Answer: b.14
Step-by-step explanation:
We have two shelves, the top shelf 
and the bottom shelf 
.
Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:
(1)
Then, we are told there are 12 books on the bottom shelf:
(2)
Substituting (2) in (1):
(3)
(4)
(5) This is the number of books on the top shelf
Hence, the correct option is b.
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.
Answer:
Step-by-step explanation:
domain:A
range: D
75 time because the proabablity of rolling any number each time is 1/10 so 250/10=25 the mutiples of 3 in 1-10 are 3,6,9 so 3*25 =75 tmes
Answer:
x = 7/2 or x = -8/3
Step-by-step explanation:
Solve for x over the real numbers:
6 x^2 - 5 x = 56
Divide both sides by 6:
x^2 - (5 x)/6 = 28/3
Add 25/144 to both sides:
x^2 - (5 x)/6 + 25/144 = 1369/144
Write the left hand side as a square:
(x - 5/12)^2 = 1369/144
Take the square root of both sides:
x - 5/12 = 37/12 or x - 5/12 = -37/12
Add 5/12 to both sides:
x = 7/2 or x - 5/12 = -37/12
Add 5/12 to both sides:
Answer: x = 7/2 or x = -8/3
