91Ó°ÊÓ

Find all numbers with absolute value \(9 .\)

Explain why the sum of a rational number and an irrational number is an irrational number.

Suppose \(t\) is an irrational number. Explain why \(\frac{1}{t}\) is also an irrational number.

Give an example of two irrational numbers whose product is a rational number.

Write each union as a single interval. $$ [2,7) \cup[5,20) $$

Simplify the given expression possible. $$ 4(2 m+3 n)+7 m $$

Write each union as a single interval. $$ (3, \infty) \cup[2,8] $$

The intersection of two sets of numbers consists bers that are in both sets. If \(A\) and \(B\) are sets, intersection is denoted by \(A \cap B\). Write each intersection as a single interval. $$ (-\infty,-6] \cap(-8,12) $$

Explain how you could show that \(51 \times 49=2499\) in your head by using the identity \((a+b)(a-b)=a^{2}-b^{2}\).

The sales tax in San Francisco is \(8.5 \%\). Diners in San Francisco often compute a \(17 \%\) tip on their before-tax restaurant bill by simply doubling the sales tax. For example, a \(\$ 64\) dollar food and drink bill would come with a sales tax of \(\$ 5.44\); doubling that amount would lead to a \(17 \%\) tip of \(\$ 10.88\) (which might be rounded up to \$11). Explain why this technique is an application of the associativity of multiplication.