A problem with extra information will be difficult to solve because you may not be able to tell what information you might need to use for the problem.
Solve for x:
x^2 + 4 x + 25 = 0 I ssume that's the notation.
Subtract 25 from both sides:
x^2 + 4 x = -25
Add 4 to both sides:
x^2 + 4 x + 4 = -21
Write the left hand side as a square:
(x + 2)^2 = -21
Take the square root of both sides:
x + 2 = i sqrt(21) or x + 2 = -i sqrt(21)
Subtract 2 from both sides:
x = i sqrt(21) - 2 or x + 2 = -i sqrt(21)
Subtract 2 from both sides:
Answer: x = i sqrt(21) - 2 or x = -i sqrt(21) - 2
B. 1 pint
2 cups = 1 pint
4 cups = 1 quart
16 cups = 1 gallon
hope this helps!
Answer: They are inverses of each other
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Explanation:
We'll need to compute h(f(x)) and f(h(x)) to see if we get x each time.
![h(x) = 9x-4\\\\h(f(x)) = 9(f(x))-4\\\\h(f(x)) = 9\left(\frac{x+4}{9}\right)-4\\\\h(f(x)) = x+4-4\\\\h(f(x)) = x\\\\](https://tex.z-dn.net/?f=h%28x%29%20%3D%209x-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%209%28f%28x%29%29-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%209%5Cleft%28%5Cfrac%7Bx%2B4%7D%7B9%7D%5Cright%29-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%20x%2B4-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%20x%5C%5C%5C%5C)
and,
![f(x) = \frac{x+4}{9}\\\\f(h(x)) = \frac{h(x)+4}{9}\\\\f(h(x)) = \frac{9x-4+4}{9}\\\\f(h(x)) = \frac{9x}{9}\\\\f(h(x)) = x\\\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%2B4%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20%5Cfrac%7Bh%28x%29%2B4%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20%5Cfrac%7B9x-4%2B4%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20%5Cfrac%7B9x%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20x%5C%5C%5C%5C)
Both composite functions lead to x each time.
The equations h(f(x)) = x and f(h(x)) = x being true means each function is the inverse of the other.
Answer:
Natasha gets 84
Step-by-step explanation:
Here, we want to know how much Natasha gets
Krutika gets 2 times as much as Natasha
If Natasha gets x, Krutika gets 2x
If Natasha gets x, Richard will get x/3 ( 3 times of this is what Natasha gets)
Now let us have a ratio;
K : N : R
2x : x : x/3
Multiply through by 3
6x : 3x : x
To get the amount Natasha gets, we add up all ratio; (6x + 3x + x ) = 10x
Natasha gets 3x of the total ratio
That will be;
3x /10x * 280
= 3/10 * 280
= 84