1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ololo11 [35]
3 years ago
13

(a) Find a simplified form of the difference quotient and (b) complete the following table.

Mathematics
1 answer:
maxonik [38]3 years ago
7 0

Answer:

a) -4

b)

x    h                   [f(x+h) - f(x)] / h

3    2                  -4

3    1                   -4

3    0.1                -4

3    0.01              -4

Step-by-step explanation:

a) The difference quotient is:

[f(x+h) - f(x)] / h

Our function is -4x + 7​, then:

f(x+h) = -4(x+h) + 7​ = -4x -4h + 7

f(x) = -4x + 7​

f(x+h) - f(x) = -4x -4h + 7 - (-4x + 7​ )= -4x -4h + 7 +4x - 7​ = -4h

Finally:

[f(x+h) - f(x)] / h =  -4h/h = -4

b)

First point in the table:

x = 3

h = 2

f(x+h) = -4(3+2) + 7​ = -13

f(x) = -4(3) + 7​ = -5

f(x+h) - f(x) = -13 -(-5) = -8

[f(x+h) - f(x)] / h = -8 / 2 = -4

Second point in the table:

x = 3

h = 1

f(x+h) = -4(3+1) + 7​ = -9

f(x) = -4(3) + 7​ = -5

f(x+h) - f(x) = -9 -(-5) = -4

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

Third point in the table:

x = 3

h = 0.1

f(x+h) = -4(3+0.1) + 7​ = -5.4

f(x) = -4(3) + 7​ = -5

f(x+h) - f(x) = -5.4 -(-5) = -0.4

[f(x+h) - f(x)] / h = -0.4 / 0.1 = -4

Fourth point in the table:

x = 3

h = 0.01

f(x+h) = -4(3+0.01) + 7​ = -5.04

f(x) = -4(3) + 7​ = -5

f(x+h) - f(x) = -5.04 -(-5) = -0.04

[f(x+h) - f(x)] / h = -0.04 / 0.01 = -4

You might be interested in
Two friends share 7 cookies equally. How many cookies does each friend get?
shusha [124]
7÷2=3.5 each of them get 3.5 cookies
5 0
3 years ago
Read 2 more answers
Skyler bought a hover board on sale for $300. She purchased the hover board on a day the offering was 40% off. What was the orig
zvonat [6]
300       40
------ =  -------
  x         100




30000=40x

x=750.

The original price was $750





4 0
3 years ago
Read 2 more answers
What Percentage is 7 out of 12
tensa zangetsu [6.8K]
58% is the answer. 7 dividing 12= 0.5833333
you much move the decimal over two places and you would get 58%
8 0
3 years ago
-7q + 12r = 3q - 4r what dose r equal
Elanso [62]

Answer:

r = 5y/8

Step-by-step explanation:

isolate the variable by dividing each side by factors that contain the variable.

6 0
2 years ago
Which line has a constant proportionality of 4
Ne4ueva [31]

Answer:

Line A

Step-by-step explanation:

Line A has a constant of proportionality (slope) of 4.

3 0
2 years ago
Other questions:
  • How many terms are there in the expression? 2x^2 + 5x + 7y - 6
    7·1 answer
  • What is 400 divided by 1 million
    8·2 answers
  • <img src="https://tex.z-dn.net/?f=%20-%201%20%2B%20%20-%202" id="TexFormula1" title=" - 1 + - 2" alt=" - 1 + - 2" align="absmi
    8·1 answer
  • The hypotenuse of a right triangle is 7 inches, and one of the legs is inches. Find the length of the other leg. .
    13·1 answer
  • I need help please.<br> Solve the inequality.<br><br> 3/4b&gt;-9/8
    5·1 answer
  • ABCD is the isosceles trapezoid with legs line AC and base line BC if the length of line AB is 7Y-4 the length of line BC is 4Y
    5·1 answer
  • Angie packed same-size cubes into a rectangular prism. Image shows a base of cubes 3 units long, 2 units wide, and with a column
    7·2 answers
  • I’ll give brainliest please help
    7·2 answers
  • graph the line that passes through the points (-3,-7) and (-2,-7) and determine the equation of the line
    15·1 answer
  • Given that ABC=DEF, what is the measure of D?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!