12, for every 2 cats there are three dogs. 8/2 is four. you multiply 3 times 4 to get 12
Answer:
the length of the hypotenuse must be 10.
Step-by-step explanation:
This is a right triangle, so we can apply the Pythagorean Theorem.
6² + 8² = 10² so the length of the hypotenuse must be 10.
72/160=?
Divide 72 by 160 to find the percent.
72/160=0.45
72 is 45% of 160.
I hope this helps :)
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
2x - 3y - 9z = -32
x + 3z = 8
-3x + y - 4z = -8
Add all the equations together.
-3y - 10z = -32
By looking at the first equation, 2x - 3y - 9z = -3y - 10z.
So 2x = -z.
By looking at the second equation, x + 3z = (-0.5z) + 3z = 8.
So 2.5z = 8, and z = 3.2.
This means that x = -1.6.
Let's substitute into our original equations!
-3.2 - 3y - 28.8 = -32
4.8 + y - 12.8 = -8
Therefore, y = 0!
Since these answers do not contradict each other, they are dependent.
The answers are x = -1.6, y = 0, z = 3.2.
