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masya89 [10]
3 years ago
6

Ken normally leaves work at 5:00 pm, but he is leaving 20 minutes late today. He decides to make up time by taking the toll road

instead of side streets. He can travel three times faster by taking the toll road. Create an equation in terms of x to represent the number of minutes after 5:00 pm he arrives home from work if he leaves late. Let x represent the number of minutes his normal commute takes when he leaves on time.
y equals one third times x plus twenty
y = 3x + 20
y equals one third times x minus twenty
y = 3x − 20
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Mathematics
1 answer:
NemiM [27]3 years ago
4 0

Answer:

y =1/3x+20

Step-by-step explanation:

He starts 20 minutes late so we need to add 20 minutes to the time

He travels 3 times faster so he takes 1/3 of the normal time x

y =1/3x+20

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Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.
Sladkaya [172]

Answer:

The most cost effective company will be Painting USA that charge $700 to paint Paul house .

As given

Paul is going to have the exterior of his home painted.

Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor.

If it takes 25 hours to paint Paul’s house.

Total amount charge by Painting USA = Painting USA charges for come out  and evaluate the house + Cost of per hour of labor × Total hours take to paint Paul house .

Total amount charge by Painting USA = 75 + 25 × 25

                                                               = 75 + 625

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As given

Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.

Total amount charge by Upscale Home Painting = Cost of per hour of labor × Total hours take to paint Paul house

                                                                                = 40 × 25

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Step-by-step explanation:

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Step-by-step explanation:

When plugging in zero into the given equation:

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Answer is in indeterminate form = use L'Hospital's Rule:

(Derivative of the top / Derivative of the bottom)

\lim_{x \rightarrow 0}  \frac{ \frac{1}{2} (x + 7)^{ \frac{-1}{2}} - 0 }{1}

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\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }

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Answer:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} = \frac{1}{2 \sqrt{7} }

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