The two linear functions ƒ(x) and g(x) are shown below.

A student took a system of equations, multiplied the first equation by and the second equation by , then added the results toget

Ierofanga [76]

Answer:

option A

-2x + 4y = 4

-3x + 6y = 6

Step-by-step explanation:

In option A, if the student multiply the first equation by 3 and the second equation by -2, then the equations become

-6x+12y = 12 and

6x-12y =-12

If she adds both equations, she will get 0 = 0

This means that the system has infinite number of solutions.

Hence, the student could have started with equations -2x + 4y = 4 and -3x + 6y = 6.

3 0

4 years ago

How do you determine the degree of a power function from a table? When do you know you have successfully determined the degree o

svp [43]

Answer:

A power function is a function that can be represented in the form

$f(x)=kx^p$

where k and p are real numbers, and k is known as the coefficient.

Example:

f(x)=1 constant function.

f(x)=x identity function

f(x)=x^2 quadratic function.

1)

we use the method of differences, g(x+1)-g(x). Keep taking differences until they are all constant.

for example:

if we have a set of values as:

x g(x)

−2 −8

−1 −1

0 0

1 1

2 8

Now when we find the difference as:

x g(x) D1 D2 D3

-2 -8

-1 -1 1-(-8)=7

0 0 0-(-1)=1 1-7=-6

1 1 1-0 = 1 1-1=0 0-(-6)=6

2 8 8-1 = 7 7-1=6 6-0 = 6

As D3 is constant hence, the degree of the power function is 3.

2)

When we get a constant difference in the table of the difference method we will successfully get our degree.

4 0

3 years ago

In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes. Complete the following: Rx Rk : (2,5)

motikmotik

The point with a coordinate of (2,5) will be translated into y=-x line. The transformation for y=-x would be:
1. x'= -y
2. y'= -x

For x=2 and y=5 would be:
x'= -y
x'= -5

y'= -x
y'= -2

The translated coordinate would be: (-5, -2)

6 0

3 years ago

There are 46 animals in a farmyard. some are cows and some are chickens. in total there are 104 legs. how many chickens are ther

Andrei [34K]

There are 40 chickens

4 0

3 years ago

The graph shows the result of a matrix transformation, where the pre-image has dashed lines Which matrix operation is represente

diamong [38]

The matrix operation is the addition subtraction and multiplication involving matrices. The coordinates of the image can be represented as a matrix obtained from the coordinates of the preimage through matrix operations

The best correct option is option D), (the y-coordinate for the point (8, -7) is to be replaced with a 7 to give (7, -7) as follows:

$\left[\begin{array}{rrrr}1&0\\0&-1\end{array}\right] \left[\begin{array}{rrrr}9&7&3&2\\-3&-7&-7&-5\end{array}\right]$

The reason the above matrix value for the matrix operation are correct are as follows:

Known parameters:

From the diagram, we have that the coordinates of the vertices of the preimage are;

(2, -5), (3, -7), (9, -3), and (7, -7)

The coordinates of the vertices of the image are;

(2, 5), (3, 7), (9, 3), and (7, 7)

Required:

The matrix operation for the transformation of the preimage points to the image points

Solution:

The transformation from the coordinates of the vertices of primage to the vertices of image involves the change in the sign from negative to positive, of the y-values of the image, which can be obtained by multiplying by (-1)

Therefore, the required matrix operation is presented as follows:

$\mathbf{\left[\begin{array}{rrrr}1&0\\0&-1\end{array}\right] \left[\begin{array}{rrrr}9&7&3&2\\-3&-7&-7&-5\end{array}\right]} =\left[\begin{array}{rrrr}9&7&3&2\\3&7&7&5\end{array}\right]$

Therefore, the best correct option is option D)

Learn more about matrix operations here:

brainly.com/question/17141646

3 0

3 years ago