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
The cost of every college is expected to increase 3.5%
lions [1.4K]

Answer:

$18,630

Step-by-step explanation:

The cost of every college is expected to increase 3.5% next year.

The cost to attend Westish College is currently $18000.

What is the expected cost to attend Westish College next year?

The increase in the cost for next year is calculated as:

3.5 % × Current cost

= 3.5% × $18,000

= $630.

The expected cost to attend Westish college next year=

$18,000 + $630

= $18,630

8 0
3 years ago
Point M is the midpoint of AB¯¯¯¯¯¯¯¯. Find the length of AB¯¯¯¯¯¯¯¯.
alina1380 [7]

Answer:

AB = 142

Step-by-step explanation:

If M is the midpoint, then AM = MB

6x+5 = 7x -6

Subtract 6x from each side

6x-6x+5 = 7x-6x -6

5 = x-6

Add 6 to each side

5+6 = x-6+6

11=x

We want to find AB

AB = 6x+5+7x-6

AB = 13x -1

     = 13(11) -1

     =143-1

     = 142

6 0
3 years ago
How do I graph this linear function <br> x &lt; -1
wolverine [178]
Hope this helps! Let me know if you need anything else.

6 0
2 years ago
Read 2 more answers
How to calculate rational numbers ​
Anuta_ua [19.1K]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

The simplest method to find a rational number between two rational numbers x and y is to divide their sum by 2.

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

8 0
3 years ago
You work in the HR department at a large franchise. you want to test whether you have set your employee monthly allowances corre
ra1l [238]

Answer:

1) Null hypothesis:\mu \leq 500  

Alternative hypothesis:\mu > 500  

z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90  

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

z_{crit}= 2.33

For this case we see that the calculated value is higher than the critical value

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

2) Since is a right tailed test the p value would be:  

p_v =P(z>5.90)=1.82x10^{-9}  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

Step-by-step explanation:

Part 1

Data given

\bar X=640 represent the sample mean

\sigma=150 represent the population standard deviation

n=40 sample size  

\mu_o =500 represent the value that we want to test  

\alpha=0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

Step1:State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 500, the system of hypothesis would be:  

Null hypothesis:\mu \leq 500  

Alternative hypothesis:\mu > 500  

Step 2: Calculate the statistic

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

We can replace in formula (1) the info given like this:  

z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90  

Step 3: Calculate the critical value

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

z_{crit}= 2.33

Step 4: Compare the statistic with the critical value

For this case we see that the calculated value is higher than the critical value

Step 5: Decision

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

Part 2

P-value  

Since is a right tailed test the p value would be:  

p_v =P(z>5.90)=1.82x10^{-9}  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

7 0
3 years ago
Other questions:
  • X÷x+4=3÷x-1<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bx%20%2B%204%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7Bx%20-%201%7D%
    9·1 answer
  • The sum of three consecutive terms x, y and z of an arithmetic progression is 45. If y=1/2(x+z), find the value of y.​
    5·1 answer
  • Who knows proportional relationships? and how to solve these both
    5·1 answer
  • A six-pack of soda costs $3.36 How much does one soda cost?
    9·1 answer
  • If U = 3 inches, V = 5 inches, W = 8 inches, X = 6 inches, Y = 8 inches, and Z = 4 inches, what is the area of the object?
    13·1 answer
  • I know I keep asking for help but I literally just got put back in my right grade pls help
    15·1 answer
  • Could triangle ABC be congruent to ADC by SSS? Explain
    6·2 answers
  • Mhanifa Please help find angle 1,2,3,4 and 5 thanks!
    12·2 answers
  • If i had 42 granola bars how many boxes whould I need?
    7·1 answer
  • Find The largest integer which is a factor of both 308 and 952.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!