Deck 12: Mathematical Problem Set

Question 1

Find two complex number roots for the equation

Answer 1

Question 2

Three sides of a fence and a wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 feet. Let x be the length of the two sides perpendicular to the wall as shown.

Write the area A of the enclosure as a function of the length x . Then find the value(s) of x for which the area is 5500 ft² .

Answer 2

Question 3

Find a polynomial of degree 3 with real number coefficients that has 3+i and -7 as zeros.

Answer 3

Question 4

Rewrite the expression using a single radical.

Question 5

Solve the inequality |x-8|>4 . Express your answer in interval notation.

Question 6

Show that the points A(1,-3), B(-8,1), C(-4,10) , and D(5,6) are the vertices of a square.

Question 7

Determine the range of
Express your answer in interval notation.

Question 8

Solve the double inequality

Express your answer in interval notation.

Question 9

What is the equation, in slope-intercept form, of the line that contains the points (-2,7) and (3,5) ?

Question 10

The table shows average salaries for employees of Mediocre Tools, Inc. Find a linear regression equation for the data and graph the equation with a scatter plot of the data. (Use x=0 for 1975 , and express values to the nearest hundredth.) Use this data to estimate the average salary in 2008 .

Question 11

The following three transformations are applied (in the given order) to the graph of
I. A vertical stretch by a factor of 3
II. A horizontal shift right 5 units
III. A vertical shift down 6 units
Write an equation for the graph produced as a result of applying these transformations.

Question 12

Use synthetic division to show that the number c=-2 is a lower bound for the zeros of
Be sure to reference any properties, theorems or tests used.

Question 13

Graph the relation defined by the parametric equations when

Question 14

Let and
Compute and state its domain in interval notation.

Question 15

For the function
what are the intercepts and what are the asymptotes?

Question 16

Which of the following could represent a completegraph of f(x)=ax+x³ whereais a real number?

A)
B)
C)
D)

Question 17

Solve the equation log (x-6)+log (x-3)=1 .
List any extraneous roots and explain.

Question 18

Solve the equation graphically.

Question 19

The graph of the function
is a circle.
What are the coordinates of the center and the length of the radius?

Question 20

Find the equation of the parabola that passes through (4,7) and has vertex (2,-5) . Express your answer in the standard form for a quadratic function.

Question 21

The table shows average salaries for employees of Fairto Middlin Corporation. Find a linear regression equation for the data and graph the equation with a scatter plot of the data. (Use x=0 for 1975 , and express values to the nearest hundredth.) Use this data to estimate the average salary in 2012 .

Question 22

Geoff invests $5,000 at 8.2% for 12 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 12 years?

Question 23

Solve the equation graphically.

Question 24

For the next eight years, a small company's business volume can be modeled by the function

where x is the number of years after 2006 and f is the sales in millions of dollars.
(a) What are the company's sales in 2006 ?
(b) What does the model project for sales in 2011?
(c) How many years are in each economic cycle for this company?

Question 25

What is the equation, in slope-intercept form, of the line that passes through the points (-3,4) and (5,7)?

Question 26

The graph of is best
represented by which graph?

A)
B)
C)
D)

Question 27

Describe transformations that can be used to transform the graph of to a graph of

Question 28

Arturo invests $2700 in a savings account that pays 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $4550?

Question 29

Simplify: (csc x-tan x) sin x cos x=

A)
B)
C)
D)

Question 30

Which transformation was not performed on y=sin x to obtain

A) Horizontal shift left by units
B) Horizontal stretch by a factor of 3
C) Vertical stretch by a factor of 2
D) Reflection through the x -axis

Question 31

Solve the equation log (x-4)+log (x+5)=1 .
List any extraneous roots and explain.

Question 32

Solve the double inequality

Question 33

In a certain state park, the number of elk present after t years is modeled by the function
(a) What was the initial population of elk?
(b) When will the number of elk be 750 ?
(c) What is the maximum number of elk possible in the park?

Question 34

Evaluate all six trigonometric functions of the angle for the triangle given below.

Question 35

Solve the right triangle for all its unknown parts if and b= 4.5.

Question 36

At the top of a radio signal tower there is an antenna with a light on the end of it. From a point on the ground 500 feet from the base of the tower, the angle of elevation to the tip of the light is and the angle of elevation to the bottom of the antenna is What is the height of the antenna, including the light?

