One the first problem on finding the constant of <span> proportionality in this situation the answer is 2. Below is the solution:
constant = unit rate
unit rate = $2/ poung
K = 2
For the second question, the equation is the below:
T = 2p or y = 2x</span>
Hi,
Answer: 7/27
<u>My work:</u> For this problem is already simplified to its simplest terms.
I Hoped I Helped!
Number of white chips = 4
Number of black chips = 6
Total number of chips = 4 + 6 = 10
Choosing the first white chip:
p(white chip) = 4/10 = 2/5
Now the numbers are:
Number of white chips = 3
Number of black chips = 6
Total number of chips = 3 + 6 =
Choosing the second white chip:
p(white chip) = 3/9 = 1/3
p(white chip followed by white chip) = 2/5 * 1/3 = 2/15
Circumcenter = (-1,0)
The circumcenter of a triangle is the intersection of the perpendicular bisectors of the sides of the triangle. So let's calculate a couple of the bisectors and determine their intersection.
Slope AB = (3 - -3)/(2 - -4) = (3+3)/(2+4) = 6/6 = 1
Perpendicular bisector will have a slope of -1 and will pass through point ((2-4)/2,(3-3)/2) = -2/2,0/2) = (-1,0)
Equation is of the form
y = -x + b
Substitute known point
0 = -(-1) + b
0 = 1 + b
-1 = b
So the equation for the perpendicular bisector of AB is
y = -x - 1
Now let's calculate the perpendicular bisector of BC
Slope BC = (-3 - -3)/(-4 - 2) = (-3 + 3) / (-6) = 0/-6 = 0. This means that the
line is horizontal and that the perpendicular bisector will be a vertical line with infinite slope. A point that line will pass through is ((-4 + 2)/2, (-3 + -3)/2) =
(-2/2, 0/2) = (-1,0). So the equation for the line is:
x = -1
Now we want the intersection between
x = -1 and y = -x - 1
Since we know that x has to be -1, just substitute it into the 2nd equation.
y = -x - 1
y = -(-1) - 1
y = 1 - 1
y = 0
So the circumcenter is (-1,0).
Let's verify that. The distance from the circumcenter to each vertex of the triangle will be the same. Using the Pythagorean theorem, C^2 = A^2 + B^2. We're not going to bother taking the square root since if the squares are equal, then square roots will also be equal.
Distance^2 from (2,3):
(2- -1)^2 + (3-0)^2 = 3^2 + 3^2 = 9 + 9 = 18
Distance^2 from (-4,-3):
(-4 - -1)^2 + (-3 - 0)^2 = -3^2 + -3^2 = 9 + 9 = 18
Distance^2 from (2,-3):
(2 - -1)^2 + (-3 - 0)^2 = 3^2 + -3^2 = 9 + 9 = 18
The distances to all three vertexes is identical, so (-1,0) is verified as the circumcenter.
