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:
A. a = 10
B. m<FNT = 120°
C. m<KTU = 60°
Step-by-step explanation:
A. (7a + 50)° and (14a - 20)° are corresponding angles. Therefore:
(7a + 50)° = (14a - 20)°
Use this equation to find the value of a
7a + 50 = 14a - 20
Combine like terms
7a - 14a = - 50 - 20
-7a = -70
Divide both sides by -7
-7a/-7 = -70/-7
a = 10
B. m<FNT = (14a - 20)° (alternate interior angles are congruent)
Plug in the value of a
m<FNT = 14(10) - 20
m<FNT = 140 - 20
m<FNT = 120°
C. m<KTU + (14a - 20)° = 180° (linear pair)
Plug in the value of a
m<KTU + 14(10) - 20 = 180
m<KTU + 120 = 180
m<KTU + 120 - 120 = 180 - 120
m<KTU = 60°
Answer: erm... the vertex it (1,-9)
Step-by-step explanation:
i think i did it right....not good at this stuff
To get the answer to this problem, first we have to subtract the marked up cost to the cost of the product. So we first minus 25.3 and 22.25. When we do this, we will get a difference of 3.05. This is the profit that you will earn. So after that, we have to divide 3.05 and 25.30 to get the mark up percentage. When we do this, we will get an answer of 0.12. So in order to convert that into a percentage, we just have to multiply it by 100 and we will get 12%.
Step-by-step explanation:
Cross Multiplying
Therefore
Hope it will help you.
