Question

A stack of bricks has a pattern where the first row has 6 bricks, the second row plus the 1st row has a total of 8. For row 3, the total number of bricks for all rows is 11 bricks, and for row 4, the total number of bricks for all the rows are 15 bricks. Make a table where rows represent the X and total bricks represent f(x). Find the pattern & write the equation. a) f(x) = 2x + 2 b) f(x) = x^2 + 1 c) f(x) = 3x - 1 d) f(x) = 4x + 3

Answer 1

The mathematical pattern in the stack of bricks is described by the equation f(x) = 4x + 3. This equation was determined by creating a table of values based on the description and comparing these values with the results of the provided equations.

Step-by-step explanation:

The question asks to identify the mathematical equation that describes the relationship between rows (X) and the total number of bricks (f(x)). We can create a table as

1. x = 1, f(x) = 6
2. x = 2, f(x) = 8
3. x = 3, f(x) = 11
4. x = 4, f(x) = 15

Let's match this pattern with the given equations.

a) f(x) = 2x + 2 does not fit as it gives us values 4, 6, 8, 10 for x = 1, 2, 3, 4 respectively.

b) f(x) = x^2 + 1 also does not fit, as it gives us values 2, 5, 10, 17 for x = 1, 2, 3, 4 respectively.

c) f(x) = 3x - 1 fits our case since it gives us 2, 5, 8, 11 for x = 1, 2, 3, 4 respectively. But it doesn't match with the total bricks given.

d) f(x) = 4x + 3 is the correct equation here as it matches with all the values of f(x) from our table, i.e., it gives us 7, 11, 15, 19 for x = 1, 2, 3, 4 respectively, which matches our table. So the correct equation that describes the pattern is f(x) = 4x + 3.

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