Homework 5 Name: Show all work. You should avoid calculator usage unless you are using it to check your work. Also, you should be doing your work in pencil. Fundamental Questions 1) Let n be a number. Translate the following English phrases into algebraic expressions. a) The sum of ve times a number and three. b) The product of 5 less than a number and three more than the same number. 0) The quotient of 2 less than a number and 6. 2) Anthony makes ac dollars an hour. Give an algebraic expression for his total earnings a week if he worked 8 hours on Monday, 6 hours on Tuesday, 7 hours on Wednesday, 9 hours on Thursday, and 4 hours on Friday. Simplify this expression. 3) The length of a side of a square is 2: inches. a) Compose an algebraic expression for the perimeter of the square. Simplify this expression. b) Compose an algebraic expression for the area of the square. Simplify this expression. 4) A $50,000 salary is increased by 10% and then decreased by 10%. What is the new salary? 5) State the relationship between distance, rate, and time of a moving object using three equivalent equations. 6) Look up the etymology of the word \"perimeter.\" Now that you see its literal translation, explain how one can argue that there is only one way to calculate the perimeter no matter what shape you are measuring. Routine Questions 7) One side of a rectangle is :3 cm, and the other side is 4 cm longer. a) Compose an algebraic expression for the perimeter of the rectangle. Simplify this expression. Find the value of this expression if as = 6. b) Compose an algebraic expression showing the area of the rectangle. Simplify this expression. Find the value of this expression if a: = 8. 8) In a triangle ABC, the side AB has a length of SL' inches. The side BC is twice as long as AB. The side AC is 2 inches longer than BC. Compose an algebraic expression showing the perimeter of the triangle. Find the value of this expression if x = 5. 9) A circle is inscribed in a square with a side of length a. Find the shaded area in terms of a. r1 LJ 10) A jacket was purchased for $264. This price was calculated after a 20% coupon was used in a state that charges 10% sales tax. What was the original price of the jacket? 11) The area A of a trapezoid with bases a, b and height h is calculated by the formula a+b 2 Using this formula, express b in terms of A, a, and h. A: h. 12) According to Newton's law of universal gravitation, m1 m2 R2 ' where F is the force between the masses of m1 and m2, G is the gravitational constant, and R is the distance between the centers of the masses. Use this equation to nd ml in terms of F, G, m2 and R. F=G- 13) A car is driven for several hours at a constant speed of 50 mph. Then the car increased its speed to 60 mph and drove for twice as much time as before. Find the time spent while driving in both intervals if the total trip elapsed 170 miles. 14) In triangle ABC, angle A is 200 greater than angle B, and angle 0 is twice the size of angle A. Find the measures of each angle in the triangle. Old Exam Questions 15) Joe works for a cleaning company and also works for a delivery service. The cleaning company pays $7 more per hour than the delivery service. Overall, Joe spent 13 hours cleaning and 17 hours making deliveries to earn a total of $571. what are the pay rates at each job? Solve the problem by composing an equation. 16) Buddy the Elf borrowed Santa's sleigh to run some holiday errands. He ew from the North Pole to the Syrup Factory making a stop at the Gingerbread Bakery. It took 3 hours to y to the Gingerbread Bakery at a constant speed. Then Buddy increased his speed by 15 km/h and spent two hours ying to the Syrup Factory. What was Buddy's speed on his way to the Gingerbread Bakery if he covered a total distance of 530 km from the North Pole to the Syrup Factory