Which problem can be solved using the equation below?

What is the simplified form of 4(2x - 5) + 2(3x + Y)?

evablogger [386]

Answer:

I think this is the answer! 2x3 + 5x2 - x - 6 let me know if it’s right :)

Step-by-step explanation:

5 0

2 years ago

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago

I need help with this question please

Novay_Z [31]

I think the answer is 80 because I’m point 2 it’s is 40 and in point 3 is 60 and in point 5 is 100 so I am guessing each goes by 20 so what is between 60 and 100 if you can’t by 20s would be 80 I don’t know if I am correct tho

4 0

3 years ago

Chin made an error in his chart showing the multiplication of the binomial by the trinomial. Which change can be made to correct

stealth61 [152]

Answer:

The expression 6x should be 6x^2.

Step-by-step explanation:

Given is the chart of multiplication of the binomial by the trinomial.

Let's check each element in the chart:-

3x times x^2 = 3x^3

3x times 2x = 6x^2

3x times 4 = 12x

2 times x^2 = 2x^2

2 times 2x = 4x

2 times 4 = 8

From the given chart, we can identify that 6x should be 6x^2.

Hence. option B is correct, i.e. The expression 6x should be 6x^2.

7 0

3 years ago

Read 2 more answers

Write an equation for the proportional relationship. Let X represent a length measured in meters and y represent the same length

anzhelika [568]

Answer:

$y=100x$

Step-by-step explanation:

Given that $x$ is the length measured in meters and

$y$ represents the same length measured in centimeters.

Let us first have a look at the relationship between meters and centimeters units of length.

1 unit of length in meters = 100 units of length in centimeters

Therefore, it can be said that:

2 units of length in meters = 200 units of length in centimeters

3 units of length in meters = 300 units of length in centimeters

4 units of length in meters = 400 units of length in centimeters

OR

$x$ units of length in meters = 100 $x$ units of length in centimeters

It is given that $y$ is the length in centimeters.

Therefore, the proportional equation can be written as:

$y=100x$

6 0

3 years ago