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Valentin [98]
3 years ago
8

Domain for g(x) = √4x – x^2​

Mathematics
2 answers:
MrRa [10]3 years ago
7 0

Answer:

\large\boxed{0\leq x\leq4\to x\in[0,\ 4]}

Step-by-step explanation:

We know: √x exist if x ≥ 0.

We have g(x)=\sqrt{4x-x^2}.

The domain:

4x-x^2\geq0\\\\x(4-x)\geq0

Find the zeros of the equation

x(4-x)=0\iff x=0\ or\ 4-x=0\\\\x=0\ or\ x=4

ax^2+bx+c=-x^2+4x\to a=-1

the parabola open down.

Look at the picture.

x\geq0\ \wedge\ x\leq4\to0\leq x\leq4\to x\in[0,\ 4]

melisa1 [442]3 years ago
4 0

Answer:

The domain is 0 ≤ x ≤ 4,

or in interval notation it is [0, 4].

Step-by-step explanation:

g(x) = √(4x – x^2)

4x - x^2 cannot have a negative value because of the square root sign.

4x - x^2 = 0

x(4 - x) = 0

x = 0 , 4.

The highest value is 4 and the lowest is 0 . Values in between like 1 are in the domain ( for example  √(4(1) - 1) = √3).

x has to be  between 0 and 4 inclusive.

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3 years ago
Which number line represents the solutions to 1-2x1 = 4?
kaheart [24]

Answer:

Third option: x = -2 and x = 2

Step-by-step explanation:

Given:

|-2x|=4

For a modulus function, if |f(x)|=a, then,

f(x)=\pm a

Here, f(x)=-2x, a=4

∴ -2x=\pm 4\\ -2x=-4\textrm{ or } -2x=4\\ x=\frac{-4}{-2}\textrm{ or }x=\frac{4}{-2}\\ x= 2\textrm{ or }x=-2

Therefore, the third option is the correct answer as the graph has x values as -2 and 2

8 0
3 years ago
The population of a city is 45,000 and decreases 2% each year. If the trend continues, what will the population be after 15 year
Sloan [31]
The answer is 31,500.
Let's clarify some things :
1% of 45,000 is 450
Maybe you're wondering why , it's actually very simple .
Just move the decimal to the left once if you want to find 10% , move the decimal twice if you want to find 1%.
We now that 1% equals 450. Then 2% equals to....
Well just add another 1% .
450 + 450 or 450 times 2
Which equals 900.
Now we want to find what's the population after 15 years.
900 times 15= 13,500
But that's not the answer ....
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That's why the answer is 31,500.
4 0
3 years ago
Solving by elimination <br> 5x+2y= -3<br> 3x+3y=9<br> please help me solve x and y
-Dominant- [34]
1) -3(5x+2y=-3)⇒ -15x-6y=9
                                             ⇒ -9x=27
     2(3x+3y=9)⇒ 6x+6y=18

2) -9x/-9=27/-9 ⇒ x=-3 

3) 3(-3)+3y=9⇒ -9+9+3y=9+9⇒ 3y/3=18/3⇒ y=6

Answer: (-3,6)

Reasoning:
Step 1) In order to eliminate, first I had to multiple the first equation by -3 and the second by 2 so that when combining the equations y would cancel each other out so that I could solve for x. <em>Note: There are many combinations as to how you could multiple the equations so that either the x or y would cancel out.
</em>
Step 2) Once y is eliminated, solve for x.

Step 3) Now plug x back into one of the original equations and solve for y. <em>Note: Plug x back into one of the original equations, not the equations that were changed by multiplication,</em> 

6 0
3 years ago
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