18g + 24 write the expression in two other ways.

The vertex of the parabola below is at the point (1,3), and the point (2,6) is

Inessa05 [86]

Answer:

B. y=3(x-1)2 + 3

Step-by-step explanation:

Given that

vertex of the parabola is at the point (1,3)

let's verify, if the option B is the correct equation of the parabola.

$y=3(x-1)^2 + 3\\ \\y=3(x^2+1-2x) + 3\\\\y=3x^2+3-6x + 3\\\\y=3x^2-6x + 6....Eq1$

comparing to standard equationof parabola (standard quadratic equation), we get

$a=3, b=-6 and c=6$

to find the vertex we use formula for x- coordinate as $x=-b/2a$

$x=-(-6)/2(3)\\\\x=6/6\\x=1$

to find y put x=1 in the Eq1, we get

$y=3(1)^2-6(1)+6\\\\y=3-6+6\\\\y=3$

vertex =(x,y) = (1, 3)

thus vertex of the parabola from the equation y=3(x-1)2 + 3 is (1,3), thus verified

7 0

2 years ago

The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

Makovka662 [10]

Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0

2 years ago

Does anyone else agree that the answer for this family of curves question is E, dy/dx = x + y?

neonofarm [45]

Yes this is the correct answer. The slope field shown is the differential equation dy/dx = x+y

All points along the line x+y = k, for some constant k, will have the same tangent slope k. For example, the line x+y = 0 will have every point with tangent slope 0 for the solution y(x). It may not be 100% clear, but this graph has horizontal tickmarks on the line x+y = 0, or the tickmarks are close to being horizontal. Using geogebra, I checked the others and they produced completely different graphs, which allowed me to rule them out.

6 0

3 years ago

A rectangular prism has a volume of 97.5 cubic inches. The length is 5 inches and the height is 3 inches. What is the width of t

const2013 [10]

Answer:

6.5

Step-by-step explanation:

3X5=15

97.5/ 15 = 6.5

3 0

2 years ago

This triangle is being rotated. The square where the three triangles meet is called the

vagabundo [1.1K]

Answer:

center point

Step-by-step explanation:

use quizlet

5 0

3 years ago