Answer:
slope = - 4, y- intercept = 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 9 is in slope- intercept form
with slope m = - 4 and y- intercept c = 9
A proportional relationship has the form
y = mx
y = - 4x + 9 is not in this form
Hence the relationship is not proportional
Answer:
on what jsoshshsisshsushshdu?
Answer:
False
Step-by-step explanation:
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.
The equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
<h3>Circle theorem</h3>
The given diagram shows two intersecting lines tangential to a circle at points A and C.
Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.
Mathematically;
<B = 1/2(arcADC - arcAC)
58 = 1/2(238 -x)
Hence the equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
Learn more on circle theorem here: brainly.com/question/26594685
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