2x^2+28x+98=0 factor completely

The image of (2,-3) after a reflection in the line y=x is ?

Amiraneli [1.4K]

(-3,2) bc that is the reflection of the two number all you do is baically flip the numbers

5 0

3 years ago

Given the parent function f(x)=|x|, write the equation of the function g(x) whose graph is pictured

kenny6666 [7]

By analyzing the graph of the transformed function, we can see that:

g(x) = 2*|x - 2| - 4

<h3>How to get the function g(x)?</h3>

In the image we have two graphs, the yellow one is the graph of g(x).

First, analyzing the vertex we can see the translation used, you need to remember:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.
If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.
If N is negative, the shift is downwards.

We can see that the new vertex is at (2, -4), so the translation is 2 units to the right and 4 units down, then we have:

g(x) = |x - 2| - 4

Now, you also can see that the yellow function is narrower, such that for each increase in the x-unit, we have an increase of 2 in the y-axis, then we need to multiply by 2 the absolute value part:

g(x) = 2*|x - 2| - 4

This is the transformed function.

If you want to learn more about transformations, you can read:

brainly.com/question/4289712

5 0

2 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Novay_Z [31]

Answer: $3+\sqrt{2}$

Step-by-step explanation:

Given the following expression shown in the picture:

$\frac{7}{3-\sqrt{2} }$

You need to use a process called "Ratinalization".

By definition, using Rationalization you can rewrite the expression in its simplest form so there is not Radicals in its denominator.

Then, in order to simplify the expression, you can follow the following steps:

Step 1. You need to multiply the numerator and the denominator of the fraction by $3+\sqrt{2}$ , which is the conjugate of the denominator $3-\sqrt{2}$ .