Y1 is the simplest parabola. Its vertex is at (0,0) and it passes thru (2,4). This is enough info to conclude that y1 = x^2.
y4, the lower red graph, is a bit more of a challenge. We can easily identify its vertex, which is (-4,0), and several points on the grah, such as (2,-3).
Let's try this: assume that the general equation for a parabola is
y-k = a(x-h)^2, where (h,k) is the vertex. Subst. the known values,
-3-(-4) = a(2-0)^2. Then 1 = a(2)^2, or 1 = 4a, or a = 1/4.
The equation of parabola y4 is y+4 = (1/4)x^2
Or you could elim. the fraction and write the eqn as 4y+16=x^2, or
4y = x^2-16, or y = (1/4)x - 4. Take your pick! Hope this helps you find "a" for the other parabolas.
Answer:
1716 ways
Step-by-step explanation:
Given that :
Number of entrants = 13
The number of ways of attaining first, second and third position :
The number of ways of attaining first ; only 1 person can be first ;
Using permutation :
nPr = n! ÷(n-r)!
13P1 = 13! ÷ 12! = 13
Second position :
We have 12 entrants left :
nPr = n! ÷(n-r)!
12P1 = 12! ÷ 11! = 12
Third position :
We have 11 entrants left :
nPr = n! ÷(n-r)!
11P1 = 11! ÷ 10! = 11
Hence, Number of ways = (13 * 12 * 11) = 1716 ways
Answer:
2x + y < 7
Step-by-step explanation:
First we find the slope of the line that passes through the given points. The formula for slope is:
Using our points, we have
The y-intercept will be the point where the data crosses the y-axis. All y-intercepts have an x-coordinate of 0; since we already have the point (0, 7), we have the y-intercept at 7. This makes our equation
y = -2x + 7
The inequalities we're given are written in standard form, Ax+By=C. This means we need x and y on the same side of the equals in our equation.
Since the inequality is graphed below the line, we want our inequality to be
y < -2x+7
To move the x-value to the other side of the equation, we will add 2x to each side:
y+2x < -2x+7+2x
y+2x < 7
2x+y < 7
The desired linear functions are given as follows:
a) x = a.
b) y = b.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
A vertical line has undetermined slope, hence it is defined by x = a, containing point (a,b).
A horizontal line has slope of 0, hence it is defined by y = b, containing point (a,b).
More can be learned about linear functions at brainly.com/question/24808124
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