The horsepowers of 12 sports cars are: 397, 320, 300, 310, 355, 362, 342, 375, 378, 402, 375, and 368.
nydimaria [60]
Answer is C. 365
Step One: (Put the numbers in order from least to greatest)
300, 310, 320, 342, 355, 362, 368, 375, 375, 378, 397, 402,
Step Two: (FInd the number(s) that are directly in the middle).
- Normally it's one number, but since this is an even number (12). There's two in the middle. 362, 368.
Step Three: (Add them then divide | only do this when there's two numbers in the middle)
362 + 368 = 730.
730 divided by 2 = 365
Well, this problem is best solved by setting up a system of two linear equations.
A linear equation can be defined
y=mx+b
where
b=initial value (when x=0), and
m=rate of increase or decrease.
In the given example, the x-axis represents hour, and the y-axis, number of cells.
Chemical #1
initial value = b = 12000 cells
rate = m = -4000 / hr
The equation is therefore
y1=-4000x+12000......................(1)
Similarly, for chemical #2
initial value = b = 6000 cells
rate = m = -3000 / hr
The equation is therefore
y2=-3000x+6000 .......................(2)
The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when y1=y2
which means
-4000x+12000 = -3000x+6000
transpose and solve for x
4000x-3000x = 12000-6000
1000x=6000
x=6 hours.
At 6 hours from the start,
y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells
So the solution is x=6, y=-12000, or (6,-12000)
Physical interpretation
Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero.
Case 1: y=0 when x=3
Case 2: y=0 when x=2
Therefore, after three hours, both trials will have zero cells.
You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.
Collinear=On the same line
N-U
N-T
U-T
I believe that is what this questions is asking. :)
The text of the question is not visible in the answering window. I'll reproduce it here:
BD bisects <ABC.
m <ABD= 2.5x + 8.6
m<CBD = 3.5x - 3.4
Find m<ABC
Answer:
Step-by-step explanation:
We have an angle ABC and a line BD bisecting it.
If an angle is bisected, then the two formed angles are congruent, that is
Substituting the algebraic expressions for both angles:
Subtracting 8.6 and 3.5x:
Operating:
The two angles are:
As expected, both angles have the same measure.
The measure of the total angle ABC is twice any of those:
Answer:
1.C
2. A
Step-by-step explanation:
