The average rate of change from x = 0 to x = 15 is about −4.667. How does the average rate of change from x = 0 to x = 20 compar

Response:

• Refer to the attached graph

• x₁ ≈ - 2.1

• x₂ ≈ 0.2

Clarification:

To analyze log (−5.6x + 1.3) = −1 − x visually, graph these equations on the same coordinate system:

• Equation 1: y = log (5.6x + 1.3)

• Equation 2: y = - 1 - x

The first equation can be graphed using these characteristics of logarithmic functions:

• Domain: values must be positive ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)

• Range: all real values (- ∞, ∞)

• x-intercept:

        log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒ x = 0.3/5.6 ≈ 0.054

• y-intercept:

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

• Choose additional values to create a table:

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

• This graph is shown in the attached image: it's represented by the red curve.

Graphing the second equation is simpler as it forms a straight line: y = - 1 - x

• slope, m = - 1 (the coefficient of x)

• y-intercept, b = - 1 (the constant term)

• x-intercept: y = 0 = - 1 - x ⇒ x = - 1

• This graph is indicated by the blue line in the image.

The resolution to the equations corresponds to the points where the two graphs intersect. The graphing method thus allows you to determine the x coordinates of these intersection points. Ordered from smallest to largest, rounded to the nearest tenth, we have:

• x₁ ≈ - 2.1

• x₂ ≈ 0.2

Determining the answer here is quite straightforward. Ella has a total of $2.16, and we need to ascertain the cost per piece of gum.
It is known that if the gum cost one cent less, she would have acquired three more pieces.
 Currently, with 8 pieces priced at 27 cents each, a reduced price would allow her to have 8.64 pieces. This outcome, even after rounding, is incorrect as it does not yield 11.
 For 9 pieces at 24 cents each, a cheaper price would mean she could have 9.39 pieces, which still does not round to 12, indicating it's incorrect.
 At 16 pieces costing 13.5 cents each, at one cent less, she would acquire 17.28 pieces, which also confirms it's wrong because rounding does not yield 19.
 When purchasing 24 pieces at 9 cents each, with the cheaper price, she could buy 27 pieces, which is valid since 27-24 equals 3.
 Therefore, the correct answer is D) 24

The response is C. Generally, you incur interest charges from your bank when you exceed your credit limit during borrowing.

He will have more than sufficient, as he only has to account for an area of 84.1425 square feet.

You will achieve this in 15 days. Both 5 and 3 have a least common multiple of 15.