Mathematics High School

Membership to two different clubs are represented by the equations below. The x-value represents the number of months dues are paid. The y-value represents the total cost of dues over time. How many months will it take for the membership of both clubs to be the same?
y = 3x − 5
4x − 3y = 5

2 months

5 months

3 months

4 months

Answers

Answer 1

It would take 2 months for the membership of both clubs to be the same

What is an equation?

An equation is an expression that shows the relationship between two numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost of dues over x months, hence given that:

y = 3x - 5 (1)

Also:

4x - 3y = 5

y = (4x - 5)/3 (2)

For the membership of both clubs to be the same:

3x - 5 = (4x - 5)/3

9x - 15 = 4x - 5

x = 2

It would take 2 months for the membership of both clubs to be the same

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Related Questions

Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?

Answers

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

What is the distance?

Distance is a measurement of time and speed.

The distance equals speed multiplied by time.

Data and Calculations:

Distance between Alice and Bob = 1,000 feet

Distance between the bird and Bob = 1,000 feet

Speed of Alice and Bob = 10 feet per second, respectively

The combined speed of Alice and Bob = 20 feet per second

Since the two are running directly toward each other, the distance each will cover at the meeting point is 50 feet (1,000/20)

The time covered at the meeting point = 20 seconds (1,000/50)

Speed of the bird = 20 feet per second

The distance covered by the bird towards Bob at their meeting point is 40 feet (20 feet x 20 seconds)

Thus, the total distance covered by the bird at the meeting point is 40 feet.

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Solve for n.
7 + 2n
||
=
submit

Answers

Answer:

Step-by-step explanation:

7+2n = 11

2n = 11-7

2n = 4

n = 4/2

therefore n = 2

The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?

Answers

The possible base and height of a second triangle are:

B = 5 H = 12

What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

To find the base and height of the triangle:

First, we must find the constant of variation (k).

The problem indicates that the base of each triangle varies inversely with the height.

So, this can be represented as below:

B = k/H

B is the base of the triangle (B=10). H is the height of the triangle (H=6). k is the constant of variation.

When we clear "k", we obtain:

B = k/H k = BxH k = 10x6 k = 60

Now, we have:

B = 60/H

We can give any value to "H" and you will obtain the base of the second triangle.

If H = 12, then:

B = 60/H B = 60/12 B = 5

Therefore, the possible base and height of a second triangle are:

B = 5 H = 12

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