I have this study guide with 4 problems, I already did it but I need to have an
ID: 3099383 • Letter: I
Question
I have this study guide with 4 problems, I already did it but I need to have an answer sheet or something to check so here they are!1. Find the value of y for a given value of x, if y varies directly with x.
If y=4.8 when x=2.4, what is y when x= 2.05
4.1
1.03
-1.03
-4.1
2. A candle is 10 inches tall after burning for 2 hours. After 3 hours, it is 8 1/2 inches tall.
A. Write a linear equation to model the height h of the candle after burning t hours.
B. Predict how tall the candle will be after burning 6 hours.
H(t)=1.5t +13; 4 inches
h(t)=-1.5+13; 4 inches
h(t)=-1.5+7; 2 inches
h(t)=1.5+13; 22 inches
[= absoulute value in the problems
3. What is the vertex of the function y=[-3x+2]-4 (-2/3,-4) (2/3, -4) (2/3, 4) (-2/3, 4) 4. Write an equation for the vertical translation. y=-2/9[x]-7; 2 units down y=-2/9[x]-9 y=-2/9[x]-2 y=-2/9[x]+2 y=-2/9[x]+9 3. What is the vertex of the function y=[-3x+2]-4 (-2/3,-4) (2/3, -4) (2/3, 4) (-2/3, 4) 4. Write an equation for the vertical translation. y=-2/9[x]-7; 2 units down y=-2/9[x]-9 y=-2/9[x]-2 y=-2/9[x]+2 y=-2/9[x]+9
Explanation / Answer
1. If y varies directly with x, then you know that they are directly proportional to each other. For the given problem, we have: y/x = y1/x1 Moreover... 4.8/2.4 = y1/2.05 [Cross-multiply] (4.8)(2.05) = 2.4 * y1 [Divide both sides by 2.4] y1 = (4.8)(2.05)/2.4 Hence, we have y = 4.1. 2a. In order to determine the linear equation, you need two points or a point and a slope. We know that "A candle is 10 inches tall after burning for 2 hours. After 3 hours, it is 8 1/2 inches tall." Here, we have: (2,10) and (3, 8.5) Since you have two points, we use the slope formula to determine the slope. The slope formula is: m = (h - h1)/(t - t1) Let: (t,h) = (2,10) (t1, h1) = (3,8.5) Furthermore... m = (10 - 8.5)/(2 - 3) m = 1.5/-1 m = -1.5 We also need to determine the equation for the given problem. Since we don't have y-intercept, use the point-slope formula, which is: h - h1 = m(t - t1) *Note: You can derive above formula by multiplying both sides by t - t1. Take any point (no matter which specific point is it) and the slope that we determined. Let's substitute (2,10) and the slope -1.5: h - 10 = -1.5(t - 2) h - 10 = -1.5t + 3 Hence, h = -1.5t + 13. *Note: You can also use slope-intercept formula to determine the equation, which gives the same answer as we have. 2b. Using the equation that we determined, substitute t with 6! h = -1.5(6) + 13 = 4 inches 3. y = (-3x + 2)² - 4 The vertex formula is y = a(x - h)² + k. The vertex is (h,k). By vertex formula, we have (-2,-4). 4. When moving units down, you are subtracting the equation by the number of units. Hence, we have y = -(2/9)x - 9. You don't subtract the slope by the number of units. I hope this helps! See the links below for more information! http://www.algebralab.org/lessons/lesson.aspx?file=algebra_quad_vertex.xml http://cs.selu.edu/~rbyrd/math/slope/