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3 years ago

The table of values represents a function f(x).

Mathematics

1 answer:

NeX [460]3 years ago

5 0

Answer:

The average rate of change over the interval [9,10] is greater than that over the interval [5,8] by 6490.

Step-by-step explanation:

The value of f(x) = 4052 for x = 9 and f(x) = 11014 for x = 10.

Therefore, the average rate of change of f(x) with respect to x over the interval [9,10] is given by

= $\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}$

= $\frac{11014 - 4052}{10 - 9} = 6962$

Now, the value of f(x) = 75 for x = 5 and f(x) = 1491 for x = 8.

Therefore, the average rate of change of f(x) with respect to x over the interval [5,8] is given by

= $\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}$

= $\frac{1491 - 75}{8 - 5} = 472$

Therefore, the average rate of change over the interval [9,10] is greater than that over the interval [5,8] by (6962 - 472) = 6490. (Answer)

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Graphing Form for Linear Equations in 2 variables.

NeX [460]

X-intercept: y = 0
y-intercept: x = 0

3x + 4y = 0

x-intercept: subtitute y = 0
3x + 4 · 0 = 0
3x = 0
x = 0 → (0; 0)

y-intercept: subtitute x = 0
3 · 0 + 4y = 0
4y = 0
y = 0 → (0; 0)

3 0

3 years ago

Rewrite the system of linear equations as a matrix equation AX = B.

iren2701 [21]

Answer:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

Step-by-step explanation:

Let's find the answer.

Because we have 3 equations and 3 variables (x1, x2, x3) a 3x3 matrix (A) can be constructed by using their respectively coefficients.

Equations:

Eq. 1 : x1 + 2x2 + 5x3 = 5

Eq. 2 : x1 + x2 + x3 = 6

E1. 3 : 4x1 + 6x2 + 5x3 = 7

Coefficients for x1 ; x2 ; x3

From eq. 1 : 1 ; 2 ; 5

From eq. 2 : 1 ; 1 ; 1

From eq. 3 : 4 ; 6 ; 5

So matrix A is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]$

And the vector of vriables (X) is:

$\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]$

Now we can find the resulting vector (B) using the 'resulting values' from each equation:

$\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

In conclusion, AX=B is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

7 0

4 years ago

under a dilation, the point (2,6) is moved to (6,18) what is the scale factor of the dilation? enter your answer in the box

Anestetic [448]

Step-by-step explanation:

The equation of line passing through the two points is $\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2} -y_{1}}{x_{2} -x_{1}}$