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Vera_Pavlovna
1 month ago
14

Which statement is true about the discontinuities of the function f(x)? F (x) = StartFraction x minus 5 Over 3 x squared minus 1

7 x minus 28 EndFraction
Mathematics
1 answer:
AnnZ [12.3K]1 month ago
6 0

Question:

Which statement is accurate concerning the function’s discontinuities f(x) = \frac{x-5}{3x^2-17x-28}

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 (x = \frac{-4}{3})

Step-by-step explanation:

Given:

f(x) = \frac{x-5}{3x^2-17x-28}

Goal:

Identify the correct statement

f(x) = \frac{x-5}{3x^2-17x-28}

We need to factor the denominator first.

f(x) = \frac{x-5}{(3x+4)(x-7)}

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

3x + 4 =

3x = -4

Divide both sides by 3:

x = \frac{-4}{3}

x - 7

x = 7

Next, evaluate the limit when (x = \frac{-4}{3}) and at (x = 7)

lim f(x) as (x = \frac{-4}{3}) = ±∞

lim f(x) as (x=7) = ±∞

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

Thus, asymptotes are found at (x = \frac{-4}{3}) and x=7

Option B is determined to be correct

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Each associate incurs a cost of $700 daily for the client, meaning that 'a' associates will cost the client 700a dollars each day. For each partner, the charge is $1500 daily, so 'p' partners will accumulate a cost of 1500p dollars daily. The cumulative bill amounts to 700a + 1500p = $14100:

700a + 1500p = 14100

700a + 1500p = 14100

Given that there are a total of 11 lawyers assigned (associates and partners), the equation a + p must equal 11.

a + p = 11

a + p = 11

\underline{\text{Formulate System of Equations:}}

Formulate System of Equations:

​

700a + 1500p =

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14100

a + p = 11

11

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Response:

354

Detailed explanation:

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Angelica is working with function machines. She has the two machines at shown at the right. She wants to put them in order so th
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Billy graphed the system of linear equations to find an approximate solution. y = A system of equations. y equals negative Start
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Response:

Second option: (2.2, -1.4)

Third option: (2.2, -1.35)

Detailed explanation:

The missing graph has been provided.

The attached image illustrates the graphing of the following system of linear equations:

\left \{ {{y=-\frac{7}{4}x+\frac{5}{2}} \atop {y=\frac{3}{4}x-3}} \right.

Notice the intersection of the lines.

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(x,y)

Represented by "x" for the x-coordinate and "y" for the y-coordinate.

Here, it's noticeable that:

- The x-coordinate of the intersection point lies between  x=2 and x=3.

- The y-coordinate of the intersection point is situated between  y=-1 and y=-2.

Therefore, you can conclude that the forthcoming points (Refer to the options given in the exercise) are potential approximations for this system:

(2.2, -1.4)\\\\\\(2.2, -1.35)

7 0
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