresponding are equal

So we have it that;

x/35 = 9/15

= 15 * x = 9 * 35

15x = 315

x = 315/15

x = 21

Max can travel 100 miles in 2 hours. At this rate, how many hours will it take him to travel 650 miles?

Answers

100miles in 2hrs
650miles in x hrs

If you think of it 650/100 = 6.5

So the distance is 6.5 times

So the time is 6.5 times 2hrs

=13 hrs total

6 students were asked the age of their oldest sibling:

21, 31, 26, 24, 28, 26.

Arrange the scores from lowest to highest.

Find the following. LABEL you answers. Q1, Q2, Q3, IQR, and Range.

Q1=

Q2 (median)=

Q3=

IQR= Q3- Q1

IQR=

Range: Max score - Min score

Range =

HELP ASAP PLEASE

Answers

Answer:

Q1= 31 AND 28

Q2= 26 AND 26

Q3= 24 AND 21

Step-by-step explanation:

2log₃4-log₃8+log₃9/8
hurry im timedd​

Answers

Answer:

[tex]2(1 - log_{3}(2) )[/tex]

Step-by-step explanation:

I have attached the explanation above, hopefully this help

if the diagonal of a square is √48 what is the area of a square​

Answers

Answer:

using Pythagoras' theorem c²=a²+b²

the diagonal is the hypotenuse of one of the triangles formed

let x represent one side of the square

√48²=x²+x²

√48²=2x²

48=2x²

48/2=2x²/2

24=x²

√24=√x²

4.8989794855663561=x

~4.90

Area of the square=side x side

4.90x4.90

24.01units²

-10ab(13c) what is the answer

Answers

Answer:

Answer:[tex]13c = 65 \ \ c = \frac{65}{13} \ \ c = 5[/tex]  More

Help multiple choice

Answers

Answer:

the first one

Step-by-step explanation:

Question 17 (5 points)
Determine the value of x in the isosceles trapezoid.
2x
х
x = 60°
x= 65°
x= 180°
*= 90°

Answers

x=65. helpshdidnskdndikdndod disks djdnd

find the size of each of the unknown angles.
plz solve this question fast as soon as possible with solution.

Answers

Answer:

Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°

Step-by-step explanation:

To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.

180 - 100 = 80

Angle a is 80°.

Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.

After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.

Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.

So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.

Please help me with this one

Answers

Answer:

71.51

Step-by-step explanation:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=3·3+7·3+7·3+1

2·﹣34+2·(3·7)2+2·(3·7)2﹣74+2·(7·7)2﹣74=71.51219

What conversion ratio was skipped in this multiple-step conversion? ​

Answers

Answer:

B

Step-by-step explanation:

B was missed. You have to convert this from hours into minutes before you can deal with seconds.

i13(12)-2give answer​

Answers

154 I might be wrong tho

Rewrite the sentences below to make them more concise. During that time period, many car buyers preferred cars that were pink in color and shiny in appearance.

Answers

Answer:

Pink, shiny cars were preferred by buyers at that time

Step-by-step explanation:

Rewriting the sentence, removing unnecessary words

Find the surface area of the
triangular prism.
7 cm
cm
7 cm
9 cm
5 cm
[?] sq cm
Please HELP ME

Answers

Hello,

I am going to calculate all the surface areas of the prism:

1) the bases: 2*(6*9)/2=64 (cm²)

2) perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

What does it means sq ? (for a foreigner) ?

All surface areas= 64+115=179 (cm²)

What is triangular prisms?

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.

Given

the bases: 2*(6*9)/2=64 (cm²)

perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

To know more about triangular prisms refer to:

https://brainly.com/question/3160908

#SPJ2

I NEED ANSWERS ASAP(WORTH 20 POINTS) WILL MARK BRAINLIEST

The graph of f(x) = |x| is transformed to g(x) = |x+1|-7. On which interval is the function decreasing?

A. (negative infinity, -7)
B. (negative infinity, -1)
C. (Negative infinity, 1)
D. (Negative infinity, 7)

Answers

Answer:

B. (negative infinity, -1)

B. Negative infinity-1

HELP ME WITH THISSS PLZZZ!!!! ahh thank youu lol

Answers

The answer is b I think

What is the solution to the equation One-fourth x + 2 = negative StartFraction 5 Over 8 EndFraction x minus 5?

x = negative 8

x = negative 7
pls hurry
x = 7

x = 8

Answers

Answer:

c = 24

Step-by-step explanation:

Which of the following expressions represents the distance between -3.9 and -4.7

Answers

Answer:

None of the above

Step-by-step explanation:

Distance is the difference between two positions. That is x1- x2  Since both numbers were negative, you would want the absolute value of one plus the other, because subtracting a negative results in a positive. For this example the distance would look more like this:

| -4.7 - ( -3.9 ) | = .8

Factorise 2ab+2ac. Please

Answers

Answer:

2a(b+c)

Step-by-step explanation:

Find HCF (2a)

Then factorise

Answer:

2a(b+c)

.............

