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3 years ago

What is the domain of f(x) = -(x-6)^2-30

Mathematics

1 answer:

son4ous [18]3 years ago

3 0

Answer:

(-∞, ∞)

Step-by-step explanation:

To find the domain, we find how far along the x axis the line goes.

Specifically, we're looking for when x <em>doesn't</em> exist, because that's much easier.

So we're looking for when x is undefined. In order to have something undefined, you need the $\sqrt{-something}$ , or $\frac{anything}{0}$ .

As we can see, there's no part where x is undefined. Therefore, the domain is

(-∞, ∞)

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at maximum speed, an airplane travels 1720 miles against th wind in 5 hours. Flying with the wind, the plane can travel the same

iragen [17]

Answer:

x = 387

Step-by-step explanation:

The wind acts in the opposite direction to the plane when the time is longer.

The wind acts in the same direction as the plane when the time is shorter.

Equation

d = r*t

Givens

d = 1720
x = plane's speed
y = wind speed
t1 = 5 hours
t2 = 4 hours.

Substitution

d = (x + y) * t
1720 = (x + y) * 4
1720 = (x - y) * 5

Since the two distances are the same, you can equate the right hand sides.

(x + y) * 4 = (x - y)*5 Remove the brackets.
4x + 4y = 5x - 5y Add 5y to both sides
4x + 4y + 5y = 5x - 5y + 5y Combine all the terms.
4x + 9y = 5x Subtract 4x from both sides
9y + 4x - 4x = 5x - 4x Combine
9y = x

Now use one of the given equations with the distance

1720 = (x + y)*4 Substitute 9y for x
1720 = (9y + y) * 4 Combine
1720 = 10y * 4 Multiply the right
1720 = 40y Divide by 40
1720/40 = 40y/40 Do the division
43 = y y = wind speek
9y = x x = 9*y
9*43 = x
x = 387 miles per hour.

4 0

4 years ago

The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains poi

ale4655 [162]

Answer:

<h3>The answer is option D</h3>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

y = 2x + 4

comparing with the above equation for a line

The slope / m = 2

Since the lines are parallel their slope are also the same

Slope of parallel line = 2

So we have

The equation of the line using point

( 3 , -2) and slope 2 is

y + 2 = 2( x - 3)

y + 2 = 2x - 6

y = 2x - 6 - 2

We have the final answer as

Hope this helps you

7 0

3 years ago

Bill removed the ten of spades and the king of hearts from a deck of standard playing cards and threw them in the trash. There w

AveGali [126]

Answer:

Step-by-step explanation:

2 if you mean 1 of each so it would be 50 cards

3 0

3 years ago

The exponent of 2√9 is

AVprozaik [17]

Answer:

the exponent is 6............

5 0

3 years ago

Can we combine different functions (quadratic, linear, exponential, cube root) into one piecewise function? If the answer is yes

yanalaym [24]

Answer: yes, because it is useful to describe changes in the behavior of the thing we are describing.

Step-by-step explanation:

A piecewise function f(x) is a function that is "different" depending on the range of the values of x, this is for example:

y = x -----> if x < 0

y = x^2 ----- if x ≥ 0

This is used to represent changes in the behavior of the thing we are describing.

For example, suppose an object that is moving with constant velocity, the velocity graph will be a constant line.

Now, the object suddenly, at a time t = t0 accelerates to a constant acceleration A, now the graph of the velocity is a linear graph with slope equal to A.

So this situation can be represent this with a piecewise function:

V(t) = c -----> if t < t0

V(t) = c + A*t -----> if t ≥ t0

So the answer is yes, we can.

8 0

3 years ago