Answer: the function g(x) has the smallest minimum y-value.
Explanation:
1) The function f(x) = 3x² + 12x + 16 is a parabola.
The vertex of the parabola is the minimum or maximum on the parabola.
If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.
The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.
When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).
Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.
Then, finding the minimum value of the function is done by finding the vertex.
I will change the form of the function to the vertex form by completing squares:
Given: 3x² + 12x + 16
Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4
That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).
Then the minimum value is 4 (when x = - 2).
2) The othe function is <span>g(x)= 2 *sin(x-pi)
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The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.
When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2
Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.
Answer:
Step-by-step explanation:
She has 290 cents.
Nickels: 6x+1
Quarters: x
Dimes: 4x
Now that we've converted it algebraically, we can add them
6x+1 + x + 4x = 11x+1 = 290
11x = 289
x = 289/11
let me know if incorrect, i will fix
Answer:
4/4
Step-by-step explanation:
1/4 plus 1/4 plus 2/4 is 4/4
Answer: 32,000
Step-by-step explanation:
the thousands place (1000) is the fourth number to the left of the decimal, so round that one either up or down based on the number just one spot closer to the decimal, in this case, the hundreds place (100).
so we have 32,420
we can ignore the numbers that are going to become zeros as a result of the rounding . .
32,400
let's round 32,XXX either up or down based on the value in the hundreds place. if that value is 5 or greater, than we round up. if it is less than 5, than we round down.
4 is in the hundreds place, so we round down
32,000 is the answer
Hope this helps!!! Good luck!!! ;)
Answer:
Five plus free equals 7
Step-by-step explanation:
I added five plus three
