For Exercises 13–18, solve the equation and related inequalities. (See Examples 2–3.)
a.
b.
c.
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- If(-5.2, g(x)) is a solution to the equation 5 – 3x=g(x), what is the value of g(x)?arrow_forwardThe function, f(x) = –2x² + x + 5, is in standard form. The What are the zeros of the function quadratic equation is 0 = -2x + x + 5, where a = -2, b = 1, and c = 5. The discriminate b2 – 4ac is 41. Now, complete step 5 to solve for the zeros of the quadratic function. f(x) = x + 5 – 2x2? x = -1±/4T -4 5. Solve using the quadratic formula. O x= 1±/41 -4 -b±yb²- 4ac_ x = 2a x = -1±/39 - 4 X = 1±/39 - 4arrow_forwardIn Exercises 8-11, graph the given quadratic function. Give each function's domain and range. 8. f(x) = (x – 3)² – 4 9. f(x) = 5 – (x + 2)° 10. f(x) = -x? – 4x + 5 11. f(x) = 3x - 6x + 1 %3!arrow_forward
- True or False The x-intercepts of the graph of a functiony = f1x2 are the real solutions of the equation f1x2 = 0.(pp. 73–75)arrow_forwardIn Exercises 31–32, each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values. S3x + 5 ifx 0 31. f(x) = а. f(-2) b. f(0) с. f(3) d. f(-100) + f(100)arrow_forwardmaximise 2.x1 +2 subject to X1 – X2 < 1, 2x1- X2 2 1, 2x1 + 2x2 2 4, X1, X2 20arrow_forward
- describes the height of the gymnast's feet above the ground, s(t), in feet, t seconds after dismounting. The graph of the function is shown, with unlabeled tick marks along the horizontal axis. Use the function to solve Exercises 65–66. s(t) 10 s(t) = -1612 + 8t + 8 8. 2 Time (seconds) 65. How long will it take the gymnast to reach the ground? Use this information to provide a number on each tick mark along the horizontal axis in the figure shown. 66. When will the gymnast be 8 feet above the ground? Identify the solution(s) as one or more points on the graph. Height (feet)arrow_forwardThe Mauna Loa Observatory in Hawaii records the carbon dioxide concentration y (in parts per million) in Earth’s atmosphere. The January readings for various years are shown in Figure . In the July 1990 issue of Scientific American, these data were used to predict the carbon dioxide level in Earth’s atmosphere in the year 2035, using the quadratic model y = 0.018t2 + 0.70t + 316.2 (Quadratic model for 1960–1990 data) where t = 0 represents 1960, as shown in Figure a. The data shown in figure b represent the years 1980 through 2014 and can be modeled by y = 0.014t2 + 0.66t + 320.3 (Quadratic model for 1980–2014) data where t = 0 represents 1960. What was the prediction given in the Scientific American article in 1990? Given the second model for 1980 through 2014, does this prediction for the year 2035 seem accurate?arrow_forward2 What are the zeroes of y =x - 1x- 20?arrow_forward
- Find the value of x T A 3 (x-4) S4arrow_forward6x² + 2x +1 lim is equal to 6x² – 3x +4 A. 0 В. 1 C. 2 D. 3arrow_forwardYou throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball’s height above the ground, y, after x seconds. Consider the given data and solve, a. Find the quadratic function y = ax2 + bx + c whose graph passes through the given points. b. Use the function in part (a) to find the value for y when x = 5. Describe what this means.arrow_forward
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