(b) (c) 2. 3. (a) (b) (c) 4. GOOD 5. ) Consider the points (-3,-1) and...

  

Transcribed Image Text:

(b) (c) 2. 3. (a) (b) (c) 4. GOOD 5. ) Consider the points (-3,-1) and (2, 3). Find the slope-intercept equation of the line passing through the two given points. Show work. Graph the line you found in (a). Find the equation of the line perpendicular to the line you found in (a) through the point (2, 3). (7 pts) The amount of gas g in gallons in a car's gas tank 1 days after a fill-up is modeled by g(t)=-0.5t-1.5t + 25 for 0 ts 5. Find and interpret the average rate of change of g over the interval [0, 5]. Show work. (9 pts) Mary wants to purchase custom-made posters to advertise her business. Custom Posters offers the following deal: Pay a design fee of $120.00 plus $6.25 per poster. State a linear function f(t) that represents Custom Posters' total charge for an order of t posters. Mary wants to place an order for 75 custom-made posters. What is the total charge? Show work/explanation. If the total charge is $570, how many posters were ordered? Show work/explanation. (10 pts) For the equation y=x + 4x+1 State the vertex State the range State the interval on which the function is increasing: State the y-intercept (5 pts) Solve the inequality x + 4x2-3 and write the solution set in interval notation. 6. A. C. 7. 8. 9. (3 pts) For f(x)=x + 2x-x-4, use the Intermediate Value Theorem to determine which interval must contain a zero off. Between 1 and 0. B. Between 1 and 2 D. Between 0 and 1 Between 2 and 3 (7 pts) Solve | 6-5x|>1 (5 pts) For z=7-2i and w=4+3i, find zw. That is, determine (7-21)(4+31) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show some work. (10 pts) Consider the equation 5x + 5 = 6x. Find the complex solutions (real and non-real) of the equation and simplify as much as possible. Show algebraic work. (b) (c) 2. 3. (a) (b) (c) 4. GOOD 5. ) Consider the points (-3,-1) and (2, 3). Find the slope-intercept equation of the line passing through the two given points. Show work. Graph the line you found in (a). Find the equation of the line perpendicular to the line you found in (a) through the point (2, 3). (7 pts) The amount of gas g in gallons in a car's gas tank 1 days after a fill-up is modeled by g(t)=-0.5t-1.5t + 25 for 0 ts 5. Find and interpret the average rate of change of g over the interval [0, 5]. Show work. (9 pts) Mary wants to purchase custom-made posters to advertise her business. Custom Posters offers the following deal: Pay a design fee of $120.00 plus $6.25 per poster. State a linear function f(t) that represents Custom Posters' total charge for an order of t posters. Mary wants to place an order for 75 custom-made posters. What is the total charge? Show work/explanation. If the total charge is $570, how many posters were ordered? Show work/explanation. (10 pts) For the equation y=x + 4x+1 State the vertex State the range State the interval on which the function is increasing: State the y-intercept (5 pts) Solve the inequality x + 4x2-3 and write the solution set in interval notation. 6. A. C. 7. 8. 9. (3 pts) For f(x)=x + 2x-x-4, use the Intermediate Value Theorem to determine which interval must contain a zero off. Between 1 and 0. B. Between 1 and 2 D. Between 0 and 1 Between 2 and 3 (7 pts) Solve | 6-5x|>1 (5 pts) For z=7-2i and w=4+3i, find zw. That is, determine (7-21)(4+31) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show some work. (10 pts) Consider the equation 5x + 5 = 6x. Find the complex solutions (real and non-real) of the equation and simplify as much as possible. Show algebraic work.