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Natali5045456 [20]
3 years ago
8

At what value of x does the graph of the following function F(x) have a vertical asymptote?

Mathematics
1 answer:
leonid [27]3 years ago
5 0

Answer:

  A.  2

Step-by-step explanation:

There is a vertical asymptote where the denominator is zero. (x-2) is zero when x=2.

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Evaluate 5x³ + 2 for x = -1.<br> 0 -3<br> 04<br> 06<br> 0-7
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9514 1404 393

Answer:

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Step-by-step explanation:

Let x and y represent the numbers of forks and spoons made, respectively.

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The revenue from sales is ...

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You can solve these by any of your favorite methods. A graph is attached. It shows the solution is (x, y) = (7, 20).

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_____

<em>Additional working out</em>

The equation coefficients are not "nice" multiples of each other, so elimination  and substitution will require multiplying both equations by some numbers. If we're going to that trouble, we may as well use Cramer's Rule or a variation of the "cross multiplication method". The latter is relatively straightforward and can be easy to remember. It tells you the solution to ...

  ax +by +c = 0

  dx +ey +g = 0

is ...

  1/(ae-db) = x/(bg-ey) = y/(cd-ga)

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  y = 38/1.9 = 20 . . . number of spoons

__

The above solution formula may be more easily remembered in terms of the cross-multiplication pattern that gives the method its name. When the coefficients are written in two rows of four, with the last being a repeat of the first:

  • a b c a
  • d e g d

each of the three denominators (of 1, x, and y) is the difference of products in adjacent columns, formed in an X fashion: ae-db, bg-ec, cd-ga. Note that the equations are written in "general" form, which is similar to "standard" form, but with all of the non-zero terms on the left of the equal sign. (This has the effect of changing the sign of the constants: 1.7x+1.3y=37.9 ⇒ 1.7x+1.3y-37.9=0)

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