HELP ME JIM! Math HW

Problem 7

Answers:

Explanation:

In step 1, there are 2 dots. So that number (2) fills in the blank for dots A.

Step 2 has 5 dots, which fills in the blank for dots B.

Problem 8

A) Quadratic

Explanation:

We have this sequence of dots: {1, 2, 5, 10, ...}

Note the increments of +1, +3, +5, ...

The increments aren't the same, so we don't have a linear sequence. But because the increment amounts go up by 2 each time, this strongly implies a quadratic sequence.

The rule for this sequence is n^2 + 1. Whatever the step number (n) is, we square it and add 1 onto that result. For instance, for step 3, we have n = 3 that leads to n^2 + 1 = 3^2 + 1 = 9 + 1 = 10. Also, note how the lone dot on the left of step 3 is tacked onto the 3 by 3 square of dots.

Problem 9

Answers:

Explanation:

Same idea as problem 7

Problem 10

B) Exponential

Explanation:

The sequence is {1, 3, 9, 27, ...}

In step 3 we have 3 rows and 9 columns of dots to give 3*9 = 27 dots total here.

The sequence is growing by a factor of 3 each time. In other words, we are tripling the terms or multiplying each term by 3 to get the next term.

Therefore, we have an exponential pattern.

The rule is 3^n

Eg: if we're on step n = 2, then we have 3^n = 3^2 = 9 dots.

6.25 grams

step-by-step explanation:

-3 degrees

step-by-step explanation: