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
Answer:
Obtuse, isosceles
Step-by-step explanation:
Classify. Two same length sides make it isosceles
A larger angle than 90° make it obtuse
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Answer:
X = 66
Step-by-step explanation:
A straight line is equal to 180 degrees so if you have one side of that line you can figure out the inside angle.
Now that you have two of the angles inside the triangle add them up. All the interior angles of a triangle will add to 180. So add up 38 and 76 to get 114. Now do 180 - 114, you should get 66
so x = 66
Answer:
46.8
Step-by-step explanation:
Answer:
12y+9.48x=0
Step-by-step explanation:
Note dozen means 12 in mathematics
So 12 muffins cost $9.48
X muffins cost $y
So let's cross multiply
12×y=9.48×x
12y=9.48x
Substrate 9.48x from both sides
12y-9.48x=0
So the final equation is 12y-9.48x=0
