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3 years ago

1. IF the function f(x) = 2(x – 3)2 – 4 is shifted vertically three units up and horizontally

Mathematics

1 answer:

hichkok12 [17]3 years ago

3 0

Answer:

I believe it is 2(x-5)²−1

Step-by-step explanation:

The parentheses represent the horizontal shift. (X-__) is a shift to the right. (X+__) is a shift to the left. The last number of the function is the vertical shift. A negative number is shifting down and a post number is shifting up.

So, if the graph shifts up three units, then you add 3 + -4 to get -1. And if the graph shifts right 2 units, then you subtract 2 from -3 to get -5.

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3 years ago

Find an equation for the line that passes through the points (5.-5) and (-4,-2)

ANEK [815]

Answer:

$\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, -5) and (-4, -2).

Substiute:

$m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}$

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

$-5=-\dfrac{1}{3}(5)+b$

$-5=-\dfrac{5}{3}+b$ add 5/3 to both sides

$-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}$

Finally we have the equation of a line in the slope-intercept form:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$ multiply both sides by 3

$3y=-x-10$ add x to both sides

$x+3y=-10$

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3 years ago

How many hours will it take to complete a 76km bike ride if you go bike ride if you go 14km per hour the whole time?

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Hours = 76 km / 14 km per hour

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Round the answer as needed.

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4 years ago

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xxTIMURxx [149]

Answer:

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Step-by-step explanation:

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3 years ago