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3 years ago

Which could be the entire interval over which the function,

Mathematics

1 answer:

Marrrta [24]3 years ago

3 0

Answer:

(-2, 1)

Step-by-step explanation:

Hi Juliadayx! How are you?

Well, maybe you already heard about the domain and the range of a function.

The domain is the set of values that the independent variable can take (usually referred to as the letter "x"), while the range is the set of values that the dependent variable takes, which is called f(x) or function of x.

In this case, the exercise asks you to evaluate for which values of “x” (right column of the table), the function “f(x)” takes positive values (left column of the table), the positive values also include zero. And in this case you can see that the function f(x) is only positive for the values of "x": -2, -1, 0 and 1. Therefore, the answer is the entire interval (-2, 1).

I hope I've been helpful!

Regards!

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3 years ago

What is the slope and the y-intercept of f(x)= -2x+6

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3 years ago

Read 2 more answers

the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle

inna [77]

Answer:

$2m$

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

$A = \frac{1}{2}bh$

They give us the area as $6m^2$ , so let's include it in the equation.

$6 = \frac{1}{2}bh$

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that $h = b-4$

So replace $h$ in the equation with $b-4$ .

You will now get:

$6 = \frac{1}{2}b(b-4)$

Now we can work towards solving. Let's get simplifying.

$12 = b(b-4)\\12 = b^2 - 4b\\$

bring everything to one side so we can make a quadratic and factor:

$0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2$

We get that $b=6$ .

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that $h = b - 4$ , so to find h, we just sub in our b value into that.

$h = (6) - 4 = 2$

We find that $h=2$

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2 years ago