Question

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Answer 1

Answer:Pattern C shows a quadratic relationship between the step number and the number of dots.

In Pattern C, the number of dots increases as the step number increases. Specifically, the number of dots in each step follows a quadratic sequence: 0, 1, 2, 3, 3. This can be observed by examining the number of dots in each step:

Step 0: 0 dots

Step 1: 1 dot

Step 2: 2 dots

Step 3: 3 dots

Step 4: 3 dots

We can see that the number of dots increases by 1 in each step until Step 3, where it remains at 3 dots for the remaining steps.

This pattern can be represented by the quadratic equation y = x², where y represents the number of dots and x represents the step number. By substituting the step numbers into the equation, we can see that the pattern follows a quadratic relationship.

For example, when x = 0, y = 0² = 0 dots.

When x = 1, y = 1² = 1 dot.

When x = 2, y = 2² = 4 dots (but limited to 2 in the pattern).

When x = 3, y = 3² = 9 dots (but limited to 3 in the pattern).

Therefore, Pattern C shows a quadratic relationship between the step number and the number of dots.

Explanation:

Answer 2

The pattern with a quadratic relationship is Pattern B. The number of dots is given by 2n^2 + 1, where n is the step number. Patterns A and C exhibit linear and constant relationships, respectively.

The three patterns of dots and asks which one has a quadratic relationship between the step number and the number of dots.

The pattern with a quadratic relationship is Pattern B.

In Pattern B, the number of dots is 2n^2 + 1, where n is the step number. This means that the number of dots increases as the square of the step number. For example, in step 1, there are 3 dots
`(2 * 1^2 + 1)`, and in step 2, there are 5 dots
`(2 * 2^2 + 1)`.

The other two patterns do not have quadratic relationships.

* In Pattern A, the number of dots increases linearly with the step number.

* In Pattern C, the number of dots increases at a constant rate.

Therefore, only Pattern B exhibits a quadratic relationship between the step number and the number of dots. Option B is the correct choice.