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:
Greater. (30)
Step-by-step explanation:
Simplest way to find out is divide.
Flip 5/6 and multiply.
25 x 6 = 150
150 / 5 = 30
I think it's 240 mile per hour
60sec.= 1min
60min.=1hour
60×60=3600secs.
3600÷15=240
Answer:
202m
Step-by-step explanation:
Please see attached picture for full solution.
Let x meters be the height of the building.
Answer:
(-6, -4)
Step-by-step explanation:
Use substitution.
Since y is already isolated, substitute it into the y of: 4x+3y=-36.
You should get: 4x+3(x+2)=-36
Simplify this and you'll get:
4x+3x+6=-36
Add both of the variables:
7x+6=-36
Add -6 to both sides, (because there is a -36 on one side, and a 6 on the other, you have to add a negative to eliminate the 6 whilst adding to the -36)
7x=-42
Divide both sides by 7:
x=-6
Now substitute this into y=x+2
y=-6+2
y=-4
