How can you use the structure of a two way frequency table to complete it

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

Answer correct answer for brainliest

neonofarm [45]

Answer:

Bro it’s a’c’d the sun the moon and the earth their energy works together pushing and pulling towards the earth creating a gravitational pull.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the slope of the line with points of (0,-1)) and (2,3)

ycow [4]

Answer:

2

Step-by-step explanation:4divided by 2 =2

3 0

2 years ago

Read 2 more answers

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The mon

kkurt [141]

The monthly cost will be $17.14

Step-by-step explanation:

Given that the monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes) then this can be presented in a table form as;

<u>Time in minutes (x)</u> <u>Cost in dollars (y)</u>

50 $12.55

102 $ 17.23

Take the values as ordered pairs to represent coordinates for points that satisfy the linear function

(50,12.55) and (102,17.23)

Finding the slope of the graph using these points

slope,m=Δy/Δx

m=Δy=17.23-12.55 =4.68

Δx=102-50=52

m=4.68/52 =0.09

Finding the equation of the linear function using m=0.09, and point (50,12.55)

m=Δy/Δx

0.09=y-12.55/x-50

0.09(x-50)=y-12.55

0.09x-4.5=y-12.55

0.09x-4.5+12.55=y

y=0.09x+8.05

So for 101 minutes , the cost will be;

y=0.09*101 +8.05

y=9.09+8.05 = $17.14

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Linear functions : brainly.com/question/11052356

Keyword : linear function

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5 0

3 years ago

The Lakewood Wildcats won 5 of their first 8 games this year. There are 32 games in the season. How many games would you expect

siniylev [52]

Answer:

x=20

Step-by-step explanation:

Rewrite the equation as

x /32 = 5/ 8

Multiply both sides of the equation by 32

32 ⋅ x /32 = 32 ⋅ 5/8

Simplify both sides of the equation.

Cancel the common factor of

32

Cancel the common factor.

Rewrite the expression.

x = 32 ⋅ 5/8

Simplify

32⋅5/8

Cancel the common factor of

8

Factor 8 out of 32

x = 8 ( 4 ) ⋅ 5/8

Cancel the common factor.

Rewrite the expression.

x = 4 ⋅ 5

Multiply 4 by 5

8 0

3 years ago