Modern states college algebra

What is the solution set to the inequality: x2+3⁢x−4<0

(-4,1)

What is the solution to the following system of equations:

(-4/3,5/3)

What is the domain of f⁡(x)=2−x, understood as a function inputting and outputting real numbers?

(-infinity,2]

Which of the following products is a real number?

(1+i)(1-i)

In the xy-plane, the point (8,10) lies on the graph of the function y=f⁡(x). Which of the following points must lie on the graph of the function y=2⁢f⁢(x−3)+5?

(11,25)

Which of the following is equal to a^b⁢c for all values of a,b, and c ?

(a^b)^c

What is the x2⁢y3 coefficient when expanding (x−y)5?

-10

Simplify the following expression:

-4/x^2-1

In the xy-plane, the graph of the function f⁡(x)=x2+b⁢x+4 does not intersect the x-axis. Which of the following must be true about b?

-4<b<4

For any positive integer n,

1

Which of the following properties is satisfied by 2? Real number Rational number Complex number

1 and 3 only

Simplify.....

100

Which of the following when added to 4⁢a^2+9 will result in a perfect square for all integer values of a?

12a

When 3+4⁢i2+i is expressed in the form a+b⁢i, what is the value of a?

2

Of the following, which is greatest?

2(3^5)

The sum of the first n terms of an arithmetic sequence a1,a2,a3,...,an is 12⁢n⁢(a1+an), where a1 and an are the first and nth terms of the sequence, respectively. What is the sum of the odd integers from 1 to 99, inclusive?

2,500

A rock is thrown straight up into the air from a height of 4 feet. The height of the rock above the ground in feet, t seconds after it is thrown is given by −16⁢t2+56⁢t+4. For how many seconds will the height of the rock be at least 28 feet above the ground?

2.5

In the xy-plane, the line given by which of the following is perpendicular to the line 5⁢x−2⁢y=7 ?

2x+5y=7

Simplify

3

What is the inverse function of f⁡(x)=2⁢x3+1 ?

3^ 1/2(x-1)

A ball is dropped from a height of h feet and repeatedly bounces off the floor. After each bounce, the ball reaches a height that is of the height from which it previously fell. For example, after the first bounce, the ball reaches a height of 23⁢h feet. Which of the following represents the total number of feet the ball travels between the first and the sixth bounce?

5 i+1 (2h)((2/3)^i

If f⁡(x)=2⁢x+1 and g⁡(x)=3⁢x−1, then

6x-1

The functions f and g are defined below. What is the value of:f⁡(g⁡(−3))?

9

If z=−1+i and z¯ denotes the complex conjugate of z, which of the following points in the complex plane above represents z+z¯?

B

Which of the following must be true?I. l⁢o⁢g3⁢3t=tII. l⁢n⁢104.3=4.3⁢l⁢n⁢10III. l⁢o⁢g10⁡(x⁢yn)=l⁢o⁢g10⁢x+n⁢l⁢o⁢g10⁢y for all positive numbers x and y

I, II and III

Which of the following define Y as a function of x?

I,II, and III

Which of the following expresssions is equal to a?

a^4b^3/a^3b^3

The plot of what function appears below?

f(x)=-(x-1)^2

Which of the following functions is increasing on its domain?

f(x)=lnx

Compute i101, where i=−1 is the imaginary unit.

i

The plot of what function appears below?

log2(x-3)

Suppose a colony of cells starts with 10 cells, and their number triples every hour. After how many hours will there be 500 cells?

log3(50)

A company's daily cost c, in hundreds of dollars, to manufacture n items of a certain product can be modeled by the function c⁡(n). According to the model, which of the following is the best interpretation of c−1⁡(5)=80, where is the inverse function of c?

manufacture 80, product 500

A circular cylindrical water tank is filled with water to 75 percent of its total volume of V cubic inches. The radius of the tank is 6 inches, and the height of the tank is h inches. Which of the following represents the height, in inches, of the water in the tank? (Note: The volume of a cylinder with radius r and height h is given by π⁢r2⁢h.)

v/48pi

Joe invests $40,000 and, at the same time, Tom invests $10,000. The value of Joe's investment decreases by $4,000 per year, while the value of Tom's investment increases by $1,000 per year. Which of the following systems of equations could be used to find the number of years, t, that it will take for the values, v of the two investments to be equal?

v=40,000-4,000t and v=10,000+1,000t

For what values of x will (x,y) be a solution of the system of equations above?

x=-3 and x=4

What are the roots of the following polynomial: x^3−9⁢x?

x=-3,0,3

Find the solutions to the equation

x=1,2

Find all solutions to

x=2+-|8i/2

When expanded, the polynomial x⁢(x−2)^2⁢(x+4) is equal to which of the following?

x^4-12x^2+16x

If a>0 and b>0, which of the following could be an equation of the line graphed in the xy-plane below?

y=ax-b

Which of the following inequalities can never be true?

|a+b|>|a|+|b|

Which of the following functions exhibits even symmetry?

|x|-2