The length of the window is 2m longer than its width and the are is 32m²

Give the function f(x) = 3 ^ x - 4x determine the average rate of change from x = 1 x = 2

yuradex [85]

Answer:

2

Step-by-step explanation:

Given the average rate of change formula, we must first find the x and y values of the function.

We are provided with the two x values, 1 and 2. We now need to find the output, or y.

ƒ(x)=3^x-4x

ƒ(1)=3-4=-1

ƒ(2)=9-8=1

Then, we use the formula (ƒ(2)-ƒ(1))/x2-x1(subscripts here, in case you multiplied) which gets us 2/1, or 2. Therefore, the average rate of change(ARC) is 2. I believe you just need to find the output and subtract if they are exactly one whole number apart, but don't quote me on that.

6 0

4 years ago

Use Lagrange multipliers to solve the following exercise. A home improvement contractor is painting the walls and ceiling of a r

mash [69]

Answer:

Let the width of the garden =x meter

Then length=(x+4) meter

Half perimeter =36 m

So perimeter of garden =(2×36)=72 meters

According to the question

⇒2(l+b)=72

⇒2(x+x+4)=72

⇒2x+2x+4=74⇒4x=64⇒x=16 meters

Hence,the width of the garden =16 meters

The length of the garden =(16+4)=20 meters

5 0

3 years ago

Evaluate -3x² + 4x-2 for x = 2.<br> A. -2<br> B. -1<br> C. -6<br> D. 18

kobusy [5.1K]

Answer:

C. -6

Step-by-step explanation:

-3(2)²+4(2)-2

-3(4) + 8 - 2

-12+8-2

-14+8

-6

5 0

2 years ago

Find the set of solutions for the linear system.

Illusion [34]

Answer:

The system has infinitely many solutions.

$\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9} \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3} \\x_4&=&s_2\end{array}\right$

Step-by-step explanation:

To find the solution for this system of linear equations $-3x_1-x_2+4x_3=2\\-3x_3 - 4x_4 = -1$ you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

A matrix is a rectangular arrangement of numbers into rows and columns.

A system of equations can be represented by an augmented matrix.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is matrix that represents the system

$\left[ \begin{array}{ccccc} -3 & -1 & 4 & 0 & 2 \\\\ 0 & 0 & -3 & 4 & -1 \end{array} \right]$

The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

Interchange two rows (or columns).
Multiply each element in a row (or column) by a non-zero number.
Multiply a row (or column) by a non-zero number and add the result to another row (or column).

Using elementary matrix operations, we get that

Row Operation 1: Multiply the 1st row by -1/3

Row Operation 2: Multiply the 2nd row by -1/3

Row Operation 3: Add 4/3 times the 2nd row to the 1st row

$\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]$

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

$\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]$

which corresponds to the system

$x_1+\frac{1}{3}x_2+ \frac{16}{9}x_4=-\frac{2}{9} \\x_3+ \frac{4}{3}x_4=\frac{1}{3}$

We see that the variables $x_2, x_4$ can take arbitrary numbers; they are called free variables. Let $x_2=s_1$ , $x_4=s_2$ . All solutions of the system are given by

$\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9} \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3} \\x_4&=&s_2\end{array}\right$

The system has infinitely many solutions.

8 0

4 years ago

The data shown are hourly wages of some employees of a small company. $5, $7, $8, $10, $24, $40 Which values, if any, are outlie

igor_vitrenko [27]

correct answer is "NONE" NOT $40. hOPE THIS HELPS!

3 0

3 years ago