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vovangra [49]
3 years ago
13

Find the slope of the tangent line to the graph of f at the given point. 

Mathematics
1 answer:
jarptica [38.1K]3 years ago
4 0

slope = 13

the slope of the tangent is f'( 4)

given f(x) = x² + 5x , then f'(x) = 2x + 5

and f'(4) = ( 2 × 4 ) + 5 = 13


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1. Kyle and John are twins who decided to plan an imaginary trip that started with cliff jumping. There were two different spots
Vikki [24]

Answer:

a) Δx = -35ft

b) Δx = -25ft

c) Kyle traveled 10ft more than John

Step-by-step explanation:

We define a coordinate reference system() in which y = 0 corresponds to the water surface.

a) The initial position of Kyle in our coordinate reference system is:

   x_{o} = 20 ft

   and his final position is:

   x_{f} = -15 ft

   Therefore, he traveled

   Δx = x_{f} - x_{o} = -15 - 20 = -35 ft

b) The initial position of John in our coordinate reference system is:

   x_{o} = 15 ft

   and his final position is:

   x_{f} = -10 ft

   Therefore, he traveled

   Δx = x_{f} - x_{o} = -10 - 15 = -25 ft

c) Then, Kyle traveled 10ft more than John

 

6 0
3 years ago
Marshall's Taffy Shop made 21 kilograms of taffy in 2 days. How much taffy, on average, did the shop make per day?
Mademuasel [1]

Ma yasakō lāgi māphī cāhanchu.

7 0
3 years ago
The length of a rectangle is 4 units less than the width. The area of the rectangle is 21 units. What is the length, in units, o
bazaltina [42]

The formula of an area of a rectangle:

A = wl

We have l = w - 4 and A = 21.

Substitute:

w(w - 4) = 21       <em>use distributive property</em>

(w)(w) + (w)(-4) = 21

w² - 4w = 21     <em>subtract 21 from both sides</em>

w² - 4w - 21 = 0

w² - 7w + 3w - 21 = 0

w(w - 7) + 3(w - 7) = 0

(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0

w = 7 ∨ w = -3 < 0

l = w - 4 → l = 7 - 4 = 3

<h3>Answer: the length = 3 u.</h3>
4 0
3 years ago
Hi if u could help me that would be great, have a nice day!!!
LenaWriter [7]

Hey there! I'm happy to help!

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

<u>OVERVIEW</u>

Random sampling is when you take a sample of something completely at random. This is done to avoid bias and other stuff like that. It makes the data a lot more pure, real, and factual.

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

<u>CHOOSING THE ANSWER</u>

OPTION A: A SCHOOL NEWSPAPER ASKS TEACHERS IN THAT MIDDLE SCHOOL HOW THEY FEEL ABOUT THE BEHAVIOR OF TWELVE YEAR OLD BOYS.

Does this seem very random to you? They're asking all the teachers who work at a certain junior high to talk about twelve year old boys. But, the teachers are definitely going to have some sort of bias towards twelve year old boys because they work with them, and since all of the samples are teachers, this is going to have biased data. Therefore, answer A is incorrect.

OPTION B: A NATIONAL SURVEY COMPANY PICKS ONE PHONE NUMBER FROM EACH AREA CODE IN AMERICA TO CALL AND ASK FOR AN OPINION ON CURRENT POLITICAL ISSUES.

This definitely seems a lot more random. There is only one phone number from each area code and there are many area codes in the United States so you get a bit of what everyone thinks about an issue. There is no bias because there is one random phone number and there are many different places this is done. Therefore, option B is correct.

OPTION C: MIGRANT WORKERS ARE SURVEYED ON THEIR OPINION OF MANDATORY HEALTH INSURANCE FOR COMPANIES.

This is not very random because they are asking a specific group of workers about a company and business ordeal. It is not very random because the migrant workers are specifically being asked, not random people. Therefore, option C is incorrect.

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

<u>THE SOLUTION</u>

Therefore, Option B is the correct answer.

I hope that this helps! Have a wonderful day!

7 0
3 years ago
Explain how you can find 4 times 754 using two different methods.
ludmilkaskok [199]
Method 1:

4(754)

=4(700+50+4)

=2800 + 200 + 16

=3000+16

=3016

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

Method 2:

4(754)

=4(250+250+250+4)

=1000+1000+1000+16

=3016
3 0
3 years ago
Read 2 more answers
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