Answer:
7.5 liters of a 10% antifreeze solution AND
7.5 liters of a 40% antifreeze solution
Step-by-step explanation:
According to the question,we were asked to find out how many liters of 10% anti freeze solution and 40% anti freeze each to make a 15 liters 25% mixture
Let’s call
the amount of liters needed of our 10% solution “x”. So, how
many liters do we need of the 40% solution? Well, there are 15
liters in total, x liters have been spoken for, so what remains
of our allotted 10 liters then, is 15-x.
Now let's solve for "x"
10% of x + 40% of (15 - x) = 25% of 15 liters
0.1x + 0.4(15 - x) = 0.25(15)
0.1x + 6 - 0.4x = 3.75
Collect the like terms and we have
0.3x = 2.25
x = 2.25 × 3
X = 7.5(Liters for the 10% anti freeze solution)
The 40% solution= 15 - 7.5 = 7.5 liters
Since "X" was used to fill for the unknown amount of 10% anti freeze solution,we have 7.5 liters of the 10% solution and another 7.5 liters for the 40% solution to end up with 15 liters of the desired 25% solution.
Answer:
Possible lengths of the silk fibre 'x' are 100, 75, 60, 50 and 30 yards respectively.
Step-by-step explanation:
Let the length of the silk fiber = x yards.
Let the number of silk fibres = a.
It is given that the silk fibers between 3 to 10 yards are combined to form a silk thread of 300 yards.
So, we get the equation,
, where 
i.e. 
,
So, the possible values of 'a' are 3, 4, 5, 6 an 10.
Thus, the possible lengths of the silk fibre 'x' are 100, 75, 60, 50 and 30 yards respectively.
The answer is A,
if you plug in the points of (2,-5) into
y=x-7
-5=2-7
-5=-5
so the equation is true
Answer:
1
Step-by-step explanation:
x-7=-5x-1
x-(-5x)-7=-1
x+5x-7=-1
6x-7=-1
6x=-1+7
6x=6
x=6/6
x=1
Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
