Let us say that:
x = mass from Earl Grey Tea
y = mass from Orange Pekoe Tea
So that:
x + y = 600
and that:
6 x + 4 y = 4.5 * 600
6 (600 – y) + 4 y = 2700
3600 – 6y + 4y = 2700
-2y = -900
y = 450 pounds
x = 600 – 450 = 150 pounds
Answer:
<span> Earl Grey Tea = 150
pounds</span>
<span>Orange Pekoe Tea = 450 pounds</span>
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.
Answer:
2x + 12
Step-by-step explanation:
2(10)+2(x+4)
distribute the 2
20 + 2x - 8
add/ subtract like terms
2x + 12
Answer:
26
Step-by-step explanation:
Half of 42 is 21.
21 + 5 = 26
Hope this helps you out ; )
