91Ó°ÊÓ

Solve equation by the method of your choice. $$ x^{2}-6 x+13=0 $$

The formula for converting Celsius temperature, \(C,\) to Fahrenheit temperature, \(F,\) is $$ F=\frac{9}{5} C+32 $$ If Celsius temperature ranges from \(15^{\circ}\) to \(35^{\circ},\) inclusive, what is the range for the Fahrenheit temperature? Use interval notation to express this range.

If a coin is tossed 100 times, we would expect approximately 50 of the outcomes to be heads. It can be demonstrated that a coin is unfair if \(h\), the number of outcomes that result in heads, satisfies \(\left|\frac{h-50}{5}\right| \geq 1.645 .\) Describe the number of outcomes that determine an unfair coin that is tossed 100 times.

If \(x\) represents a number, write an English sentence about the number that results in an inconsistent equation.

In a round-robin chess tournament, each player is paired with every other player once. The formula $$ N=\frac{x^{2}-x}{2} $$ models the number of chess games, \(N,\) that must be played in a round-robin tournament with \(x\) chess players. Use this formula to solve. In a round-robin chess tournament, 21 games were played. How many players were entered in the tournament?

In a round-robin chess tournament, each player is paired with every other player once. The formula $$ N=\frac{x^{2}-x}{2} $$ models the number of chess games, \(N,\) that must be played in a round-robin tournament with \(x\) chess players. Use this formula to solve. In a round-robin chess tournament, 36 games were played. How many players were entered in the tournament?

Explaining the Concepts. Describe ways in which solving a linear inequality is different than solving a linear equation.

Use the Pythagorean Theorem and the square root property to solve. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth. A rectangular park is 4 miles long and 2 miles wide. How long is a pedestrian route that runs diagonally across the park?

Explaining the Concepts. Describe how to solve an absolute value inequality involving the symbol \(>.\) Give an example.

Use the Pythagorean Theorem and the square root property to solve. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth. A baseball diamond is actually a square with 90 -foot sides. What is the distance from home plate to second base?