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Which expression represents the relationship between the step number, \(n\), and the total number of small squares in the pattern?
\(n^2+1\)
\(n^2-1\)
\(n^2-n\)
\(n^2+n\)
Each figure is composed of one or more large squares and some small squares. The side length of the large square is \(x\). Write an expression for the area of the shaded part of each figure.
Figure A
Figure B
Here are a few pairs of positive numbers whose difference is 5.
Find the product of each pair of numbers. Then, plot some points to show the relationship between the first number and the product.
| first number |
second number |
product |
|---|---|---|
| 1 | 6 | |
| 2 | 7 | |
| 3 | 8 | |
| 5 | 10 | |
| 7 | 12 |
Here is a pattern of dots.
| step | total number of dots |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 |
Technology required. A rope with a length of 4 meters is tied from a stake in the ground to the top of a tent. It forms a 20 degree angle with the ground. How tall is the tent?