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Solving Nonlinear Equations and Analyzing Functions: A Comprehensive Overview

Explore various mathematical problems involving positive integers, equations, and real-world applications. This document addresses solutions for equations such as (x + 5y = 25), graphing functions including (y = x^2 - a), and determining systems of equations. Topics also include trigonometric evaluations, period analysis of cosine functions, and practical scenarios like ticket sales for an ice hockey game. Perfect for students looking to enhance their problem-solving skills and understanding of algebra and functions.

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Solving Nonlinear Equations and Analyzing Functions: A Comprehensive Overview

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  1. Assuming x and y are positive integers; determine how many possible solutions the following equation has for x. X + 5y = 25 a) 1 c) 3 b) 2 d) 4

  2. Determine the set of solutions that satisfy the following euation: √|x| = 3 a) {-3, -1, 0, 1, 3} d) {-9, 9} b) {-9, 0, 9} e) {9} c) {-9}

  3. Graph the following function: y = x2 - a a) c) b) d)

  4. Determine the solution of the following system of equations. x + 2y = 3 2x + 3y = 4 a) (1 , -2) c) (3 , 2) e) No solution b) (-3 , -2) d) (-1 , 2)

  5. Find the perimeter of the following triangle. a) 6x + 16 c) 12x2 -15 e) None of the above b) 12x3 + 135 d) 7x + 17

  6. If sin2x + cos2x = k , what is the graph of y = kx2 . b) a) c) d)

  7. Determine which of the following is equal to zero. a) cos 30⁰ d) sin 180⁰ b) sin 45⁰ e) cos 180⁰ c) tan 45⁰

  8. Which of the following has the largest period. a) cos(2x) d) cos(3x) b) cos(x/2) e) cos(x/4) c) cos(x)

  9. Determine the value of k given that -2 is a root of x3 – 2x2 + 3x + k a) 22 d) 20 b) -22 e) 6 c) 10

  10. Which is the equation of the following graph. a) 6cos(2x) d) 6cos(x/2) b) 3cos(x/2) e) 3cos(x) c) 3cos(2x)

  11. The admission at an ice hockey game is $15 for adults and $11 for children. A total of 650 tickets were sold. How many children tickets and how many adult tickets were sold if a total of $8790 was collected? a) 250 adult, 400 children b) 320 adult, 330 children c) 400 adult, 250 children d) 410 adult, 240 children e) 370 adult, 280 children

  12. Determine which of the following relations is a function. a) b) d) c)

  13. Evaluate the expression -|4-10| + |-3| - |5| a) 5 d) 10 b) 7 e) -6 c)-8

  14. Evaluate the expression, given p = -5, q = -3, r = 4. 6p – 2q2 -3r a) 2 d) -5 b) 6 e) 4 c) 9

  15. Solve for the specified variable E I = For s. R + s E E E a) c) s = s = + R R + I I E s = E b) d) s = - R I + R I E e) s = R + E

  16. If ( 3x2 – 2x + 7) = 0, what is ( x – 1/3)2 = a) 7/9 d) -20/9 b) 20/9 e) None of the above c)-7/9

  17. Which of the following statements is true? I II III a) m1 > m2 c) |m1| > |m2| e) m3 > m2 b) |m1| = |m2| d) m1 = m2= m3

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