What table shows a proporioal relationship between x and y

8. The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat

Natali [406]

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

3 0

2 years ago

Read 2 more answers

9 is the difference between two numbers, and their sum is 31. Find the numbers.

algol [13]

Answer:

The first number is 20, the second one is 11

Step-by-step explanation:

Let the first number be x and the second number be y

Since it says "9 is the difference between two numbers", the first equation will be x-y=9

It also says that "their sum is 31". That means the second equation will be x+y=31

here are the two equations:

x-y=9

x+y=31

You can solve this any way you like, but I'll show elimination

add the two equations

x-y=9

x+y=31

2x=40

divide by 2

x=20

Substitute 20 as x in one of the equations

20+y=31

subtract 20 from both sides

y=11

That means the two numbers are 20 and 11

Hope this helps!

4 0

3 years ago

(-7x+8y-2z)+(-9x-y+6z)

Svetach [21]

Answer: the answer is -16x+7y+4z

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

An appliance repair shop charges $80 for the first hour of labor and $65 for each additional hour. The total labor charge for an

VikaD [51]

Answer:

C. 80+65x=665

The total repair time is 9 hours.

Step-by-step explanation:

The first hour is $80, no matter what. That is the first part of your equation.

x = the number of hours minus 1.

It would be -1 because it is $65 per ADDITIONAL hours, after the first hour.

So that would be 65x, because you don't know the number of hours it took (yet), but you know that it would be $65 per extra hour.

So you have your equation: 80+65x=665

1. Get rid of subtraction/addition.

You want to get rid of the number from both sides. It's subtracting 80 and not adding 80 because the 80 is positive, and you want to cancel out that 80.

80+65x=665

-80 -80

You are left with 65x=585

2. Get rid of multiplying/dividing.

Here, we want to get the variable by itself, so we will have to divide the 65x by 65. You want to do the opposite operation to cancel the 65 out.

65x=585

65x/65 = 585/65

You are left with x = 9

3 0

3 years ago

1. Draw, in BLACK, the triangle with vertices (−1, 5), (−6, 3), and (−4, 8). 2. In BLUE, draw the triangle when the BLACK triang

Oxana [17]

Answer:

oplkmlkm

Step-by-step explanation:

hellolkmlkmkjjjjjjjjjjjjjjjjjjjjj

6 0

3 years ago