2 years ago

20 points What is the linear function equation represented by the graph?

Mathematics

1 answer:

tigry1 [53]2 years ago

4 0

Answer:

F(x) = 2/3x + 3

Step-by-step explanation:

I found this out by first starting off with the equation, f(x) = mx + b. (b is the y intercept, m is the slope.) The y intercept, where the line passes through the y axis, is 3. (f(x) = mx + 3) Now, look at rise over run, and see that the slope is 2/3, since for every one it goes over, it goes up 2/3. your final equation is f(x) = 2/3x + 3

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A batter strikes a baseball. the equation y = -0.005^2 +0.7x + 3.5 models its path, where x is the horizontal distance, in feet,

hram777 [196]

Answer:

(D)144.8 feet

Step-by-step explanation:

Given the equation which models the path of the baseball

$y = -0.005x^2 +0.7x + 3.5$

where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.

To determine how far from the batter the ball will land, we determine the distance x at which the height, y=0.

$y = -0.005x^2 +0.7x + 3.5=0$

$-0.005x^2 +0.7x + 3.5=0$

We use the quadratic formula to solve.

In the quadratic equation above, a=-0.005, b=0.7, c=3.5

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\=\dfrac{-0.7\pm\sqrt{0.7^2-4(-0.005*3.5)} }{2*-0.005} \\=\dfrac{-0.7\pm\sqrt{0.49+0.07} }{-0.01}\\=\dfrac{-0.7\pm\sqrt{0.56} }{-0.01}\\x=\dfrac{-0.7+\sqrt{0.56} }{-0.01} \: or\: x=\dfrac{-0.7-\sqrt{0.56} }{-0.01}\\x=-4.83 \: or\: x=144.83$

Since x cannot be negative, x=144.8 feet to the nearest tenth of a foot.

<u>The correct option is D.</u>

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Step-by-step explanation:

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