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pishuonlain [190]
3 years ago
5

What is the range of f(x)=x^2-2x-6

Mathematics
2 answers:
mihalych1998 [28]3 years ago
4 0

Answer:

?≤y≤?

Step-by-step explanation:

Eva8 [605]3 years ago
3 0

Answer:f(x)=1

Step-by-step explanation:

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The EU has challenged the U.S."s position in the global economy. True or False
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Answer:

False

Step-by-step explanation:

EU and the US are very good friends and they often trade with them.

4 0
3 years ago
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A rocket is fired with an initial vertical velocity of 40 m/s from a launch pad 45 m high, and its height is given by the formul
N76 [4]

Answer:

1) 125 meters

2) For 9 seconds.

Step-by-step explanation:

The rocket's height is given by the formula -5t^2+40t+45.

Notice that this is a quadratic.

Part 1)

Since this is a quadratic, the highest height the rocket goes will be the vertex of our quadratic. Remember that the vertex of a quadratic in standard form is:

(-\frac{b}{2a}, f(-\frac{b}{2a}))

So, let's identify our coefficients. The standard quadratic form is:

ax^2+bx+c

Therefore, in this case, our a is -5, b is 40, and c is 45.

So, let's find the x-coordinate of our vertex. Substitute 40 for b and -5 for a. This yields:

x=\frac{-(40)}{2(-5)}

Multiply and reduce. So:

x=-40/-10=4

Now, substitute 4 for t to find the height. So:

-5(4)^2+40(4)+45

Evaluate:

=-5(16)+40(4)+45

Multiply and add:

=-80+160+45=125\text{ meters}

Therefore, the highest the rocket goes up is 125 meters.

Part 2)

To find out for how much time the rocket is in the air, we can think about after how many seconds after launch will the rocket land.

If the rocket lands, the height h will be 0. So, we can set our expression equal to 0 and solve for t:

-5t^2+40t+45=0

First, let's divide everything by -5. This yields:

t^2-8t-9=0

We can factor:

(t+1)(t-9)=0

Zero Product Property:

t+1=0\text{ or } t-9=0

Solve for t:

t=-1\text{ or } t=9

In this case, since t is our time in seconds, -1 seconds does not make sense. So, we can remove -1 from our solution set.

Therefore, 9 seconds after launch, the rocket will touch the ground.

Therefore, the rocket was in the air for 9 seconds.

And we're done!

6 0
3 years ago
Which parabola has the graph shown?
ryzh [129]

The vertex is (-1, 2).

The equation of parabola:

x=(x-k)^2+h where (h, k) is the vertex

We have h = -1 and k = 2.

Substitute:

x=(y-2)^2-1\ \ \ \ |+1\\\\(x+1)=(y-2)^2

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3 years ago
Mrs. Tomas says that the number of students in her class on this week has no variability. Her student, Pierce, says that it does
user100 [1]

Answer:

Step-by-step explanation:

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2 years ago
A company claims that 80% of its customers are under 30. You suspect it is less than this. You take a random sample of 200 custo
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Step-by-step explanation:

What we are trying to show is the alternative hypothesis. Here, we are trying to show that what the company claims is wrong; less than 80% of the company's customers are under 30.

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