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.
Human characteristics of your neighborhood come from humans ideas and actions. They include bridges houses, and parks. Human characteristics of places also include land use, density of population, language patterns, religious, architecture, and political systems. The theme of place helps flesh out information about location
Answer:
D. $680
Step By Step Explanation:
100 pages are typed. Each page coast $5 to type.
100 x 5 = 500
40 pages are revised once. It costs $3 to revise a page once.
40 x 3 = 120
10 pages are revised twice. It costs $3 to revise a page once so it will cost $6 to revise it twice
10 x 6 = 60
To find the total cost we add all the amounts together
500 + 120 + 60 = 680
The final answer is $680
Part A:Bees: f ( t ) = 1,500 * 0.88^tFlowering plants: g ( t ) = 800 - 25 tPart B :f ( 6 ) = 1,500 * 0.88^6 = 696.6 ≈ 697
g ( 6 ) = 800 - 25 * 6 = 800 - 150 = 650Part C :f ( 7 ) = 1,500 * 0.88^7 = 613g ( 7 ) = 800 - 7 * 25 = 625f ( 7 ) ≈ g ( 7 )After approximately 7 months.
Answer:
m = (3/4) n
Step-by-step explanation:
4m + 2n = 5n
The subtraction property of equality states that we can subtract 2n from both sides to isolate the m and its coefficient to get
4m = 3n
The division property of equality states that we can divide 4 from both sides to isolate only the m (we divide by 4 because anything divided by itself equals 1) to get
m = (3/4) n
