A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few years. Write an equation representing the relationship, where x is time in years, and y is the number of songs available. a) y = 1500 * 3^x b) y = 1500 + 3x c) y = 1500 * x³ d) y = 1500 / (3^x)

Answer:

To find the perimeter of the original rectangle, we first need to find the dimensions of the rectangle.

Let's assume the length of the original rectangle is L cm and the breadth is B cm.

According to the given information, if the length is decreased by 4 cm, the new length becomes (L - 4) cm. Similarly, if the breadth is increased by 2 cm, the new breadth becomes (B + 2) cm.

We are told that this new rectangle with dimensions (L - 4) cm and (B + 2) cm is actually a square with the same area as the original rectangle.

The area of a rectangle is given by length multiplied by breadth. So, the area of the original rectangle is L * B square cm.

The area of the new square is equal to the area of the original rectangle. Therefore, we can set up the equation:

(L - 4) * (B + 2) = L * B

Expanding the equation:

LB - 4B + 2L - 8 = LB

Simplifying the equation:

2L - 4B - 8 = 0

2L = 4B + 8

L = 2B + 4

Now that we have an equation relating the length and breadth of the original rectangle, we can find the perimeter.

The perimeter of a rectangle is given by the formula: 2 * (length + breadth).

Substituting the value of L from the equation above, we get:

Perimeter = 2 * [(2B + 4) + B]

Perimeter = 2 * (3B + 4)

Perimeter = 6B + 8

Therefore, the perimeter of the original rectangle is 6B + 8 cm.

Step-by-step explanation:

Answer:

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Step-by-step explanation:

1. The domain and range of relation S are as follows:

Domain: The domain refers to the set of all input values in a relation. In this case, the domain of S is {3, 2, 1}, which corresponds to the first element of each ordered pair in the relation.

Range: The range refers to the set of all output values in a relation. In this case, the range of S is {4, 3, 2, 1}, which corresponds to the second element of each ordered pair in the relation.

2. No, relation S is not a function.

To be considered a function, each input value (or element in the domain) should have only one corresponding output value (or element in the range). However, in the given relation S, the input value 2 is associated with both the output values 3 and 1.

Since one input value is associated with multiple output values, S fails the definition of a function.

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(3,4) and (4,-6)

The distance between them is

We have the final answer as

Hope this helps you