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# Grade 9 homework questions on 2.4 and 2.5

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### Grade 9 homework questions on 2.4 and 2.5

1. 1. 2.4 Problem 57<br />Your class wants to make a rectangular spirit display, and has 24 feet of decorative board to enclose the display.<br />Write an equation in standard form relating the possible lengths l and widths w of the display. <br />Solution:<br /> 2l + 2w = 24 there are two sides of length and two sides of width since it’s a rectangle<br />b. Graph the equation from part (a). C. Make a table of at least five possible pairs of dimensions for the display. <br />2(6) + 2w = 24 Put l in the equation <br />12 + 2w = 24 Subtract by 12<br />-12 -12<br />2w = 12 Then divide by 2 <br /> w = 6<br />16<br />12<br />8<br />4<br />4 8 12 16<br />
2. 2. 2.5 Problem 30<br />Give an example of two real-life quantities that show direct variation. Explain your reasoning. <br />Solution:<br />If you earn an hourly wage, the amount of money you earn varies directly with the number of hours you work. If you work 4 hours and make \$28, the equation relating the number of hours h worked and the amount of money m you earn is m = 7h. If you are traveling at a constant speed, the distance d you travel varies directly with the time t you travel. If you drive for 4 hours and travel 248 kilometers, the direct variation equation is d = 62h. <br />
3. 3. Problem 36<br />Let (x1, y1) be a solution, other than (0,0), of a direct variation equation. Write a second direct variation equation whose graph is perpendicular to the graph of the first equation. <br />Solution:<br />Y = ax Put x1 and y1 into the equation for x and y.<br />Y1 = a(x1) Then divide each side by x1<br /> = a<br />Then put the y1/x1 back into place for a.<br />Y = x; y = x <br />
4. 4. Problem 39<br />Hail 0.5 inch deep and weighing 1800 pounds cover a roof. The hail’s weight w varies directly with its depth d. Write an equation that relates d and w. Then predict the weight on the roof of hail that is 1.75 inches deep. <br />Solution:<br />W represents y and d represents x. Place it back into the y = ax formula.<br />1800 = a (0.5) Divide 1800 by 0.5.<br />3600 = a<br />Write 3600 back into the y = ax formula. <br />w = 3600d Then plug 1.75 into the formula.<br />w = 3600(1.75) Then multiply through.<br />w = 6300<br />So the weight when the hail is 1.75 inches deep weighs 6300 pounds. <br />
5. 5. Problem 41<br />The ordered pairs (4.5,23), (7.8, 40), and (16.0, 82) are in the form (s, t) where t represents the time (in seconds) needed to download an internet filed of size s (in megabytes). Tell whether the data show direct variation. If so, write an equation that relates s and t. <br />Solution:<br />Because the direct variation equation y = ax can be written as y over x = a, a set of data pairs (x, y) shows direct variation if the ratio of y to x is constant.<br /> 23/4.5 = 5.1 40/7.8 = 5.1 82/16.0 = 5.1<br />Because the ratios are approximately equal, the data shows direct variation. Now we want to write an equation that relates s and t. <br />t = 5.1s<br />
6. 6. Problem 44<br />Each year, gray whales migrate from Mexico’s Baja Peninsula to feeding grounds near Alaska. A whale may travel 6000 miles at an average rate of 75 miles per day.<br />A. Write an equation that gives the distance d1 traveled in t days of migration.<br />D1 = 75t<br />B. Write an equation that gives the distance d2 that remains to be traveled after t days of migration.<br />D2 = 6000 – 75t<br />C. Tell whether the equations from parts (a) and (b) represent direct variation. Explain your answers.<br />Part (a) represents direct variation because the graph goes through the origin. Part (b) does not represent direct variation because the graph does not go through the origin. <br />