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1. If 6x + 9 = 30, what is the value of 2x + 3?
x2 + y2 = 9
y = x2 - 4
A system of two equations and their graphs in the xy-plane are shown above. How many solutions does the system have?
3. A total of 300 tickets were sold for a performance of a school play. The ticket prices were $5 for each adult and $3 for each child, and the total revenue from tickets was $1,400. Solving which of the following systems of equations would yield the number of adult tickets sold, a, and the number of children's tickets sold, c?
5a + 3c = 300
5a + 3c = 1,400
3a + 5c = 1,400
3a + 5c = 1,400 × 2
4. Which of the following expressions is equivalent to 2(x - 4)2 - 5x?
Note: Figure not drawn to scale
A rectangular solid above has dimensions 3, a, and b, where a and b are integers. Which of the following CANNOT be the areas of three different faces of this solid?
6. The cost in dollars, C, to manufacture n necklaces is given by the equation C(n) = an + b, where a and b are positive constants. In this equation, what does a represent?
7. Line l intersects the graph of the function f(x) = 2x2 - 4x + 1 at two points where x = -1 and x = 2, respectively. What is the slope of line l?
8. Which of the following equations represents a parabola in the xy-plane with a vertex that lies on the x-axis?
9. If the function m(x) satisfies the equation for all values of x greater than 1, then m(x) =
10. In the mesosphere, the atmospheric layer between 50 km and 80 km in altitude, the average atmospheric temperature varies linearly with altitude. If the average temperature at 50 km altitude is 10°C and the average temperature at 80 km is -80°C, then at what altitude is the average temperature -50°C?
11. The graph of the equation y = 2x2 - 16x + 14 intersects the y-axis at point A and the x-axis at points B and C. What is the area of triangle ABC?
12. What is the total number of x- and y-intercepts in the graph of the equation y = (x + 2)2(x - 3)2?
13. If the complex number A satisfies the equation A(2 - i) = 2 + i, where , what is the value of A?
14. If k > 2, which of the following could be the graph of y + x = k(x - 1) in the xy-plane?
15. The function g(x) = ax3 + bx2 + cx + d has zeroes at x = -2, x = 3, and x = 6. If g(0) < 0, which of the following must also be negative?
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