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1. a solution of 61% fertilizer is to be mixed with a solution of 20% fertilizer to form 287 liters of a 57% solution. how many liters of the 61% solution must be used?

Let x be the  liters of 61%  solution.....then    287−  x  = the liters of 20% solution

And we have

.61x    +   .20 (287 − x)   =  .57 (287)     multiply through by 100 to clear the  decimals 

61x  + 20 (287 − x)   = 57 (287) simplify

61x + 5740 − 20x   =  16359

41x +  5740   = 16359     subtract 5740 from each side

41x   = 10619  divide both sides by 41

x = 259 liters  = 61%  solution   ...... and  287 −  259  = 28 liters of 20% solution

287 l of 57%  = 163.59 l of pure fertilizer

x = amount of 20%       .20 x

287-x = amount of 61%  =  (287-x)(.61)

.20x + (287-x)(.61) = 287(.57)

.20x +175.07 - .61x = 163.59

-.41x = - 11.48

x = 28 liters of 20%      287-28 = 259 liters of 61%

I don't get your question.

I don't get your question.

why doesn't it make sense? 

answer: 8.8163265306122449

rounded: 8.8

Use the calculator. The answer is 2.

why is there any purpose of you asking this??

-24 - (1/8)p = (3/8)p    add 1/8p to both sides

-24  =  (4/8) p         [ 4/8  = 1/2]

-24  = (1/2)p     multiply both sides by 2

-48   =  p

0.4

0.4

Plug your algebraic equation into the calculator and it will simplify it for you

You are most welcome.

Thanks so much!, I appreciate you breaking the problem down so that I could fully understand to be able to continue to solve these types of problems. I truly thank you

You could have just entered this on the calculator that this website is about. Anyway the answer is -30

EP: An increase of 1.85% is compound increase in temperature. That is: 1.85% x 2.5 =0.04625 degress - average annual increase in temp. compounded annually. Both, your calculation and mine are accurate: yours is a simple average annual increase; mine is a compound average annual increase.

.....and please realize, these are made up numbers for your question....don't believe the temps have gone up quite that much:

"For example, the average annual temperature for the globe between 1951 and 1980 was around 57.2 degrees Fahrenheit (14 degrees Celsius). In 2015, the hottest year on record, the temperature was about 1.8 degrees F (1 degree C) warmer than the 1951–1980 base period."

13x = 0.5   divide both sides by 13

13x /13 = .05/13

x = .05/13 = 0.0038461538461538

I think you'll need to use the ACTUAL  KELVIN degrees (not just the absolute value of the increase) to calculate the PERCENTAGE increases of temperature over the years. (actual temps not given in question)

1.85% x 50 years = would be a 93 % increase in temperature !

The question asks what is the value of y. There is a triangle that has the measurements (2y+20)dg, (5x)dg, and 40dg. I need to solve for the value y. How do I do this, I was a bit confused? I know how to solve for x though, is it similiar or?

(2y+20) + 5x + 40 =180

(2y+20) =5x + 40

Solve the following system:
{60 + 5 x + 2 y = 180 | (equation 1)
2 y + 20 = 5 x + 40 | (equation 2)
Express the system in standard form:
{5 x + 2 y = 120 | (equation 1)
-(5 x) + 2 y = 20 | (equation 2)
Add equation 1 to equation 2:
{5 x + 2 y = 120 | (equation 1)
0 x+4 y = 140 | (equation 2)
Divide equation 2 by 4:
{5 x + 2 y = 120 | (equation 1)
0 x+y = 35 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{5 x+0 y = 50 | (equation 1)
0 x+y = 35 | (equation 2)
Divide equation 1 by 5:
{x+0 y = 10 | (equation 1)
0 x+y = 35 | (equation 2)
Collect results:
Answer: |x = 10        and           y = 35

2.5 F degree s / 50 years = .2.5/50 = 0.05 degrees F per year

2.5^(1/50) =1.018495 - 1 =0.018495 x 100 =~1.85% per year - average increase in temperature.

Thank you so much for helping, I thought that 45 was incorrect, but I was able to check my answer and make sure it was right. God bless

CPhill: I was of the opinion that the cheese is more of circle, like pizza, rather than a sphere!! No?. They obviously have more thickness to them than a pizza. Besides, as a practical matter, I have never seen or heard of piece of cheese weighing in at more than 3 1/2 tons!!. I think my answer is closer to the true answer in this case!.

Excuse me, I have mistakenly entered this function:

\(f(x)=e^x-3e^{-x}>0\)

Here the graph of the correct function:

\(e^x-3e^{-x}+2>0\)

Guest two has right

\(e^x-1>0\)

That is whenever \(x>0\)

              !

\(\)

801^801 = 6.4512724511 x 10^2325

x + 2x + 3x = 180

6x = 180

x =180 / 6

x = 30 degrees - one angle

30 x 2= 60 degrees - the 2nd angle.

30 x 3 = 90 degrees - the 3rd angle.