Write a formula that will help Juan determine how much he will earn in one week.

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the resulting values to the corresponding l

belka [17]

The correct solution to the limits of x in the tiles can be seen below.

$\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }$ $\mathbf{ = -\dfrac{1}{52} }$

$\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }$ $\mathbf{=\dfrac{1}{79} }$

$\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }$ = -31

$\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }$ $\mathbf{ =\dfrac{1}{98}}$

<h3>What are the corresponding limits of x?</h3>

The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.

From the given diagram, we have:

1.

$\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }$

So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9

$\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }$

Simplifying the quadratic equation, we have:

$\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }$

Replacing the value of x = 9

$\mathbf{ = (-\dfrac{1}{9+43}) }$

$\mathbf{ = -\dfrac{1}{52} }$

2.

$\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }$

-x²-63x+568 is positive when x → 8⁻.

Thus |-x²-63x+568| = -x²-63x+568

$\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }$

$\mathbf{=\dfrac{1}{8+71} }$

$\mathbf{=\dfrac{1}{79} }$

3.

$\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }$

x -7 is positive, therefore |x-7| = x - 7

$\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }$

$\mathbf{ \lim_{x \to 7^+} (-x-24)}$

$\mathbf{ \lim_{x \to 7^+} (-7-24)}$

= -31

4.

$\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }$

x-6 is negative when x → 6⁻. Therefore, |x-6| = -x + 6

$\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }$

$\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }$

$\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }$

$\mathbf{ =\dfrac{1}{98}}$

Learn more about calculating the limits of x here:

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7 0

2 years ago

What is the volume of a cube with an edge length of 2.7 centimeters?

Soloha48 [4]

For the volume you have to cube (hence the name) the edge length:

(2.7)³ = 19.683 cm³

5 0

3 years ago

Read 2 more answers

Five less than area of a square is 59 square feet, find the side length of the square

Ne4ueva [31]

Answer:

8 ft

Step-by-step explanation:

Add back those 5 square feet and you find the area of the square to be 64 square feet. Its side length is the square root of that: 8 ft.

8 0

3 years ago

(PLEASE ANSWER QUICK!) Why is it important to understand properties of angles and figures to solve problems?

kaheart [24]

Answer:

The relationships, properties, and theorems will be easier to understand when ... Just like you don't want to do a geometry problem without all the given ... In case you want to get a head start… here are arguably some of the most important theorems for triangles: ... In the figure below, both congruent angles have one arch.

Step-by-step explanation:

4 0

3 years ago

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as ed

Mamont248 [21]

9514 1404 393

Answer:

2440

Step-by-step explanation:

The difference in fixed costs is ...

37815 -16465 = 21350

The difference in variable costs is ...

20.50 -11.75 = 8.75 . . . . per book

Then the number of books that must be produced for the difference in variable costs to be equal to the difference in fixed costs is ...

21350/8.75 = 2440

For production of 2440 books, the costs of the two methods will be the same.

_____

<em>Additional comment</em>

You can write expressions for total cost of each production method. When you set them equal and solve for the number of books, you find the math you end up doing is the same as that shown above.

4 0

3 years ago