When asked to write the domain for the equation y= |x - 6| + 3, Mary wrote the Domain is y < 3. What mistake(s) did Mary make? Write the correct domain for Mary using inequality notation. Explain to Mary how you found your answer.

Ok, the domain is the set of values that we can input in a function.

In this case, we have:

y = Ix - 6I + 3.

Notice that there is no restriction here, x can actually take any value, then the domain will be the set of all real numbers.

The correct domain is x, x ∈ R

Now, if we had (for example) something like:

y = Ix - 6I < 3

Now we have a restriction in the domain because we can not have y equal or larger than 3.

To find the domain, we can break the absolute value:

Ix - 6I < 3

is equivalent to:

-3 < x - 6 < 3

now let's add 6 in each side.

-3 + 6 < x - 6 + 6 < 3 + 6

3 < x < 9

That will be the domain in that case.

Step-by-step explanation:

To find the lengths of the enlarged triangle, we would find the scale factor from the given length

22.5/5 = 4.5

So to find the other sides you would multiply 3 and 6 by 4.5

3 * 4.5 = 13.5

6 * 4.5 = 27

So all 3 lengths of the triangle are 22.5, 13.5, and 27

To find the perimeter you add all

22.5 + 13.5 + 27 = 63

Your answer is 63