Given the function
f(x)=4x−1
, evaluate and simplify the expressions below. See special instructions on how to enter your answers.
f(a)=
f(a+h)=
f(a+h)−f(a)h=
Instructions: Simplify answers as much as possible. Expressions such as 4(x+2)and (x+5)2 should be expanded. Also collect like terms, so 3x+x should be written as 4x.

Answers

Answer 1

Answer:

[tex]f(a) = 4a - 1[/tex]

[tex]f(a+h) = 4a+4h - 1[/tex]

[tex]f(a + h) - f(a)h= 4a + 5h - 4ah- 1[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 4x - 1[/tex]

Solving (a): f(a)

Substitute a for x

[tex]f(a) = 4a - 1[/tex]

Solving (b): f(a + h)

Substitute a + h for x

[tex]f(a+h) = 4(a+h) - 1[/tex]

[tex]f(a+h) = 4a+4h - 1[/tex]

Solving (c):f(a + h) - f(a)h

[tex]f(a + h) - f(a)h= f(a + h) - f(a) * h[/tex]

Substitute values for f(a + h) and f(a)

[tex]f(a + h) - f(a)h= 4a + 4h - 1 - (4a- 1) * h[/tex]

Open bracket

[tex]f(a + h) - f(a)h= 4a + 4h - 1 - 4ah+ h[/tex]

Collect like terms

[tex]f(a + h) - f(a)h= 4a + 4h + h - 4ah- 1[/tex]

[tex]f(a + h) - f(a)h= 4a + 5h - 4ah- 1[/tex]


Related Questions

No solution is the answer when both lines have the same slope with a different y-
intercept.
o True
o False

Answers

When lines have the same slope and different y-intercepts they are parallel lines. Parallel lines never intercept. Because these lines never intercept, they have no solution. Since they have no solution they are not consistent, dependent or independent like the last two systems we looked at.

A tissue box has a base of 36 in2 ? and is 5 inches tall. What is the volume of the tissue box?

Answers

Answer:

180 [tex]in^{2}[/tex]

Step-by-step explanation:

36 times 5 = 180

Answer: the value is 90

Step-by-step explanation:

what is the shape and direction of f(x)=(x+7)(x+11)

Answers

Given:

The function is

[tex]f(x)=(x+7)(x+11)[/tex]

To find:

The shape and direction of the given function.

Solution:

We have,

[tex]f(x)=(x+7)(x+11)[/tex]

It can be written as

[tex]f(x)=x^2+11x+7x+77[/tex]

[tex]f(x)=x^2+18x+77[/tex]

It is a quadratic function and the power of [tex]x[/tex] is 2 so the graph of this function is a vertical parabola.

The leading coefficient is positive so the parabola opens upward.

Therefore, the given function is a vertical parabola that opens upward.

12 to the 3rd power divided by 12 to the 7th power ​

Answers

Answer:

0.000048..............

Answer:

0.00004822

Step-by-step explanation:

12^7= 35,831,808

12^3= 1728

4:08 - 1:15 =
time calcuation

Answers

4:08 - 1:15 = 2:53
time calculation

Answer:

2:53

Step-by-step explanation:

You spin the spinner twice.
8
7
What is the probability of landing on an 8 and then landing on a 7?
Write your answer as a fraction or whole number.

Answers

two over four is the probability that you will land on seven or eight

Answer:

P( landing an an 8 then on  a 7 ) = 1/ 16

What is a Probability?

Its is the branch of mathematics concerning numerical description of how likely an event is to occur .

P( landing an an 8 then on  a 7 ) = P ( landing on an 8) * P ( landing on a 7 )

P(Landing on an 8) = 1/4

P(Landing on an 7) = 1/4

P = 1/4 * 1/4

P= 1 / 16

Learn more about Probability:

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#SPJ2

During a guided tour of Sindrow Castle, a group of tourists climbed to the top of Fineview Tower.
At the top, the guide asked the six children in the group to guess how many steps they had
climbed. Their guesses were 155, 157, 167, 168, 179 and 183.
The guide revealed that the closest guess was only 3 more or less than the correct number and
that two of the other guesses were no more than 10 away.
How many steps had they climbed?
A 160
B 164
C 171
D 176

Answers

Answer:

C

Step-by-step explanation:

y=3x-4 slope intercept form

Answers

Answer:the slope is 3 and the y intercept is -4

Step-by-step explanation:

Help

Which product are greater than 2 and 5\6? Select all that apply

Answers

Answer:

B, C, & E

Step-by-step explanation:

B C AND E
that’s the answer g

Through: (1,-4) and (-3,1)

Answers

Answer:

of a slope?

Step-by-step explanation:

Subtract -4 and -11 with the help of number line. pls answer as soon as possible pls​

Answers

Answer:

7

Step-by-step explanation:

-4 - -11 = 7

remember negative + or - equals a positive same way with a positive + or - positive will give you a  positive.

Maria is starting a small DVD business online. She makes $3 on each DVD she sells. To start her business though, she had to invest $750. How many DVDs does she need to sell before she starts to make a profit?

Answers

Answer:

750 divided by 3. Equals 250

Step-by-step explanation:

If it says how much is needed and it gives the amount the person has, you will need to divide.

if you get it right and you are the first one than i will give you all stars and thanks and a crown but if you are just right then only the stars and the thanks

Answers

Answer:

Periodic Table

Step-by-step explanation:

? that should be it.

Graph x > -2. PLEASE HELP!!!!!