Other Questions
Redbud Company uses a certain part in its manufacturing process that it buys from an outside supplier for $44 per part plus another $6 for shipping and other purchasing-related costs. The company will need 10,000 of these parts in the next year and is considering making the part internally. After performing a capacity analysis, Redbud determined that it has sufficient unused capacity to manufacture the 10,000 parts but would need to hire a manager at an annual salary of $40,000 to oversee this production activity. Estimated production costs are determined to be:Direct material $ 28 Direct labor 12 Variable overhead 6 Fixed overhead (includes manager at $4 per unit) 10 Total unit cost $ 56A) Identify the relevant costs to make this part internally. (Select all that apply)A) Historical cost B) Direct labor C) Direct material D) Variable overhead E) Fixed overhead F) New manager's salaryB) Should Redbud produce the part or continue to buy it from the outside supplier? (Select the right answer)A) Redbud should produce the part. B) Redbud is indifferent about the decision. C) Redbud should continue to buy it from the outside supplier.C.What are the other factors that Redbud Company should consider in deciding to make the part internally? (Select all that apply.)A) Total sales quantity.B) The potential for improved control over the availability of the parts by having it when needed and the potential for improved quality of the parts.C) Since Redbud Company is considering the use of currently available capacity, it should evaluate any relevant opportunity costs of using this capacity for more profitable activities. Participating in sports can be a great way for teens to remain healthy and active. But sports teams are a small-scale version of society, consisting of people with the same concerns and issues as the rest of society. Just as teens will compare themselves to an image on TV, athletes will also make unhealthy body comparisons in sports environments. These comparisons can be to professional athletes, competitors, or teammates. Some sports, such as gymnastics, wrestling, figure skating, and boxing, require a certain look or to be in a certain weight class, pressuring athletes toward eating disorders.Teens may look up to athletes and want to emulate or copy them. Which physical attributes may cause some teens to establish a negative body image? Check all that apply.endurancebroad chestpetite body compositioncompetitive spiritthin waist Re-write the following expression using ADDITION ONLY:12- 3+16 - 37 - (-20) what is a damplease tell Solve: |4x+3|=|2x+1| If a car is moving on a straight line with a velocity of 40 m/s and it changes its velocity to 60 m/s in 4 seconds, calculate its acceleration. true or false? A circle could be circumscribed about the quadrilateral below. I am writing an essay, and really need help with a some key points to discuss..! The topic is: How is music connected to politics? WILL GIVE BRAINLIEST A three-story building had its lightweight roof uplifted. Hint: low-rise three-story, non-residential, roof uplifted completely, but no damage to walls. a. Damage Indicator Number:_________b. Degree of Damage:_________ c. Expected Wind Speed:_________ d. EF-scale Rating: _______ Find the measure of the missing angle using the triangle angle sum theorem If you were one of the inhabitants of the Mediterranean climatic region, what economic activities would you follow? why? Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicatedvalue of x to be less than 0.0001. en If a nation is rich in resources then it can be developed' justify mhe statement. Two men p and q set off from a base camp r prospecting for o,p moves 40km on a bearing 205 degree and q moves 30km on a bearing of 060 degreea. Find the distance of q from pb. The bearing of q from p A young patient is short in stature, with his limbs and trunk in proportion. His mental development appears to be appropriate for his age. Determine and discuss the type of hormonal disorder he likely has. at which point is the Kinetic energy the lowest? If you are driving 90 km/hkm/h along a straight road and you look to the side for 2.8 ss , how far do you travel during this inattentive period pleasee help me,A train travels from station P to station Q at a speed of 90km/h in 3hours 40minutes.The train stops at station Q for 25minutes before returns to station P.The time taken from station P to station Q.Calculate the average speed,in km/h,of the whole journey of the train Plot point C in GeoGebra to verify that it indeed lies on AB. You can enter the coordinates in the Input window to plot the point . Also , verify the distances you calculated in question 3 using GeoGebra . Take a screenshot showing the distances displayed by GeoGebra , and paste it below . What plan has been made for the human resource development in our country nepal?