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)
</span>
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.
You've written "then" before 3, so i assume the real question is:
(40 * 40 * 40 + 26 - 98 + 45 * 78 * 78 * 78) / 3
Use "PEMDAS" first solve under the parenthesis, then after it.
= (64000 + 26 - 98 + 21354840) / 3
= 21418768 / 3
= 7139589.33
In short, Your Answer would be: 7139589.33
Hope this helps!
Answer:
it would be 128 because 8 divded 2 is 4. 4 is the number of cereal boxes now multiply 4 x32 which would be 128
Answer:
308 Calories
Step-by-step explanation:
So we start off with 280 as usual, but I will focus on the percent. The given percent is 110% "effort". What we would need to do here is, Firstly, change the percent into a decimal, and this is done by moving the decimal spot of 110%. What I mean is that 110.% and you move that little period over 2 times to the left and also remove the percent as for now because we will not need it. After that you would get 1.10. This is what we will multiply by. So if we did 280x1.10 it equals 308, and that is how I got 308
Hope this helps!
( 3 1 ) 2 +3 2 =left parenthesis, start fraction, 1, divided by, 3, end fraction, right parenthesis, squared, plus, 3, squared
Fynjy0 [20]
Answer:
I guess that we have the equation:
(1/3)^2 + 3^2 =
And we want to solve it.
Here just remember that:
3^2 = 3*3 = 9
then:
(1/3)^2 = (1/3)*(1/3) = 1/9
replacing these in the expression, we get:
(1/3)^2 + 3^2 = 1/9 + 9
If we want to write this as a single fraction, we can rewrite:
1/9 + 9 = 1/9 + (9/9)*9
= 1/9 + 81/9 = (1 + 81)/9 = 82/9
