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tatyana61 [14]
3 years ago
6

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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Can someone solve this? and tell me how?
maksim [4K]

Answer:

1/3

Step-by-step explanation:

When working with balanced expressions (stuff on both sides of the equal sign), "what you do to one side, you do to the other", which keeps it balanced.

The first thing we notice is the exponent 1/4, which is one both sides, so we can get rid of it on both sides by using the <u>reverse operation</u>.

The reverse of exponents is <u>square root</u>.

(4x + 10)^{\frac{1}{4}} = (9 + 7x)^{\frac{1}{4}}\\\sqrt[\frac{1}{4}]{(4x + 10)^{\frac{1}{4}}} = \sqrt[\frac{1}{4}]{(9 + 7x)^{\frac{1}{4}}}\\\\4x + 10 = 9 + 7x

Isolate x to solve. Separate the variables and non-variables.

4x + 10 = 9 + 7x

4x - 4x + 10 = 9 + 7x - 4x          Subtract 4x from both sides

10 = 9 + 3x                

10 - 9 = 9 - 9 + 3x            Subtract 9 from both sides

1 = 3x            Divide both sides by 3 to isolate x

x = 1/3           Answer

8 0
3 years ago
A bouncy ball is dropped such that the height of its first bounce is 5.5 feet and each successive bounce is 64% of the previous
ahrayia [7]

Answer:

  0.4 ft

Step-by-step explanation:

It can be convenient to let a spreadsheet compute the values for you. Here, we have written an explicit formula for the height of the n-th bounce:

  h = 5.5×0.64^(n-1)

We have written the formula this way because we are given the height of the first bounce, not the starting height. Each bounce multiplies the height by a factor of 0.64. Then the 7th bounce will have a height of ...

  h = 5.5×0.64^6 ≈ 0.378 ≈ 0.4 . . . . feet

6 0
3 years ago
If the artist wanted to add a smaller cube with an edge length of 2/3to the sculpture, what size would the cube be?
Westkost [7]

Answer:


Step-by-step explanation:


6 0
3 years ago
HELP ASAP
almond37 [142]

Answer:

Step-by-step explanation:

let the number of dimes=x

and number of quarters=y

x=2y

0.10 x+0.25 y=2.25

or 10x+25y=225

divide by 5

2x+5y=45

2 ×2y+5y=45

4y+5y=45

9y=45

y=45/9=5

x=2y=2×5=10

Hence dimes=10

quarters=5

6 0
3 years ago
Please help me with my transition math please lots of questions I’m stuck with tonight, I’m bad at geometry
Natalija [7]
The answer is A. (AB and CD)
3 0
3 years ago
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