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
xeze [42]
3 years ago
12

The graph of f(x) = x + 1 is shown in the figure. Find the largest δ such that if 0 < |x – 2| < δ then |f(x) – 3| < 0.4

.

Mathematics
2 answers:
MArishka [77]3 years ago
8 0
SO what you need to do is:
<span>Start with |f(x) - 3| < 0.4
and plug in f(x) = x+1
to get |f(x) – 3| < 0.4
|x+1 – 3| < 0.4
|x - 2| < 0.4
   -0.4 < x - 2 < 0.4
  -0.4+2 < x < 0.4+2
  1.6 < x < 2.4
So delta would be 2.3
Hope this is what you were looking for
</span>
Harrizon [31]3 years ago
4 0

The largest δ such that if 0 < |x – 2| < δ is 0.4

<h3>Further explanation</h3>

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

<em>m → gradient of the line</em>

<em>( 0 , c ) → y - intercept</em>

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

\large {m = \frac{y_2 - y_1}{x_2 - x_1}

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

y - y_1 = m ( x - x_1 )

Let us tackle the problem.

Given:

f(x) = x + 1

If |f(x) - 3| < 0.4 , then :

|f(x) - 3| < 0.4

|x + 1 - 3| < 0.4

|x -2| < 0.4

Since the absolute value of a function is always positive, then:

0 < |x -2| < 0.4

From the relationship above, then the largest δ such that :

0 < |x - 2| < \delta

<h2>→ δ = 0.4</h2>

<h3>Learn more</h3>
  • Infinite Number of Solutions : brainly.com/question/5450548
  • System of Equations : brainly.com/question/1995493
  • System of Linear equations : brainly.com/question/3291576

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

You might be interested in
My 4 closet friends have weekly allowance of $13, $17, $24, $30. What are the possible values of my weekly allowance if the medi
Nata [24]

Answer:

The median is 20.5

the average is 21

Step-by-step explanation:

5 0
3 years ago
What is the product of 7/8 x 4/7
DIA [1.3K]

Answer:

1/2

Step-by-step explanation:

7x4= 28

8x7= 56

simplify: 28/56=1/2

8 0
2 years ago
Read 2 more answers
Find the inverse function for y=3/4+x
Sonja [21]

The inverse of this function is y = x - \frac{3}{4}


You can find the inverse of any function by switching the x and y values and then solving for the new y value. Once you've done that, what will be left over is the inverse function.


y = \frac{3}{4} + x ----> Swap x and y

x = \frac{3}{4} + x -----> Subtract 3/4 from both sides.

x - \frac{3}{4} = y ----> rearrange to appropriate order

y = x - \frac{3}{4}


And that is your inverse function.

8 0
2 years ago
What + 89= 9(6+5) please solve for my answer and explain how you got your answer
nlexa [21]
The answer would be 10.

6 + 5 = 11
11 x 9 = 99

This means 9(6+5) = 99

99 - 89 = 10
6 0
3 years ago
I need help with #3 and #4 part b please help​
Svetradugi [14.3K]
<h3>Answer:</h3>

3)  likely

4)  1/2; equally likely

<h3>Step-by-step explanation:</h3>

3) You are being asked to translate a numerical value to a subjective statement. There are no hard-and-fast rules for this. Generally, the meanings of the terms you're asked to choose from are ...

  • impossible: probability is zero. The outcome cannot occur.
  • unlikely: chances are less than even; often, "unlikely" means a probability of 10%, 5%, 1% or lower, depending on the context.
  • equally likely: probability is near 50%
  • likely: more likely than not. Again, this depends on the context.
  • certain: probability is 1. There is no chance the outcome will not occur.

An 80% probability is greater than 50%, so might reasonably be called "likely."

___

4) a. Four of the eight numbers are even, so the probability of obtaining an even number at random is 4/8 = 1/2.

  b. A probability of 50% might reasonably be called "equally likely", as the probability the event will occur is equal to the probability it won't.

4 0
3 years ago
Other questions:
  • Help Me For Number 5 Through 8
    12·2 answers
  • 2.21 is 2.5% of what
    7·1 answer
  • -5&lt;-2; Add 7 to both sides
    10·1 answer
  • Subtract.
    6·2 answers
  • A woman leaves home 7:00am and drives to o new york city 200 miles away.if she average 50 miles per hour,what time will she arri
    14·2 answers
  • Can you please help me?​
    10·1 answer
  • PLEASE HELP ITS EASY
    14·1 answer
  • Question is in the picture!
    9·1 answer
  • Find the area of the figure.
    14·1 answer
  • -9+(-14)=??<br><br> please help!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!