Math 107 Quiz 3: Foundations of Mathematics - Complete Solutions

This document contains the complete solutions for Math 107 Quiz 3, a mathematics quiz worth 140 points. The quiz covers a range of topics including simplifying algebraic expressions, solving equations (linear and quadratic), working with formulas, and applying regression analysis. The solutions provide detailed answers to all 30 problems, including those involving factoring, inequalities, complex numbers, geometric problems, and logarithmic functions. The solutions include step-by-step explanations and answers to each question. The quiz is open book and open notes, and students were allowed to use any resources to complete it. This resource is beneficial for students studying foundations of mathematics and preparing for similar quizzes or exams. The solutions provide a valuable resource for understanding the concepts and practicing problem-solving techniques.

Math 107
Quiz 3: Instructions:
 The quiz is worth 140 points. There are 30 problems but there is 35 possible
answers, each worth 4 points. Your score on the quiz will be converted to a
percentage and posted in your assignment folder with comments.
 This quiz is open book and open notes, and you may take as long as you like
on it provided that you submit the quiz no later than the due date posted in our
course schedule of the syllabus. You may refer to your textbook, notes, and
online classroom materials, but you may not consult anyone.
 Please type your work in your copy of the quiz, or if you prefer, create a
document containing your work. Scanned work is also acceptable. Be sure to
include your name in the document. Please make your responses easy to see.
There are 30 problems/35answers with each answer being worth 4 points. A total
of 140 points.
1. Simplify 5x – 3{2x – 2[x – 2(1 – x)]}
a) 17x - 12
b) 17x + 12
c) 12 - 17x
d) 12x – 17
SOLUTION: (a) 17x - 12
2. Find the product
a)
b) 5x2y7
c)
d)

SOLUTION: (d)
3. The sign is division – not plus. It is a little difficult to see.
a)
b)
c)
d)
e)
SOLUTION: (d)
4. Simplify the expression -3(4x – 2) – 2(5x – 4)
a) -22x - 14
b) - 22x – 6
c) 9x + 14
d) -22x + 14
e) -9x + 14
SOLUTION: (d) -22x + 14
5. Solve the formula for b: A = ½bh
Answer = b= 2 A
h

6. Solve the equation (4m – 2)² - 2(4m – 2) = 15
a) {1/4}
b) {7/4, -1/4}
c) {-7/4, 4}
d) {4/7, -4}
e) None of the above
SOLUTION: (b) {7/4, -1/4}
7. A farmer has 2000 feet of fencing available to enclose a rectangular field. One
side of the field is a river, so only three sides require fencing. Express the area A as a
function of x, where x is the length of the side parallel to the river.
a) A = -x²/2 + 2000x
b) A = -x²/2 + 1000x
c) A = x² - 2000x
d) A = x² + 1000x
e) A = -x² + 1000x
SOLUTION: (b) A = -x²/2 + 1000x
8. If f(x) is a linear function such that f(-2) = 4 and f(3) = 14, which of the following
could represent f(x)?
a) f(x) = 2x² - 3
b) f(x) = 2x² + 12
c) f(x) = 2x + 8
d) f(x) = ½ x + 5
e) f(x) = none of these
SOLUTION: (e) f(x) = none of these
9. The length of a rectangular poster is one foot more then the width and the diagonal
of the poster is 5 feet. What are the length ____________ and width ____________ ?
SOLUTION: 3ft. and 4ft.

10. The function w(x) = -0.01x² + 0.27x + 8.60 can be used to estimate the number of
self-employed workers in America in millions, x years after 1980. For what years
were there (or will be there) 9.7 million self-employed worker in America?
Answers: x = 11years and x= 5 years
11. Solve using the quadratic formula 2x² + 2x = 3
a) x = -1 ± √7
2
b) x = -2 ± √26
4
c) x = 2 ± √26
4
d) x = 1 ± √7
4
e) x = -1 ± √26
2
SOLUTION: (a) x = -1 ± √7
2
12. Write in lowest terms: b² + 6b - 16
b² + 5b – 24
a) b – 2
b – 3
b) 2
3
c) 6b – 16
5b - 24
d) 6b – 2
5b - 3
e) none of the above
SOLUTION: (a) b – 2
b – 3
13. Solve the inequality |-2x - 5| ≤ 6

