Answer:
-1/3 - (-3/5) = 4/15
Step-by-step explanation:
Reduce to simplest form
-1/3 - (-3/5)
= -1/3 + 3/5
Find the Lowest Common Multiple of 3 and 5
Lowest Common Multiple of 3and 5 is 15
Use the LCM to Simplify
= {(-5*1)+(3*3)} / 15
= (-5+9) / 15
= 4/15
Therefore,
-1/3 - (-3/5) = 4/15
He will mix some 20% solution and some 70% solution to make 60% solution.
Let x = number of liters of 20% solution.
Let y = number of liters of 70% solution.
He wants to make 50 liters of 60% solution, so
x + y = 50 First Equation
The amount of acid in x amount of 20% solution is 20% of x, or 0.2x
The amount of acid in y amount of 70% solution is 70% of y, or 0.7y
The amount of acid in 50 liters of 60% solution is 60% of 50 liters, or 0.6 * 50 = 30
Now we add the amounts of acid.
0.2x + 0.7y = 30 Second Equation
x + y = 50
0.2x + 0.7y = 30
-0.2x - 0.2y = -10
0.2x + 0.7y = 30
------------------------
0.5y = 20
y = 40
x + y = 50
x + 40 = 50
x = 10
Answer: He needs 10 liters of 20% solution and 40 liters of 70% solution.
Subtract the part from the total:
102.50 - 15 = 87.50
Now divide the remainder by rate:
87.50 / 25 = 3.5 hours
The number of doughnuts in bags is 4 times the number of bags of doughnuts. So the number in B bags of doughnuts will be
... 4B
The number of doughnuts in cartons is 10 times the number of cartons of doughnuts, so the number in C cartons will be
... 10C
The total number of doughnuts (T) is the sum of those in bags and those in cartons:
... T = 4B +10C
Pythagoras Theorem:
hipotenuse²=leg₁²+leg₂²
First posible triangle:
hypotenuse=13 (13²=169)
leg₁=12 ( 12²=144)
leg₂=5 (5²=25)
13³=144 + 25
Answer:can be side lengths of a triangle
Second triangle:
hypotenuse=12.6 (12.6²=158.76)
leg₁=6.7 ( 6.7²=44.89)
leg₂=6.5 (6.5²=42.25)
leg₁²+leg₂²=44.89+42.25=87.14≠158.76
Answer: cannot be side lenghts of a triangle.
third triangle:
hypotenuse=13 (13²=169)
leg₁=12 ( 12²=144)
leg₂=11 (11²=121)
leg₁²+leg₂²=144+121=265≠169
Answer: cannot be side lenghts of a triangle.
fourth triangle:
hypotenuse=13 (13²=169)
leg₁=6 ( 6²=36)
leg₂=4 (4²=16)
leg₁²+leg₁²=36+16=52≠169
Answer: cannot be side lenghts of a triangle.