Question 37

For the function y=2 ln (x+3) , what is the inverse function, ?

Question 38

Determine the range of
Express your answer in interval notation.

Question 39

Rewrite the expression using a single radical.

Question 40

Show that the points A(4,2), B(-1,0), C(-3,5) , and D(2,7) are the vertices of a square.

Question 41

Question 42

Let and
Compute and state its domain in interval notation.

Question 43

Find the equation of the parabola that passes through (-6,22) and has vertex (2,-5) . Express your answer in the standard form for a quadratic function.

Question 44

Find two complex number roots for the equation

Question 45

Describe transformations that can be used to transform the graph of y=ln x to a graph of 5-ln (x-4) .

Question 46

Find a polynomial of degree 3 with real number coefficients that has as zeros.

Question 47

Which of the following could represent a complete graph of where a is a real number?

A)
B)
C)
D)

Question 48

For the function y=4+ln (x+1) , what is the inverse function,

Question 49

Evaluate all six trigonometric functions of the angle for the traingle given below.

Question 50

Use synthetic division to show that the number c=-3 is a lower bound for the zeros of
Be sure to reference any properties, theorems or tests used.

Question 51

For the function
what are the intercepts and what are the asymptotes?

Question 52

The graph of for a>1 is best represented by which graph?

A)
B)
C)
D)

Question 53

Question 54

In a certain national forest, the number of moose present after t years is modeled by the function

(a) What was the initial population of moose?
(b) When will the number of moose be 850 ?
(c) What is the maximum number of moose possible in the forest?

Question 55

Martha invests $6,000 at 7.5% for 8 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 8 years?

Question 56

The following three transformations are applied (in the given order) to the graph of
I. A vertical stretch by a factor of 0.3
II. A horizontal shift left 5 units
III. A vertical shift up 6 units
Write an equation for the graph produced as a result of applying these transformations.

Question 57

The graph of the function is a circle.
What are the coordinates of the center and the length of the radius?

Question 58

Graph the relation defined by the parametric equations when
y(t)=t+2 .

Question 59

Three sides of a fence and a wall form a rectangular enclosure. The total length of a fence used for the three sides is 160 feet. Let x be the length of the two sides perpendicular to the wall as shown.

Write the area A of the enclosure as a function of the length x . For what values of x will the area be 5,500 square feet?

Question 60

Solve the inequality in interval notation.

Question 61

By augmented matrix, solve the following system:
x-y-z=3
3 x+4 y+5 z=1
y+2 z=-2

Question 62

A)
B)
C)
D)
E)

Question 63

Use the discriminant to identify the graph of

A) The graph is a circle.
B) The graph is an ellipse.
C) The graph is a hyperbola.
D) The graph is a parabola.

Question 64

Question 65

Question 66

For the next 15 years, a small company's business volume can be modeled by the function
where x is the number of years after 2006 and f is the sales in millions of dollars.
(a) What are the company's sales in 2006?
(b) What does the model project for sales in 2013?
(c) How many years are in each economic cycle for this company?

Question 67

At the top a radio signal tower there is an antenna with a light on the end of it. From a point on the ground 800 feet from the base of the tower, the angle of elevation to the tip of the light is and the angle of elevation to the bottom of the antenna is . What is the height of the antenna, including the light?

Question 68

Solve the system graphically. Round the answer to the nearest hundredth.

Question 69

Find the equation that describes the set of all points (x, y, z) that are 5 units from the point (2,-1,6).

Question 70

Which transformation was not performed on y=cos x to obtain

A) Vertical stretch by a factor of 4
B) Horizontal stretch by a factor of 2
C) Horizontal shift left by units
D) Reflection through the x -axis.

Question 71

Solve the system by any method.
3 x+4 y-6 z=4
x+2 y=8
5 x+2z=4

Question 72

Question 73

What is the focus of the graph of

Question 74

Question 75

Sketch the region of feasible points and solve the linear programming problem.
Maximize C=4 x-5 y , subject to:

Question 76

Simplify:

A)
B)
C)
D)

Question 77

Question 78

Question 79

The matrix is the inverse of https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/. Solve the following system by the inverse matrix method.
x+y+z=4
3 x+5 y+4 z=3
3 x+6 y+5 z=2

Question 80

Write the equation of the ellipse graphed below.