Answers

Answer:

x > -2

Step-by-step explanation:

B/c the sign is  > it will be an open circle

B/c the sign is  > it will be an infinity line

Also, use math-way, it'll help u with everything

Select all the multiples of the number 3​

Answers

3
6
9
12
15
18
21
24
27
30
33
36
39
42
45

State whether each pair of expressions are equivalent. Show your work.

4(5 + g) + 8(4g + 3 i NEED HELP

Answers

well solve them
4(5+g) + 8(4g+3)
=20 + g + 32g +3
=23 + 33g

Answer:

36g + 44

Step-by-step explanation

20+4g+8(4g+3) =

8(4g+3) : 32g + 24 =

20+4g+32g+24 =

20+4g+32g+24 = 36g + 44

I hope this helps you! Have a great day :)

7.
Judy can decorate 3 cakes in 5 hours. Which graph has a slope that best represents the
number of cakes per hour Judy can decorate?
A
Cake Decorating
Cake Decorating
Number of Cakes
30
27
24
21
18
15
12
Number of Cakes
30
27
24
8 21
18
15
12
9
G
3
0 1 2 3 4 5 6 7 8 9 10
Time (hours)
0 1 2 3 4 5 6 7 8 9 10
Time (hours)
B
Cake Decorating
D
Cake Decorating
y
30
2
30
27
24
21
Number of Cakes
200
18
15
Number of Cakes
19

Answers

Answer:

B

Step-by-step explanation:

is the one that shows how many cakes were made in an hour

hour is 60 minutes so u will divide 60 by 3 it equal to 20

it means they make 20 cakes in 1hour


[tex]18 - 4 \div {2}^{2} \times 10[/tex]
whats the answer​

Answers

The answer is 8
Order of operations:(Please Excuse My Dear Aunt Sally)
Parentheses
Exponents
Multiplication
Division
Add
Subtract
When it comes down to multiplication and division you do whichever comes first , left to right same with add and subtract so..
Step1: 2 squared = 4
Step2: 4/4=1
Step3: 1x10=10
18-10=8 . Final answer is 8

which expression would be easier to simplify if you used the commutative property to change the order of the numbers​

Answers

Answer:

The answer is C

Step-by-step explanation:

Triangle NOP is similar to triangle RST. Find the measure of side RS. Round your
answer to the nearest tenth if necessary. Figures are not drawn to scale

Answers

Answer:

Step-by-step explanation:

Remark

Try to make sure that when you set up your proportion, that the side you are trying to find is the numerator. Then all you have to do is multiply both sides by the numerator underneath the unknown side.

Equation

x / 11 = 27 / 7

Solution

Multiply both sides by 11

11 * x / 11 = 27 * 11 / 7

x = 297 / 7

x = 42.43

Over the summer, Teagan and Maya read a total of 36 books. Teagan reads three times as many books as Maya. How many books does each girl read?

Answers

maya read 9, teagan read 27

(DUE TODAY) Paul wants to build this model with clay, but he does not know how much clay to purchase. Draw a line to separate the model into two rectangular prisms. Then write an expression for the volume of the model. What is the volume?

Answers

Answer:

first draw a horizontal line through the middle, (you prob know where)

top prism: 5x4x5

bottom prism: 9x5x3

volume: 5x4x5+ 9x5x3

=235cm²

Step-by-step explanation:

There you go, hope this helps!

Look at the picture.
Thank u!

Answers

There is a solution to each equations!
Yeah what she said ^

Hey guys can someone help me out?

Answers

Answer: yes with what

Step-by-step explanation:

Help me solve this 9(n + 2) n = 1/4 the choices are A. 3 B. 9 C. 10 D. 19

Answers

Answer:

d

Step-by-step explanation:

HELP PLSSSSSSSI ASKING YOU ╰(‵□′)╯PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

Answers

I think you put only 1/2 on the first ones! But you should try thattttttttttttttt

If the area of a rectangle is (15x2 - 16x - 15) square feet, and its length is (3x - 5) feet, find its width

Answers

Answer:

255

Step-by-step explanation:

(15x2 - 16x - 15) = 270

(3- 5) = -15

 270

-  -15

= 255

The breadth of the rectangle is (-5x-3).

Area of rectangle

The area of a rectangle is given as the product of its length to its breadth.

[tex]\rm{Area\ of\ Rectangle = Length \times breadth\\[/tex]

Given to us

area of a rectangle = (15x2 - 16x - 15)

length = (3x - 5)

Width

[tex]Area\ of\ Rectangle = Length \times breadth\\(15x^2-16x-15)=(3x-5)\times breadth\\\\(3x-5)\times breadth=(15x^2-16x-15)\\\\breadth = \dfrac{(15x^2-16x-15)}{(3x-5)}\\\\breadth = (-5x-3)[/tex]

Hence, the breadth of the rectangle is (-5x-3).

Learn more about Rectangles:

https://brainly.com/question/10046743

What is the answer to 14v+6=2(5+7v)

Answers

Answer:

0=4

Step-by-step explanation:

14v+6=2(5+7v)

14v+6=10+14v

6=10

0=4

PLZ HELP!!! WILL MAKE BRAINLIEST!!!​

Answers

Multiply all 3 of those numbers to get your answer

35. A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of being selected as does any other group (drawing 6 slips without replacement from among 45). a. How many selections result in all 6 workers coming from the day shift

Answers

Answer:

38760 selections result in all 6 workers coming from the day shift.

Step-by-step explanation:

The order in which the workers are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

a. How many selections result in all 6 workers coming from the day shift:

20 workers are employed on the day shift, so this is a combination of 6 from a set of 20.

[tex]C_{20,6} = \frac{20!}{6!(20-6)!} = 38760[/tex]

38760 selections result in all 6 workers coming from the day shift.

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