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Rashid [163]
3 years ago
7

A - g(x) = |x-5|+5 B - g(x) = |x-5| C - g(x) = |x|+5 D - g(x) = |x+5|+5

Mathematics
1 answer:
n200080 [17]3 years ago
5 0

Answer:

g(x) =  |x|  + 5

Step-by-step explanation:

Since both the original and transformed graph have the same x value for their vertex, there was no horizontal shift. However the vertex shifted up. Specifically it shifted up 5 units. Therefore:

g(x) = f(x) + 5

The plus 5 performs a translation up 5 units. Plugging in for f(x) it can be seen that:

g(x) =  |x|  + 5

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Complete question:

Anty was riding his bike to school at a speed of 12 mph. When he was <u>half </u>of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?

Answer:

His average speed is 19.2 mph

Step-by-step explanation:

Given;

speed of Anty to school half of the way, v₁ = 12 mph

speed of Anty when his mother drove him half of the way, v₂ = 48 mph

The average speed of Anty is calculated as;

V_{average} = \frac{Total \ distance }{Total \ time }

The value of the average speed is closer to 12 mph than 48 mph because Anty spent more time moving at 12 mph than at 48 mph.

Let the equal distance travel at each speed = 96 miles

Time taken at 12 mph = \frac{96 \ mile}{12 \ m/h} = 8 \ hours

Time taken at 12 mph = \frac{96 \ mile}{48 \ m/h} = 2 \ hours

Average speed = \frac{Total \ distance}{Total \ time } = \frac{96 \ mile \ + \ 96 \ mile}{2\ hr \ + \ 8\ hr} = \frac{192 \ miles}{10 \ hrs} = 19.2 \ mph

Also, you can assume any other equal distance traveled at each speed, the average speed will still be 19.2 mph.

<u>Check:</u> let the equal distance traveled at each speed = 480 miles

Time taken at 12 mph = 480/12 = 40 hours

Time taken at 48 mph = 480/ 48 = 10 hours

Average speed = (480 + 480) / (40 + 10)

                          = 19.2 mph

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