Explanation

Let x be the side of the square. Then diagonal =\(x \times \sqrt{2}=2\)which gives \(x=\sqrt{2}\) area of square = \(x^{2}=2\)

The price of a watch is decreased by 10% to \(\$3600\). What will be its original price?

Find the roots of this polynomial: \({x^2} - 9x + 8\).

A painter mixes gallons of paint in a large cylindrical bucket so that there will be no difference in colour among individual gallons. If one gallon of paint has a volume of approximately \(8000 \mathrm{~cm}^{3}\), what is the maximum number of whole gallons of paint that can be poured into the bucket?

What is the missing term in the proportion?

\(\frac {9}{x}=\frac{15}{10}\)

A new roll of insulated electrical wire has 200 feet of wire. Mr. Saunders needs pieces that are \(6\frac{1}{4}\) feet long. How many full pieces of this length can he cut from the roll?

John was building a new fence, and he wants it to stand \(8\frac{1}{2}\) feet above ground level. To make sure it is secure he must place it \(2\frac{3}{4}\)feet into the ground. How long of a post should John buy?

The product of \(\sqrt{24 a}\) and \(\sqrt{5a}\) is?

Jeff has one million dollars in his bank account. He cashes out only in \( \$100\) bills. How many \(\$100 \) currency notes should he collect?

A boy buys one dozen apples and two dozen mangoes. Apples per dozen cost \(\$20\) and mangoes per dozen cost \(\$30\). The storekeeper gives a concession of \(\$10.3\). What is the money the boy paid?

Attorney A charges a fixed fee on \(\$250 \)for an initial meeting and \(\$150\) per hour for all hours worked after that. Attorney B charges \(\$150 \)for the initial meeting and \(\$175 \)per hour. Find the charge for 26 hours of work for each attorney. Which is the better deal?

Stephen borrowed \(\$500\) from a bank and agreed to pay 6% annual interest on the loan for a term of 24 months. How much money will he have paid the bank at the end of the term of the loan?

When visiting Orlando, Maria needs to rent a taxi to get from a hotel to a restaurant. The taxi company charges a flat fee of \(\$3.00\) for using the taxi and \( \$0.75 \) per mile. Write an equation in slope-intercept form that models this situation.

Adding \(4\frac{1}{2}\) to \(3\frac{3}{4}\) and then subtracting \(2\frac{2}{5}\)from the sum results in which value?