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:
When you go shopping for anything, you know that the more of that something you buy, the more money you are going to spend. In other words, the amount of money you spend depends directly upon the amount of stuff you buy. So the number of boxes of cookies you buy is the independent variable and the amount of money you spend on the cookies is the dependent variable.
Answer:
x=4
Step-by-step explanation:
3x-3=9
+3=+3
3x=12
3x=12
divide both sides by 3
leaving x by itself
12/3=4
x=4
Tom is correct, and Dan is wrong. A quadrilateral is a closed figure with four sides, for example, like a kite. A parallelogram is a four sided rectangular figure with opposite sides that are parallel.
Answer:
Step-by-step explanation:
At home depot
Price of Christmas tree = $149.00
Discount = 15%
Amount discounted = 15% of $149
Amount discounted = 15/100 * $149
Amount discounted = 15 * 1.49
Amount discounted = $22.35
Amount she paid = $149-$22.35
Amount she paid = $126.65
At Lowe's:
Price of Christmas tree = $175.00
Discount = 260%
Amount discounted = 20% of $175
Amount discounted = 20/100 * $175
Amount discounted = 0.2 * 175
Amount discounted = $35
Amount she paid = $175-$35
Amount she paid at Lowe's = $140
<u><em>From the prices above, it can be seen that Home Depot has a better deal since the price after removing discount is lower than that of Lowe's.</em></u>
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<u><em>Amount she will save will be $140 - $126.65 = $13.35</em></u>
