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3 years ago

9

How do you solve these ? I really need help I have a test coming up so please anyone i can't sleep because im scared I'll do bad

on the test

1 answer:

White raven [17]3 years ago

5 0

Here is your answer, you just count to 10... Simple as that.

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

3 0

2 years ago

PLEASE HELP ME ASAP :D

Ivanshal [37]

Answer: The answer is 5^5.

Step-by-step explanation:I don't know

sorry for taking so long

i got this from my sis and she just didn't give me an explanation.

3 0

8 months ago

At 12:00 noon two Mississippi steamboats are 126 miles apart. At 6:00 p.m. they pass each other going in opposite directions. If

Anna35 [415]

Just add 126 + 9 = 135 easy

4 0

3 years ago

There are 15 girls and 10 boys in a 5th grade class. What is the ratio of girls to boys? Write this as a simplified fraction :

notsponge [240]

Step-by-step explanation:

15 + 10 = 25 people

15 are girls and 10 are boys and that makes 15/10 ratio.

15/10 divided by 5 each is 15/5=3 and 10/5=2 which gets you a simplified fraction of

3/2

Hope this helped!

7 0

3 years ago

There are 27369 wild horses on land being managed. estimated that 48.4% of this total is in nevada. how many horses are in nevad

bixtya [17]

48.4% of 27369....turn percent to decimal..." of " means multiply

0.484(27369) = 13246.596....round down to 13246 horses

8 0

3 years ago