Answer:
Any value of k makes the equation true.
All real numbers
Interval Notation:
(
−
∞
,
∞
)
Answer:
1 7/9 ounces
Step-by-step explanation:
The final solution will be 9 parts water and 1 part hydrogen peroxide (so that hydrogen peroxide makes up 1 of 10 parts of the solution).
Then each "part" is (16 ounces)/9 = 1 7/9 ounces.
1 7/9 ounces of hydrogen peroxide must be added to 16 ounces of water to make a 10% solution.
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<em>Check</em>
The total amount of solution is 16 +1 7/9 = 17 7/9 ounces = 160/9 ounces. The amount that is hydrogen peroxide is 16/9 ounces, so the fraction that is hydrogen peroxide is ...
(16/9) / (160/9) = 16/160 = 1/10 = 10%
The function in vertex form is ⇒ 3rd answer
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
- a is the coefficient of x²
- (h , k) are the coordinates of the vertex point
- , wher b is the coefficient of x
- k = f(h), that means value f(x) when x = h
∵ f(x) = x² + x + 1
∴ a = 1 , b = 1
∵
- Substitute the values of a and b to find h
∴
∴
Substitute the value of x in f(x) by the value of h to find k
∵ f( ) =
∴ f( ) =
∴ f( ) =
- k is the value of f(x) when x = h
∵ h =
∴ k = f( )
∴ k =
Substitute the values of a, h and k in the vertex form
∵ f(x) = a(x - h)² + k
∵ a = 1 , ,
∴
∴
The function in vertex form is
Learn more:
You can learn more about the quadratic functions in brainly.com/question/9390381
#LearnwithBrainly
Answer:
[x] f(x)
[-6] 13
[-3] 4
[0] 1
[3] 4
[9] 28
Step-by-step explanation:
f(0) = (1/3)(0^2)+1 = 1
f(3) = (1/3)(3^2)+1 = 4
f(9) = (1/3)(9^2)+1 = 28