X = 6{2 + 3[2(7 − 3) + (4 + 1) − 3]}

WILL MARK BRAINLIEST what is the domain of (f/g) (x)?

tatyana61 [14]

Given that $f(x) = \sqrt{7-x}$ and $g(x) = \sqrt{x + 2}$ , we can say the following:

$\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).

Thus, let's set what is under both square roots to be greater than 0:

$\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7$

$\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2$

Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

$x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}$

Now, let's look back at the function entirely, which is:

$\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Since $\sqrt{x + 2}$ is on the bottom of the fraction, we must say that $\sqrt{x + 2} \neq 0$ , since the denominator can't equal 0. Thus, we must exclude $\sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2$ from the domain.

Thus, our answer is Choice C, or $\boxed{ \{ x | -2 < x \leq 7 \}}$ .

If you are wondering why the choices begin with the $x |$ symbol, it is because this is a way of representing that $x$ lies within a particular set.

6 0

2 years ago

7.5.5. I usually walk from home to work. This morning, I walked for 10 minutes until I was halfway to work. I then realized that

olya-2409 [2.1K]

Answer:

Given:

I usually walk from home to work. This morning, I walked for 10 minutes until I was halfway to work.

I then realized that I would be late if I kept walking.

I ran the rest of the way. I run twice as fast as I walk.

Find:

The number of minutes in total did it take me to get from home to work

Step-by-step explanation:

Had I kept walking, the second half of my trip would have taken 10 more minutes.

By doubling my speed for the second half of my trip,

I halved the amount of time it took me to finish.

So, the second half of my trip took 5 minutes, for a total trip time of 10+5 = 15 minutes.

The number of minutes in total did it take me to get from home to work is 15 minutes.

3 0

1 year ago

Read 2 more answers

10, 30, 90 continue the pattern

Novosadov [1.4K]

The answer is 270, the pattern is multiplying by 3. So, 10 • 3 = 30 30 • 3 = 90 90 • 3 = 270, and so on. Hope this helps! Let me know if you need any further assistant.

7 0

2 years ago

Read 2 more answers

An investment of $5000 has an annual growth rate of 8% for 3 years

Fudgin [204]

Answer: The final balance is $6,341.21.

The total compound interest is $1,341.21.

Step-by-step explanation:

8 0

2 years ago

Bob decided to go to college, the cost of going to school will be $4,474 per semester, (there are 2 semesters per year) plus $38

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

1 semester = 4474

8 semester = 8* 4474 35792

1 semester books = 389

8 semester books = 8* 389 3112

Total 38904

If he is going to pay this off in 10 years, he would have to have an increase of 3890.40 (after all income taxes) to pay it off. Fewer years would mean dividing by the number of years.

So for 8 years for example, he would need 4863 every year.

That number is obtained by dividing 38904 / 8

In 6 years he would need

38904/6 = 6484 extra dollars.

5 0

3 years ago