Help ! I’m confused

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

8 0

Angle 1 and angle 2 are what are called alternate angles. Two opposite angles between parallel lines. this means they are equal to each other.

So we have an equation: 2x + 20 = 3x + 10

Subtract 2x and 10 from each side

We now have 10 = x, so we know what x is

now plug in x to angle 1: (2 x 10) + 20 = 40, so angle 1 = 40.

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What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

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Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.

For example:

Type of change Effect on y = f(x)

$y = f(x - c)$ horizontal shift: c units to right

Considering the function

$f(x) = x^2$

The graph is shown below. The first figure is representing $f(x) = x^2$ .

Now, considering the function

$\:f\left(x\right)=\left(x-6\right)^2$

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shown below in second figure. It is clear that the graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shifted 6 units to the right as compare to the function $f(x) = x^2$ .