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2 years ago

PLEASE HELP, THIS MY LAST QUESTION. I WILL MARK BRAINLEST.

Mathematics

1 answer:

dalvyx [7]2 years ago

7 0

Answer:

Part 1: 30.35 runners

Part 2: 2024

Step-by-step explanation:

We will need to find an equation that best fits this data

The equation of best fit for this data is y = 2.16x - 4291.81

Now in order to figure our part 1, we will need to plug in 2001 for our x value to solve for y and we get:

y = 2.16(2001) - 4291.81 which then simplifies to y = 30.35

Then to figure out part 2, we need to plug in 80 (NOT 80,000 because the y-values are in thousands, meaning we only need to use the number 80) for our y-value and solve for x and we get:

80 = 2.16x - 4291.81
Adding 4291.81 to both sides we get: 4371.81 = 2.16x
Then dividing both side by 2.16 we get 2023.98 = x ≈2024

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Using a graphing utility, find the exact solutions of the system. Round to the nearest hundredth and choose a solution to the sy

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Answer:

Part 1) The exact solutions are

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ and $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

$y=x^{2} +3x$ ----> equation A

$y=2x+5$ ----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

Find the exact solutions of the system

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$ax^{2} +bx+c=0$

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in this problem we have

$x^{2} +x-5=0$

$a=1\\b=1\\c=-5$

substitute in the formula

$x=\frac{-1\pm\sqrt{1^{2}-4(1)(-5)}} {2(1)}$

$x=\frac{-1\pm\sqrt{21}} {2}$

The solutions are

$x_1=\frac{-1+\sqrt{21}} {2}$

$x_2=\frac{-1-\sqrt{21}} {2}$

Find the values of y

First solution

For $x_1=\frac{-1+\sqrt{21}} {2}$

$y=2(\frac{-1+\sqrt{21}} {2})+5$

$y=-1+\sqrt{21}+5\\\\y=4+\sqrt{21}$

The first solution is the point $(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$

Second solution

For $x_2=\frac{-1-\sqrt{21}} {2}$

$y=2(\frac{-1-\sqrt{21}} {2})+5$

$y=-1-\sqrt{21}+5\\\\y=4-\sqrt{21}$

The second solution is the point $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Round to the nearest hundredth

First solution

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ -----> $(1.79,8.58)$

$(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$ -----> $(-2.79,-0.58)$

see the attached figure to better understand the problem

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