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elena-14-01-66 [18.8K]
3 years ago
13

Solve this identifying holes, vertical asymptotes, and horizontal asymptotes for

Mathematics
1 answer:
USPshnik [31]3 years ago
6 0

x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{Vertical asymptotes:}\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\\boxed{x=-4\ and\ x=1}\\\\\text{Horizontal asymptotes:}

\lim\limits_{x\to\pm\infty}\dfrac{x^2+7x+12}{-x^2-3x+4}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\dfrac{7}{x}+\dfrac{12}{x^2}\right)}{x^2\left(-1-\dfrac{3}{x}+\dfrac{4}{x^2}\right)}=\dfrac{1}{-1}=-1\\\\\boxed{y=-1}

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Hannah,her dad,and her grandmother each ate 2/8. How much pizza did they eat altogether?
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Answer:

6/8

Step-by-step explanation:

2/8 + 2/8 + 2/8 = 6/8.

Add the tops. Hope this helps :)

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Officials estimate that 320,000 Boston-area partygoers attended last year's Independence Day celebration on the banks of the Cha
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40 ton x 2000 = 80,000 pounds

320000/8000 = 40 pounds per person

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3 years ago
The table shows the number of cups of water required when cooking different amounts of rice.
swat32

Answer:

  • The amount of water is the dependent value.
  • The amount of rice is the independent value.

Step-by-step explanation:

The wording "the amount of water required for different amounts of rice" suggests that the "output" value of the table is the amount of water, and the "input" value is the amount of rice.

That makes "water" the <em>dependent</em> variable, and "rice" the <em>independent</em> variable.

  The amount of water is the dependent value.

  The amount of rice is the independent value.

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3 years ago
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On the attached drawing what is the name for Angle LHJ? Obtuse, acute, complementary or right?
Natasha2012 [34]

Answer: Right (Last option)

Step-by-step explanation:

As you can see in the figure, the parallel lines AD and GJ are intersected  by two lines.

The line EL intersects the parallel lines and there are two angles that are formed by this intersections which are located on the exterior of AD and GJ, but  on opposite sides of EL, (these angles are called "Alternate exterior angles" and they are congruent), which are:

 ∠LHJ and ∠EBA

You can observe that the angle ∠EBA is indicated with a square. This means that the measure of that angle is 90° (Right angle).

Therefore, if ∠EBA=90°, then ∠LHJ =90°

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In 2020, dawn earned $248,000. social security tax is 6.2% to a maximum income of $137,700. what was your monthly gross pay? in
Dovator [93]

Monthly gross pay is $20,666.67; Dawn reached the maximum taxable social security income in July; the amount of social security tax Dawn paid in February, July and November are $1,281.33, $849.42, and $0 respectively.

<h3>How do we calculate Social Security Tax?</h3>

Annual gross pay = $248,000

Monthly gross pay = $248,000 / 12 = $20,666.67

Maximum taxable social security income = $137,700

Social Security Tax Rate = 6.2%

Total Social Security Tax = Maximum social security income * Social Security Tax Rate = $137,700 * 6.2% = $8,537.40

Monthly Social Security Tax = Monthly gross earnings * Social Security Tax Rate = $20,667 * 6.2% = $1,281.33

Number of months Don reached the maximum taxable social security income = Maximum social security income / Monthly gross pay = $137,700 / $20,666.67 = 6.66 months

Since 6.66 months is greater than 6 but less than 7, this implies that the month Don reached the maximum taxable social security income is the 7th month which is July 2020.

Also, the 6.66 months imply that Dawn will fully pay his Total Social Security Tax in July.

Social security tax Dawn paid in February = Monthly Social Security Tax = $1,281.33

Social security tax Dawn paid in July = Total Social Security Tax - (Monthly Social Security Tax * 6) = $8,537.40 - ($1,281.33 * 6) = $849.42

Social security tax Dawn paid in November = $0

Note that $0 was paid in November because Dawn had already paid fully his Total Social Security Tax in July.

Learn more about Total Social Security Tax here: brainly.com/question/18268724.

#SPJ1

3 0
1 year ago
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