We are given that:
t = time required for Sprinkler System A
t + 4 = time required for Sprinkler System B
Hence the rates are:
1 / t = rate for Sprinkler System A
1 / (t + 4) = rate for Sprinkler System B
The overall equation is:
1 / t + 1 / (t +
4) = 1 / 1.5
Solving for t by multiplying everything by t*(t + 4):
t + 4 + t = (1 / 1.5) (t) (t + 4)
3 t + 6 = t^2 + 4 t
t^2 + t = 6
Completing the square:
t^2 + t + 0.25 = 6 + 0.25
(t + 0.5)^2 = 6.25
t = -0.5 ± 2.5
t = -3, 2
Since time cannot be negative, therefore:
t = 2 hours
t + 4 = 6 hours
Alone, Sprinkler System A takes 2 hours while Sprinkler
System B takes 6 hours.
3
24
2
16
you just do (3 x 1/3 x 8/2 x1/8 x 2)
at least I think this is right
If Jim were jogging for have an hour his heart would beat 4,500 times. 4,500 minus 2,100, the amount of time his heart would beat in half an hour if he was resting, would be 2,400. So Jim's heart beats 2,400 more times when he is jogging for half an hour than it would be if he was resting for half an hour.
The GCF stands for greatest common factor. To represent a sum by its GCF we need to use the distributive property and we need to first find the GCF of the numbers. Let's break each number by its factors:
We now multiply the numbers that appear on both.
We now apply the distributive property:
The square of an odd number:
We're to conjecture, not do algebra, apparently. 1²=1, 3²=9, 5²=25, 7²=49, ...
We conjecture the square of an odd number is odd.
The product of two evens and an odd:
Again, we'll run some examples.
(2)(2)(1)=4
(2)(4)(3)=24
(4)(6)(5) =120
(4)(8)(1)=32
Conjecture: The product of two evens and an odd is a multiple of 4
Counterexample: The product of two fractions is never an integer
How about
3/4 × 4/3 = 1
