Question

1. find n.

\\( \frac { 1 } { 2 } n = 21 \\)
\\( n = \\)

1. how many grams are there in

7.5 kilograms?

1. how many diagonals does a

rectangle have?

1. write the expression

x increased by 12.

Explanation:

Step1: Solve for \(n\) in \(\frac{1}{2}n = 21\)

Multiply both sides by \(2\) to isolate \(n\).
$$\frac{1}{2}n\times2=21\times2$$

Step2: Calculate the value of \(n\)

Simplify the left - hand side (\(\frac{1}{2}\times2 = 1\)) and the right - hand side (\(21\times2=42\)).
$$n = 42$$

Step3: Convert kilograms to grams for \(7.5\) kilograms

Since \(1\) kilogram \(= 1000\) grams, use the conversion formula \(g=kg\times1000\).
For \(kg = 7.5\), we have \(g=7.5\times1000\)
$$7.5\times1000 = 7500$$

Step4: Determine the number of diagonals of a rectangle

The formula for the number of diagonals \(d\) of an \(n\) - sided polygon is \(d=\frac{n(n - 3)}{2}\). For a rectangle \(n = 4\).
Substitute \(n = 4\) into the formula: \(d=\frac{4\times(4 - 3)}{2}=\frac{4\times1}{2}=2\)

Step5: Write the expression for \(x\) increased by \(12\)

The phrase "increased by" means addition. So the expression is \(x+12\)

Answer:

1. \(n = 42\)
2. \(7500\) grams
3. \(2\) diagonals
4. \(x + 12\)