Answer:
Slope: 5/3
y-intercept: (0, -4)
Step-by-step explanation:
Slope-Intercept Formula: y = mx + b
<em>y</em> is your output.
<em>m</em> is your slope.
<em>b</em> is your y-intercept.
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.
Cost of lack increased by 30%
new cost of lack will be = 100% + 30% = 130%
We are given that new cost = £65
Thus 130% of original cost = 65
100% of original cost = 65 × 100/130 = £50
Thus original price was £50
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
(value/total value)×100%.
So,
9/45=0.2 x 100= 20%
Answer= 20%
Answer:
2744 pennies.
Step-by-step explanation:
Let x represent the number of pennies Al have initially.
We have been given that Al agreed to give 3/7 of his pennies to Bev, so number of pennies Bev will get would be 
.
We are also told that Bev gave 3/7 of what she got from Al to Carl, so number of pennies that Carl will get would be 
.
Further, Carl gave 3/7 of what he got from Bev to Dani, so number of pennies that Dani will get would be 
.
We are also told that Dani received 216 pennies. Now, we will equate 216 to 
and solve for x as shown below:
Therefore, Al have 2744 pennies initially.
