# 25 Algebra Problems : Trigonometry, Graphing, Matrices, Simplifying Expressions and Solving Equations

The flow rate V (in cm/s) of a storm drainpipe follows the following expression. Find the value of V when t = 2.500 s.

a. 33.56

b. 5.42

c. 132.6

d. 22.5

A boat approached a harbor and the captain takes two bearings to calculate the distance to the harbor. Bearing 1 is read at 0 degrees and bearing 2 is read at 30 degrees. The captain knows that the bearings are 10 km apart. If the harbor is located at bearing 2, how far away is the harbor?

a. 17.3

b. 20

c. 10.12

d. 11.54

Which matrices would be used to solve the following system of equations?

a.

b.

c.

d.

What is the value of x in the following expression?

a. 1953125

b. 1.196

c. 1.69e-5

d. 1.291

Solve the following expression for E. The resulting equation must be in its simplest form.

a.

b.

c.

d.

What are the slope, y-intercept, and equation of the line passing through the points (-1,1.2) and (3,-2)?

a. slope = -0.8, y-intercept = 0.4, y = -0.8x+0.4

b. slope = 0.8, y-intercept = 0.4, y = 0.8x+0.4

c. slope = -0.8, y-intercept = 1.5, y = -0.8x+1.5

d. slope = -1.25, y-intercept = 0.05, y = -1.25x+0.05

What is the equation of the following curve? (Each tick mark on the axes represents one unit.)

a.

b.

c.

d.

Given a triangle with following given parts

a = 5.00, b = 2.56, C = 49 degrees

find the value of side c.

a. 14.76

b. 3.84

c. 4.33

d. 3.04

What is the exponent value resulting from the following algebraic operation?

a. 12

b. 2

c. 35

d. -2

If the tires on a bicycle have an angular velocity of 1 rad/s and a radius of 0.5 m, what is the linear velocity of the tire? How far will the bicycle travel in 10 seconds?

a. linear velocity = 5 cm/s, distance = 50 meters

b. linear velocity = pi m/s, distance = 10 pi meters

c. linear velocity = 1 m/s, distance = 10 meters

d. linear velocity = 0.5 m/s, distance = 5 meters

A hardwood sport court is always proportionally designed so that its length is 1.5 times its width. If a contractor has been given 250 square feet of material to build the court, what is the length and width of the finished court?

a. length = 25 ft, width = 10 ft

b. length = 25 ft, width = 16.7 ft

c. length = 19.4 ft, width = 12.9 ft

d. length=20 ft, width = 13.3 ft

The apparent power S in an electric circuit in which the power is P and the impedance phase angle is A is given by S = P sec A. Given P = 6 V*A and A = 35 degrees, find S.

a. 49.1 V*A

b. 3.44 V*A

c. 7.32 V*A

d. 6.64 V*A

One can solve a system of three linear equations with three unknowns by the method(s) of

a. Determinants

b. Using the quadratic formula

c. Algebraic Substitution

d. Both A and C

Find the period of the given function.

a. 1/2

b. 1/5

c. 5 * pi

d. 5

Solve the following system of equations.

a.

b.

c.

d.

What term describes the following type of equation?

a. linear

b. exponential

c. quadratic

d. logarithmic

If lines A, B and C are parallel and length a=2.8, c=3, b=3.2, what is length d?

a. 1.88

b. 3.43

c. 3

d. 3.2

a. 4

b. 6

c. 8

d. 12

Find the remainder:

a. -2

b. -1

c. 0

d. 1

e. 2

Is the following algebraic statement true or false?

a. True

b. False

What is the inverse of the following matrix?

a.

b.

c.

d.

For a polynomial of degree n,

a. there are n roots.

b. there are always either 1 or 3 complex roots.

c. the roots are always real numbers.

d. answers (a) and (c)

What is the equation of the following curve?

a.

b.

c.

d.

e.

Solve the following set of equations for x, y, and z.

a.

b.

c.

d.

Calculate the quotient.

a.

b.

c.

d.

Indicate which answer is a simplification of

a.

b.

c.

d.

The circumference of a circle with a radius of 4 cm is

a. 25.1 cm

b. 50.3 cm

c. 12.57 cm

d. 3.1416 cm

Find the horizontal and vertical components of the vector shown below.

a. Vertical = 22.3 cos 114

Horizontal = 22.3 sin 114

b. Vertical = 22.3 sin 66

Horizontal = -22.3 cos 66

c. Vertical = 66 sin 22.3

Horizontal = 66 cos 22.3

d. Vertical = 22.3 tan 22.3

Horizontal = 22.3 cos 22.3

Which is a correct addition rule?

a.

b.

c.

d.

e.

Given the following equation, what is the angle in degrees?

a. 58.001

b. 1.0123

c. 0.99996

d. 0.86286

Solve:

(x + 1)(x - 3) = 5

a. x = 2, 8

b. x = 0, 0.24

c. x = -2, 4

d. x = -2, 6

If j designates an imaginary number, what is the value of the following expression? (Answer is not necessarily in simplest form.)

a. 2/(5j)

b. -2/(5j)

c. -2/5

d. 2/5

e. 2j/5

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#### Solution Summary

Twenty-five algebra problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.