Algebra homework assignment

1. Find the area of the triangle formed by the coordinate axes and the line 4x + 6y – 24 = 0. (1pt)

2. Solve the equation  graphically in the interval [–9, 6]. Round your answer to two decimal places. (1pt)

3. A riverboat theater offers bus tours to groups on the following basis. Hiring the bus costs the group $180, to be shared equally by the group members. Theater tickets, normally $30 each, are discounted by 25 cents times the number of people in the group. How many members must be in the group so that the cost of the theater tour (bus fare plus theater ticket) is less than $42 per person? At least __________ members (1pt)

4. A jeweler has three small solid spheres made of gold, of radius 3 mm, 6 mm, and 8 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be? __________ mm (1pt)

5. Find all real solutions of the equation. (1pt)

6. A rectangle has vertices of A(5, 5), B(11, 5), C(5, 2), and D(11, 2) on a coordinate plane. Find the area of the rectangle. (1pt)

7. In the short growing season of the Canadian arctic territory of Nunavut, some gardeners find it possible to grow gigantic cabbages in the midnight sun. Assume that the final size of a cabbage is proportional to the amount of nutrients it receives, and inversely proportional to the number of other cabbages surrounding it. A cabbage that received 35 oz of nutrients and had 10 other cabbages around it grew to 30 lb. What size would it grow to if it received 17.5 oz of nutrients and had only 5 cabbage neighbors? Round to the nearest tenth, if necessary. __________ lbs (1pt)

8. A box with a square base and no top is to be made from a square piece of cardboard by cutting y inch squares from each corner and folding up the sides, as shown in the figure. The box is to hold 245 in 3 . How big a piece of cardboard is needed if y = 5 inches?

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Give the length (in inches) of the starting piece of cardboard. __________ inches (1pt)

9. Use the discriminant to determine the number of real solutions of the equation.  Do not solve the equation.

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x 2 - 5.15x + 3.39 = 0 (1pt)

10. Evaluate the expression  and write the result in the form a + bi . (1pt)

11. Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile to the nearest hundredth of a foot when it contains 1,000 ft 3 of grain? (1pt)

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__________ feet (1pt)

12. Do the graphs of  and  intersect in the viewing rectangle  by [-1, 3]?

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Determine the number of points of intersection.  If there are no points of intersection, answer 0. (1pt)

13. The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 47 mi/h can stop in 245 ft. What is the maximum speed it can be traveling if it needs to stop in 155 ft? Please round the answer to the nearest tenth.

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s = __________ mi/h (1pt)

14. Find the slope of the line sketched in the graph.

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m = __________ (1pt)

15. Express the statement as a formula. y is directly proportional to x. If x = 11 and y = –33, what is the constant of proportionality? (1pt)

16. Evaluate the expression  and write the result in the form a + bi . (1pt)

17. The pressure P of a sample of gas is directly proportional to the temperature T and inversely proportional to the volume V. (1pt)

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Find the constant of proportionality if 90 L of gas exerts a pressure of 35 kPa at a temperature of 200 K (absolute temperature measured on the Kelvin scale). Round your answer to three decimal places. k = __________ (1pt)

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If the temperature is increased to 800 K and the volume is decreased to 70 L, what is the pressure of the gas? Round your answer to three decimal places. P = __________ kPa (1pt)

18. Find all real solutions of the equation. (1pt)

19. Evaluate the expression  and write the result in the form a + bi . (1pt)

20. Find all real solutions of the equation. ( x + 5 ) 2 - 8( x + 5 ) + 15 = 0 (1pt)