Huixian needs to pack 171 pens, 63 pencil, and 27 erasers into identical bags so that each item is equally distributed among the

Step-by-step explanation:

∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹

This represents a finite geometric series where n equals 4, a₁ is -144, and r is ½.

S = a₁ (1 − rⁿ) / (1 − r)

S = -144 (1 − (½)⁴) / (1 − ½)

S = -270

If you wish to calculate the infinite sum (n = ∞):

S = a₁ / (1 − r)

S = -144 / (1 − ½)

S = -288

Question:

Which statement is accurate concerning the function’s discontinuities

A) There are gaps at x = 7 and.

B) Asymptotes exist at x = 7 and.

C) Asymptotes exist at x = –7 and.

D) Gaps are present at (–7, 0) and.

Answer:

B) Asymptotes exist at x = 7 and

Step-by-step explanation:

Given:

Goal:

Identify the correct statement

We need to factor the denominator first.

To express x in terms of (3x+4) and (x-7):

3x + 4 =

3x = -4

Divide both sides by 3:

x - 7

x = 7

Next, evaluate the limit when and at (x = 7)

lim f(x) as = ±∞

lim f(x) as (x=7) = ±∞

Since both scenarios result in the denominator approaching zero, they represent asymptotes.

Thus, asymptotes are found at and x=7

Option B is determined to be correct

Answer:

To summarize the answer:

Step-by-step explanation:

Given:

Here is the graph associated with this question:

The second function, denoted as , does not qualify as a function.

Keep in mind that the g(x) function is the inversion of the f(x) function. Recognizing this pattern indicates a reflection on the Y-axis.

Reflection on the axes:

In the x-axis:

Enhance the function by -1 to illustrate an exponential curve around the x-axis.

In the y-axis:

Decrease the input of the function by -1 to depict the exponential function around the y-axis.