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tangare [24]
3 years ago
8

Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the coefficient 'k' in the factored form? 6x3 + 4x2 − 6x − 4 = 2(x

+ k)(x − k)(3x + 2) k= ____________ Numerical Answers Expected! Answer for Blank 1:
Mathematics
1 answer:
anastassius [24]3 years ago
5 0

6x^3+4x^2-6x-4 =\\ 2(3x^3+2x^2-3x-2) =\\ 2(x^2(3x+2)-1(3x+2))=\\ 2(x^2-1)(3x+2)=2(x+1)(x-1)(3x+2).

So k=1.

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Given the function graphed below, what is the average rate of change between f(3) and f(7)?
Shkiper50 [21]
Answer: choice D) 20

-------------------------------

Explanation:

Locate 3 on the x axis number line. Draw a vertical line through 3 and this vertical line will cross the parabola at some point P. Mark this point P on the parabola. Then draw a horizontal line from P to the y axis. The horizontal line will land on y = 10. In short, this all shows us that (3,10) is a point on this parabola.

Repeat those steps above, but now for x = 7. You'll see that (7,90) is another point on this parabola.

We need to find the slope of the line through the two points (3,10) and (7,90). The average rate of change from x = 3 to x = 7 is the same as the slope of the line through those two points.

To find the slope, we use the slope formula
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the two points, and m is the slope

In this case,
(x1,y1) = (3,10) and (x2,y2) = (7,90)
further breaking down to
x1=3
y1=10
x2=7
y2=90
So we'll plug those four pieces of info into the equation and simplifying to get...
m = (y2 - y1)/(x2 - x1)
m = (90 - 10)/(7 - 3)
m = 80/4
m = 20

The slope of the line is 20, so therefore, the average rate of change is 20.

6 0
3 years ago
The following six independent length measurements were made (in feet) for a line: 736.352, 736.363, 736.375, 736.324, 736.358, a
horrorfan [7]

Answer:

Assuming population data

\sigma = \sqrt{0.000354}=0.0188

Assuming sample data

s = \sqrt{0.000425}=0.0206

Step-by-step explanation:

For this case we have the following data given:

736.352, 736.363, 736.375, 736.324, 736.358, and 736.383.

The first step in order to calculate the standard deviation is calculate the mean.

Assuming population data

\mu = \frac{\sum_{i=1}^6 X_i}{6}

The value for the mean would be:

\mu = \frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359

And the population variance would be given by:

\sigma^2 = \frac{\sum_{i=1}^6 (x_i-\bar x)}{6}

And we got \sigma^2 =0.000354

And the deviation would be just the square root of the variance:

\sigma = \sqrt{0.000354}=0.0188

Assuming sample data

\bar X = \frac{\sum_{i=1}^6 X_i}{6}

The value for the mean would be:

\bar X = \frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359

And the population variance would be given by:

s^2 = \frac{\sum_{i=1}^6 (x_i-\bar x)}{6-1}

And we got s^2 =0.000425

And the deviation would be just the square root of the variance:

s = \sqrt{0.000425}=0.0206

6 0
3 years ago
A hat is on sale for 20% off. If the original price was $32.00, what is the sale price? (HINTI not the amount taken off)
maria [59]

Answer:

6.4

Step-by-step explanation:

This is because 20% of 32 is 6.4.

6 0
3 years ago
What is the answer to 4[5(12 3)-2]-7
AleksandrR [38]
4[5(12*3)-2]-7 4[5(36)-2]-7 4[180-2]-7 4[178]-7 712-7= 705 :)
6 0
2 years ago
The balance in Meg's savings account can be calculated using the
Zielflug [23.3K]

Answer:

do you have a picture of the question?

7 0
2 years ago
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