How much money does Conor earn each minute he does yard work, if he works 3.25 hours at $9 an hour?

babunello [35]

Hey there! The topic for this problem is Limit of Function!

As for the question, we are given the quadratic function and we have to find the limit, the value that approaches to a.

$\large \boxed{lim_{x \longrightarrow a} f(x)}$

We call this, "The limit of f(x) when x approaches a."

Then you may ask, "How do we find the limit of function?". That is a very nice question! The answer to your problem is just substitute x-value in. Although this substitution method only applies when the approaching value doesn't make the denominator to 0. I believe that in the beginning of Limit topic, we learn how to find or evaluate the basic limit that only requires substitution.

So from the question, we receive:

$\large{lim_{x \longrightarrow 2} ( {x}^{2} - 3x - 1)}$

Next step is to substitute x = 2 in the function.

$\large{lim_{x \longrightarrow 2} ( {2}^{2} - 3(2) - 1)}$

Evaluate the value.

$\large{lim_{x \longrightarrow 2} ( 4 - 6 - 1)} \\ \large{lim_{x \longrightarrow 2} ( - 3)}$

Cancel the limit out and there you have it!

$\large \boxed{ - 3}$

Answer

The limit of quadratic function when x approaches 2 is -3.

Now whenever you learn limit, you must know that limit is when we substitute the approaching value. That means x —> 2 is not x = 2 but x approaches 2.

Regarding the limit, any questions and doubts can be asked through comment and I will get back to you soon!

Thank you for using Brainly and I hope you have a fantastic day! Good luck on the assignment.

8 0

3 years ago

A coffee mixture contains beans that sell for $0.08 per pound and $0.32 per pound. If 110 pounds of beans create a mixture that

garik1379 [7]

Answer:

B = 87.08 pounds @ $0.32

A = 22.92 pounds @ $0.08

Step-by-step explanation:

given,

cost of beans (A)= $ 0.08/pound

and another beans cost (B) = $ 0.32 /pound

total weight of the pound = 110 pound

selling price of mixture = $ 0.27/pound

cost of each bean = ?

A + B = 110

A = 110 - B-------(1)

0.08 A + 0.32 B = 0.27 x 110

0.08 A + 0.32 B = 29.7

Putting value of A

0.08(110 - B) + 0.32 B = 29.7

8.8 - 0.08 B + 0.32 B = 29.7

0.24 B = 20.9

B = 87.08 pounds @ $0.32

A = 22.92 pounds @ $0.08

8 0

4 years ago

Directions: find the measure of each missing numbered angle for each diagram below.

anzhelika [568]

1) 40

2) 40

3) 140

4)145

5)35

6) 35

7)105

8)105

9) 75

10)120

11) 120

12) 60

13)45

14)45

15)135

16)27

17) 27

18)153

19)90

20)90

21)60

22)50

23)70

24)90

25)35

26)55

3 0

3 years ago

The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for

erastova [34]

Answer:

C) 2/3x + 3y = 3

Step-by-step explanation:

The attached graph shows only choice C intersects the desired point.

Essentially, the given graph is irrelevant. What you want to know is which equation has (3/4, 5/6) as a solution.

There are at least a couple of ways you can figure this out:

try the given point in the equations to see which one works
examine the features of the given equations to see which might work

__

If we consider the second approach, we realize all of the equations have negative y-intercepts except choice C*. For an equation with a negative y-intercept to be the solution, the x-intercept must be less than 3/4. That is not the case for any of choices A, B, or D, leaving only choice C as a viable possibility.

We can check to see if the given point satisfies choice C. Filling in for x and y, we get ...

(2/3)(3/4) + 3(5/6) = 2/4 +5/2 = 3 . . . . . . the point is on this line

_____

In the attached graph, choice C is the black line.

_____

* For an equation of the form ax+by=c, the y-intercept is c/b and the x-intercept is c/a. The sign of the quotient can be figured from the signs of a, b, and c without doing any division.

_____

Comment on intercepts

Considering the signs and values of the x- and y-intercepts can tell you a lot about the solution to a system of equations. They tell you where the line segment between the axes lies, and they can give you a clue as to the location (quadrant) of the intersection point of two lines. Often, the intercepts are all you need to create a useful graph of an equation.

5 0

4 years ago

Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not ad

sasho [114]

The graph of the pH function can be created by plotting the output of

input values of the hydronium ions, x, in the range 0 < x ≤ 1.

Correct responses:

First part:

Please find attached the graph of the pH function

From the attached graph of the pH function, we have;

The point where the pH value is 0 is $\underline{(1, \, 0)}}$

The point where the pH value is 1 is $\underline{(0.1, \, 1)}$

The pH level if the hydronium ion is raised to 0.50 is approximately 0.3

Second part

Please find attached the graph of the transformations, f(x) + 1, and f(x + 1) of the parent log function.

The transformation that results in a y-intercept is $\underline{f(x, \, 1)}$ , because, at x = 0, f(x + 1) = 0.

<h3>Which method can be used to find the pH values using a graph?</h3>

First part

The pH function is; f(x) = -log₁₀x

Please find attached the graph of the pH function created with MS Excel

Where;

x = Amount of hydronium ions

f(x) = pH level

When the pH is 0, we have;

-log₁₀x = 0

Which gives;

x = 10⁰ = 1

When the pH value is 0, the point on the graph is $\underline{(0, 1)}$

When the pH value is 1, we have;

-log₁₀x = 1

log₁₀x = -1

x = 10⁻¹ = 0.1

The point on the graph where the pH value is 1 is $\underline{(0.1, \, 1)}$

From the graph, the ideal pH level if the amount of hydronium ions is raised to 0.50 is pH = 0.301029996 ≈ 0.30

Second Part

The given transformations are;

f(x) + 1, and f(x + 1)

The graph of the transformations created with MS Excel is attached

At the y-intercept, x = 0

From the transformation, f(x) + 1, we have;

At x = 0, the transformation = -log₁₀(0) + 1

log₁₀(0) = Does not exist (DNE)

Therefore;

f(x) + 1 = -log₁₀(0) + 1 = DNE

The transformation, f(x + 1), at x = 0, gives;

f(0 + 1) = -log₁₀(0 + 1) = -log₁₀(1) = 0

Therefore;

The function f(x + 1) = -log₁₀(x + 1) is defined at x = 0, and therefore, has a y-intercept

The transformation that has a y-intercept is $\underline{f(x + 1)}$

Learn more about the pH values here:

brainly.com/question/3610155

4 0

3 years ago