Exam 2: Equations and Inequalities

The boundary of a city is a circle of diameter L = 7 miles. As shown in the figure, a straight highway runs through the center of the city from A to B. The highway department is planning to build a 8-mile-long freeway from A to a point P on the outskirts and then to B. Find the distance from A to P. (Hint: APB is a right triangle.) Round the answer to the nearest tenth of a mile.

Solve the equation.

Solve the equation

Solve the inequality.

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 18 - year - old child whose mental age is 21.6.

Solve the equation

Solve the equation

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the mental age of a person 18 years old whose IQ is 140.

A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $500 per year. Car B costs $12,600 and has an mpg rating of 50, and insurance is $550 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.

Find the values of x and y, where x and y are real numbers.

Solve the equation

Solve the equation

A student in an algebra course has test scores of 69, 79, 75, and 80. What score on the next test will raise the student's average to 80?

During a nuclear explosion, a fireball will be produced having a maximum volume V ₀ . For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^o K.) Approximate t when V is 84% of V ₀ . Round the answer to the nearest thousandth of a second.

A bullet is fired horizontally at a target, and the sound of its impact is heard 1.3 seconds later. If the speed of the bullet is 3,000 ft/sec and the speed of sound is 1,100 ft/sec, how far away is the target?

Solve the equation.

Find the values of x and y, where x and y are real numbers.

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 16 - year - old child whose mental age is 21.6.

Solve the inequality.

The boundary of a city is a circle of diameter L = 9 miles. As shown in the figure, a straight highway runs through the center of the city from A to B. The highway department is planning to build a 10-mile-long freeway from A to a point P on the outskirts and then to B. Find the distance from A to P. (Hint: APB is a right triangle.) Round the answer to the nearest tenth of a mile.