Which of the following may have an outcome that is not a polynomial ? A. The addition of two polynomials B. The multiplication o
1 answer:
You might be interested in
Answer:
a) maximum; the parabola opens downward
b) positive; it must lie above the x-axis
c) x = 1.5
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.
The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.
__
<h3>a, b.</h3>If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.
__
<h3>c.</h3>The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:
x = (-2 +5)/2 = 3/2
The x-coordinate of the vertex is x = 1.5.
______
<em>Additional comment</em>
The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.
<u>Answer:</u>
40%
<u>Step-by-step explanation:</u>
We are given that last month, Joe's puppy weight 5.4 pounds while this month, the puppy weighed 7.56 pounds.
We are to find the percentage increase of the weight of the puppy
We know that the formula of percentage increase if given by:
<em>Percentage increase = (new value - initial value)/initial value × 100</em>
So substituting the given values to get:
Percentage increase in puppy's weight = = 40%
<span>x=3y-8
3x-4y=-9
We are told that:
</span>x=3y-8
So replace x in 3x-4y=-9 with x=3y-8 like so:
3(3y-8)-4y=-9
Start by distributing the 3:
Now you have:
Combine like terms, now you have:
add 24 to both sides
Now you have:
Divide both sides by 5 to get:
y=3
Now that you know y=3 plug it into:
x=3y-8
x=3(3)-8
x=1
Final answer:
(1,3)
3x-4y=-9
We are told that:
</span>x=3y-8
So replace x in 3x-4y=-9 with x=3y-8 like so:
3(3y-8)-4y=-9
Start by distributing the 3:
Now you have:
Combine like terms, now you have:
add 24 to both sides
Now you have:
Divide both sides by 5 to get:
y=3
Now that you know y=3 plug it into:
x=3y-8
x=3(3)-8
x=1
Final answer:
(1,3)