to find the equation of a linear equation given two points:
1) find the slope y=mx+b
here's the equation: (y2-y1)/(x2-x1)
y2- y value of the 2nd point y1- y value of 1st point
x2- x value of 2nd point x1- x value of 1st point
1st point- (0, 12) 2nd point- (1,3)
so your slope equation is this: (3-12) / (1-0) or -9/1 or -9
m is -9
2) find the y intercept y=mx+b
b is whatever y is when x is 0. There's a long way to find it, but you already have it, because one of your points is (0,12). They told you what y was when x was 0.
b is 12.
your linear equation is y=-9x+12
to find the equation of an exponential equation given two points:
1) find a y=a(b)<span>×
</span>if one of your points has a 0 as the x value, the y value is a. you do have a point like this: (0,12) so...
<span>a is 12
</span>2) find b y=a(b)<span>×
put what you know a is in the equation: y=12(b)</span><span>×
then put the x and y values of the other point in for x and y in the equation
so (1,3) 1 is x and 3 is y
3=12(b)^1
when the exponent is 1, it disappears:
3=12b
simplify: b= 3/12 or b=1/4
then put all that in the equation:
y=12(3/4)</span><span>×</span>
Answer:
<em>Area of sector: 48π in^2; Option D</em>
Step-by-step explanation:
<em>~ We can see that the bolded portion of the circle must be the the sector that we need to compute the area of... ~</em>
Let us plan out this problem. If we were to find the area of the circle provided a radius of 12 inches, we could create a proportionality between the degree of the sector, and the degree of the circle ( 360 ) and the area of the sector and the area of the circle.
1. To calculate the area of this circle, let us apply the formula πr^2, such that r is 12 inches ( and let us keep π in terms of π ) ⇒ π * ( 12 )^2 ⇒ 144 * π ⇒ <em>Area of Circle: 144π</em>
2. Let us see this as a proportionality:
<em>Degree of sector/ Degree of circle = Area of sector/ Area of circle</em>
3. Now let us say x ⇒ Area of the sector. Substitute values into this formula, and solve for x through algebra:
120 / 360 = x / 144π,
120 * 144π = 360 * x,
17,280π = 360 * x,
x = 17,280π / 360,
<em>Area of sector: 48π in^2</em>
Answer: B.y = 2x + 1. Step-by-step explanation: By first sketching a line of best fit then comparing it to the given equations, the equation that best matches the graph is y = 2x + 1
Average rate of change = slope so lets get our y's and x's and plug them into y2-y1 / x2-x1. (14-9)/(308-195) and that equals 5/113
Answer:
Group A.
Step-by-step explanation:
As shown by the dot plots, Group A has one 9-year-old painter, seven 10-year-old painters, and 24 painters between the ages of 15 and 20. Group B has seventeen painters between the ages of 10 and 20 and thirteen painters between the ages of 25 and 30. Since mean is the average of everything, Group A most likely has a lower mean age of painting students than Group B does.
