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MrRa [10]
3 years ago
12

Paul owes PAula $.35 and has a pocket full of five cents $.10 coins and $.25 coins that he can use to pay her what is the differ

ence between the largest in the smallest number of coins he can use to pay her
Mathematics
1 answer:
coldgirl [10]3 years ago
4 0
He can use:
a quarter and a dime (difference: 15)
a quarter and two nickels (difference: 20)
a dime and three nickels (difference: 5)
two dimes and a nickel (difference: 5)
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A contestant has to eat 45 hot dogs in 9 minutes to beat the record for hot dog eating. How much time does the contestant have t
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Answer:

5

Step-by-step explanation:

If the contestant has 9 minutes for 45 hotdogs, then you would have to divide 45 by 9 to get the answer. 45 divided by 9 is 5.

Then, to see if your answer makes sense, you would multiply 9 by 5 to see if you get 45, which you do.

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Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2. ​
insens350 [35]

Answer:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

Step-by-step explanation:

Given

p(x) = \frac{x^2-2x-3}{x+2} -- Missing from the question

Required

The behavior of the function around its vertical asymptote at x = -2

p(x) = \frac{x^2-2x-3}{x+2}

Expand the numerator

p(x) = \frac{x^2 + x -3x - 3}{x+2}

Factorize

p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}

Factor out x + 1

p(x) = \frac{(x -3)(x + 1)}{x+2}

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

x -> -2^{-} Say x = -3

p(x) = \frac{(x -3)(x + 1)}{x+2}

p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

x->-2^{-}, p(x)->-\infty

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: x>-2

Say x = -2.1

p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

x->-2^{+}, p(x)->-\infty

So, the behavior is:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

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At the fair,Kate found a strange machine with a sign on it labeled, enter a number. When she pushed the number 15, the machine d
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apparently subtracting 6

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