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3 years ago

Identify the vertical asymptotes of f(x)=x+6 over x^2-9x+18

1 answer:

7 0

$\bf \cfrac{x+6}{x^2-9x+18}
\\\\\\
x^2-9x+18=\underline{0}\implies (x-6)(x-3)=0\implies x=
\begin{cases}
6\\
3
\end{cases}$

vertical asymptotes occur, at zeros of the denominator, so long the value doesn't make the numerator zero.

so, in this case are x = 6 and x = 3.

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7 0

2 years ago

A pair of flip flops is $30. How much will they cost after a 20% discount and 6.5% tax. Please show your work.

jeka94

Answer:

The flip flops cost $25.56 after the discount and tax.

Step-by-step explanation:

A pair of flip flops is $30. This is our starting amount.

The tax will be applied on the price the flip flops are bought for. This means we must apply the discount first.

The discount is 20%. Let's find what the flip flops were sold for.

If the discount is 20%, the flip flops were sold for 80% of their original price. Let's find 80% of 30.

80% of 30 = ?

0.80 • 30 = ?

= 24

The flip flops were sold for $24.

Now we have to apply a 6.5% tax. To find the amount of money added to the total, we need to find 6.5% of 24.

6.5% of 24 = ?

0.065 • 24 = ?

= 1.56

The tax was $1.56.

We need to add the tax to the discounted price.

1.56 + 24 = ?

= 25.56

The flip flops cost $25.56 after the discount and tax.

Hope this helps!

6 0

3 years ago

This year, a small business had a total revenue of $72,900. If this is 35% more than their total revenue the previous year, what

ziro4ka [17]

Answer:

Therefore there revenue was $540,000.

Step-by-step explanation:

Let their total revenue last year be x

35% of x = $72,9000 - x

or, 35/100 × x = 729000 - x

or, 7x/20 = 729000-x

or, 7x = 20(729000-x)

or, 7x = 1458000- 20x

or, 7x + 20x = 14580000

or, 27x = 14580000

or, x = 14580000/27

so, x = $540,000

4 0

3 years ago

A bag has 6695 blue marbles and 6696 red marbles. We repeatedly remove 2 marbles from the bag. If the two chosen marbles are of

Rasek [7]

9514 1404 393

Answer:

blue

Step-by-step explanation:

If two red marbles are removed, 1 red is returned. The number of reds is reduced by 1, and the number of blues is unchanged.

If two blue marbles are removed, 1 red is returned. The number of reds is increased by 1, and the number of blues is decreased by 2.

If one of each is removed, one blue is returned. The number of reds is reduced by 1, and the number of blues is unchanged.

So, at each step, the number of blue marbles is unchanged or reduced by 2. That is, it only changes by an even number. The number of blues is initially odd, so can never reach zero.

The last marble in the bag is blue.

5 0

3 years ago

Garys Rentals charges a 10 percent fee on all late returned vehicles. Tim returned his car late. If Tim's rental costs $405.34 a

Zina [86]

Answer:

Step-by-step explanation:

8 0

3 years ago