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Mathematics

1 answer:

sattari [20]2 years ago

7 0

Answer:

Muliple choice A.

Step-by-step explanation:

Here, we have two sets that need to be subtracted from eachother. So, first we start off like we're reading a book. From top to bottom, from left to right. And we need to match up the numbers together to subtract. (i.e. the top left from both set A and B will be 5 and 1, so we subtract these. And we do that for all the numebrs.

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WILL MARK BRAINLIEST <br><br> 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 $\boxed{ \{ x | -2 < x \leq 7 \}}$ .

<em>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.</em>

6 0

2 years ago

Need help with the picture

BaLLatris [955]

Answer:the y=x graph will have a slope of positive one and the y intercept would be 0. The y=-x+4 graph will have a slope of negative one ( line going down) and have a y intercept of 4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint

Vikki [24]

Answer:

Generally given that the number of cups of blue to that of red paint is 3: 1 then the Lara mixed 3 cups of blue paint with 1 cup of red paint

The number is $x= \frac{1}{3}$