What is the equation of the line through the origin and (-5, 6)?
1 answer:
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The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.
Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.
Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.
-3x+6 = 0
-3x = -6
x = 2
x+4 = 0
x = -4
Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.
Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.
y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24
What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.
y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27
Thus the vertex is (-1, 27)
The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)
As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.
Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.
Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.
-3x+6 = 0
-3x = -6
x = 2
x+4 = 0
x = -4
Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.
Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.
y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24
What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.
y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27
Thus the vertex is (-1, 27)
The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)
As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)
The standard deviation for the number of people with the genetic mutation in such groups is 3.1305.
<h3>Standard Deviation</h3>In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Let X be the number of people with genetic mutation is a group of 500,
The formula of standard deviation is given as
The standard deviation of the given sample is 3.1305
Learn more on standard deviation here;
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By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.
This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.
Then:
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are <em><u>same-side interior angles</u></em>. Because AB and DC are <em><u>parallel</u></em>, the same-side interior angles must be <em><u>supplementary</u></em> by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
