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Natali5045456 [20]
2 years ago
9

Find the horizontal asymptote for y= 5x/x+6 . y = 0 y = −6 none y = 5

Mathematics
2 answers:
gayaneshka [121]2 years ago
5 0

Answer:

y

=

5

x

x

+

6

Find where the expression

5

x

x

+

6

is undefined.

x

=

−

6

Consider the rational function

R

(

x

)

=

a

x

n

b

x

m

where

n

is the degree of the numerator and

m

is the degree of the denominator.

1. If

n

<

m

, then the x-axis,

y

=

0

, is the horizontal asymptote.

2. If

n

=

m

, then the horizontal asymptote is the line

y

=

a

b

.

3. If

n

>

m

, then there is no horizontal asymptote (there is an oblique asymptote).

Find

n

and

m

.

n

=

1

m

=

1

Since

n

=

m

, the horizontal asymptote is the line

y

=

a

b

where

a

=

5

and

b

=

1

.

y

=

5

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

x

=

−

6

Horizontal Asymptotes:

y

=

5

No Oblique Asymptotes

image of graph

olga_2 [115]2 years ago
5 0

Answer:

y = 5

Step-by-step explanation:

Given function:

y=\dfrac{5x}{x+6}

\implies y=5 \left( \dfrac{x}{x+6}\right)

\textsf{As }x \rightarrow +\infty, \  \dfrac{x}{x+6} \rightarrow1  

\implies y\rightarrow5

\textsf{As }x \rightarrow -\infty, \  \dfrac{x}{x+6} \rightarrow1  

\implies y\rightarrow5

As x approaches infinity and negative infinity, y approaches 5 (but never gets there).    Therefore, the horizontal asymptote is y=5

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Pie

Answer:

  o = 54

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. The definition of a linear pair tells you the two angles of a linear pair total 180°. Together, these relations tell you that an exterior angle of a triangle is equal to the sum of the remote interior angles.

In this geometry, the angle marked 78° is exterior to the left-side triangle. That means ...

  78° = o° +24°

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The value of 'o' is 54.

__

<em>Additional comment</em>

n° is the supplement of 78°, so is 102°.

m° is the difference between 102° and 22°, so is 80°.

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Mkey [24]

First, you need to write to expressions to model each situation:

Plan A: 10+0.15x

Plan B: 30+0.1x


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10+0.15x=30+0.1x

<em>*Subtract 0.1x from both sides to isolate the variable*</em>

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<em>*Subtract 10 from both sides*</em>

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<em>*Divide both sides by 0.05*</em>

x=400


The plans would have the same cost after 400 minutes of calls.


To find how much money the plans cost at 400 minutes, plug 400 into either expression.  We'll use Plan A:

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3 0
3 years ago
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup o
Alik [6]

Answer:

To maximize profit, the amount of each type of coffees made are;

The number of regular latte made = 52 cups

The number of low-fat latte made = 48 cups

Step-by-step explanation:

The given parameters are;

The number of espresso in a regular latte = 1 shot

The number of cups of 2% milk in regular latte = 1 cup

The amount of whipped cream in a regular latte = 0.5 cup

The number of cups of skim milk in the low-fat latte = 1.25 cup

The number of espresso in a low-fat latte = 1 shot

The amount of whipped cream in a low-fat latte = 0 cup

The number of cups of espresso in the journey = 100 shots

The number of cups of skim milk in the journey = 60 cups

The number of cups of 2% milk in the journey = 60 cups

The amount of profit the airline makes on each regular latte = $1.58

The amount of profit the airline makes on each low-fat latte = $1.65

Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;

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y ≤ 60

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Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made

Therefore, the number of low-fat latte made, y = 48

Therefore, the number of regular latte made, x ≤ 100 - 48 = 52

For maximum profit, the maximum number of low-fat latte, 'x', should be made

Therefore, x = 52

The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte

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