a) x ≥ -11/2
b) x ≤ -1/2
c) -11/2 ≤ x ≤ 1/2
d) -1/2 ≤ x ≤ 11/2
e) none of the above
SOLUTION: (e) none of the above
14. If i = √-1, then (i + 1)(6i – 10) is equivalent to
a) -10 -10i
b) -12i - 20
c) -16 + 16i
d) 16 + 16i
e) -16 – 4i
SOLUTION: (e) -16 – 4i
15. Find the area of the following triangle.
a) A = x/y
b) A = 2 x/y
c) A = ½ xy
d) A = 2xy
e) A = x² + y²
SOLUTION: (c) A = ½ xy
16. Find the missing side of the triangle.

Answer is √ ¿2+y2)
17. Solve for ‘p’ from this formula from optics.
1/F = 1/m + 1/p
p = F.m / (m – F)
18. Regression analysis problem: Determine the correlation coefficient and
coefficient of determination for the following data. Interpret the relationship between
X and Y.
X 5 3 6 3 4 4 6 8
Y 13 15 7 12 13 11 9 5
Correlation coefficient is 0.8299
Coefficient of determination is 68.8 %
Interpretation: Linear Equation
19. The following equation y = 6x + 121, estimates the number of faculty members at
two year colleges, in thousands, where x is the number of years after 1970. For what
year will there be more then 360,000 faculty members?
Answer 2010

20. Find the zero for the function f(x) = 4x² - 11x - 3
Answer -1/4 and 3.
21. Which of these functions is(are) always increasing?
(I) f(x) = -x2 + 2x + 1
(II) f(x) = 2x - 1000
(III) f(x) = |x - 4| + 255
(IV) f(x) = -e-x
A) (I) and (II) only
B) (II) only
C) (II) and (IV) only
D) (I) and (III) only
E) (III) and (IV) only
Solution: (B) (II) only
22. Solve 3x² - 2 = -4x
a) -4 ± √10/4
b) 4 ± √10
3
c) -2 ± √10
d) - 2± √10
3
e) none of the above
SOLUTION (d): - 2± √10
3
23. Use synthetic division to find the function value for f(x) = x³ - 6x² +11x - 6, find
f(3)
Answer: (x-1) (x-2) (x-3)=0; x =1,2,3. F(3) = 0
24. The Slope (m) of a line containing (x1, y1) and (x2, y2) is given by (y2 – y1)/(x2
– x1)

25. To stop a moving car takes some time and distance. The stopping distance d of a
car after the brakes have been applied varies directly as the square of the speed r. If a
car traveling 60 mph can stop in 200 feet, how fast can a car travel and still stop in 72
feet?
Answer : 36 MPH
26. Science problem concerning a rocket. S(t) = -16t² + 80t + 224 is the function that
represent the height of a rocket. In this equation, given the height S, in feet, of a
model rocket launched with a velocity of 80 ft/sec from a hill that is 224 feet high,
where t is the time in seconds. When will the rocket reach the ground?
Answer time = 7 sec.
27. Regression analysis problem: Determine the correlation coefficient and
coefficient of determination for the following data. Interpret the relationship between
X and Y.
X 5 3 6 3 4 4 6 8
Y 13 15 7 12 13 11 9 5
Regression equation is Y = 9.71 – 0.455X
Determine the value of Y when X is 7. Answer is Y= 6.525
28. Find the x intercepts and the zeros of the function
f(x) = 2x² -13x -7
Answers: x intercepts -1/2 and 1
Zeros -1/2 and 1
29. Solve for x, where log4 x = -3
a) 1/64
b) -12

c) -16
d) -64
e) none of these
SOLUTION: (a) 1/64
30. Find the distance between the points (-2, 3) and (4, -5)
a) 5√2
b) 10
c) 2√5
d) √30
e) 8
SOLUTION: (b) 10