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svp [43]
4 years ago
11

Shonda jogs 5 miles per hour. Graph the relationship between the number of hours Shonda jogs and the total number of miles jogge

d.

Mathematics
2 answers:
Phoenix [80]4 years ago
7 0
I think if you graph this relationship the plot would be a linear relationship. In the x axis would be the time and in the y axis the distance. For the first hours, the point would be at (1, 5). For the next hour, (2,10) and so on. Hope this answers the question. Have a nice day.
arsen [322]4 years ago
5 0

Let

x-------->  the number of hours Shonda jogs

y---------> the total number of miles jogged

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

in this problem

the unit rate 5\frac{miles}{hour} represent the slope of the linear equation or the value of the constant of proportionality k

so

the linear equation is

y=5x

using a graphing tool

see the attached figure

the answer in the attached figure

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find the vertex of the quadratic passing through the point f(3/2)=9, has an x-intercept of 3 and the axis of symmetry is x=2
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The vertex of the quadratic is (2 , 12)

Step-by-step explanation:

The vertex form of the quadratic function is f(x) = a(x - h)² + k, where

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∵ The function of quadratic

∴ f(x) = a(x - h)² + k

∵ The axis of symmetry of the function is x = 2

∵ The axis of symmetry of a quadratic function is a vertical line at x = h

∴ h = 2

- Substitute h by 2 in f(x)

∴ f(x) = a(x - 2)² + k

∵ The quadratic passing through the point f(3/2) = 9

- That means the coordinates of the point are (\frac{3}{2},9)

∴ x = \frac{3}{2}  and y = 9

- Substitute x and y in the equation by the values above

∴ 9 = a( \frac{3}{2} - 2)² + k

∴ 9 = a( \frac{-1}{2} )² + k

∴ 9 = \frac{1}{4} a + k

- Multiply each term by 4

∴ 36 = a + 4 k

∴ a + 4 k = 36 ⇒ (1)

∵ x intercept of f(x) = 3

- That means the graph of f(x) intersects x-axis at point (3 , 0)

∴ x = 3 and y = 0

- Substitute x and y in the equation by the values above

∴ 0 = a(3 - 2)² + k

∴ 0 = a(1)² + k

∴ 0 = a + k

∴ a + k = 0 ⇒ (2)

Now we have system of equation let us solve it to find k

∵ a + 4 k = 36 ⇒ (1)

∵ a + k = 0 ⇒ (2)

- Subtract equation (2) from equation (1) to eliminate a

∴ 3 k = 36

- Divide both sides by 3

∴ k = 12

∵ (h , k) are the coordinates of the vertex of the quadratic function

∴ (2 , 12) are the coordinates of the vertex of the quadratic function

The vertex of the quadratic is (2 , 12)

Learn more:

You can learn more about quadratic in brainly.com/question/9390381

#LearnwithBrainly

4 0
3 years ago
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