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# Basic Algebra

### Logarithm Simplification

Write the following in terms of simpler forms: 3^(p*log_3(q)) (Here a^b denotes "a to the power b" and log_b denotes "logarithm in base b".)

### Exponential Density Function

The exponential density f(x) is 0 for x<0, and is e&#61485;x for x&#61619;0. Compute E[e&#61485;X].

### Exponentials: simplifying and solving equations

(In this problem, the notation b^x stands for "b to the power x"; for example, b^2 stands for "b squared".) (A) Simplify the expression: 10^(3x-1)10^(4-x). (B) Solve the following equation for x: 5^(3x)=5^(4x-2). (C) Solve the following equation for x: (1-x)^5=(2x-1)^5.

### Algebraic Properties 8b

Given the algebra <S;f,g,a>, where f and g are unary operations and a is a constant of S, suppose that f(f(x)) = g(x) and g(g(x)) = x for all x &#949; S. Show that f(f(f(f(x)))) = x for all x &#949; S.

### Crytic math questions

Cryptic Math p Q R S T U V W X 1. Each letter stands for one of the numbers 1 - 9. 2. S + Q = V and S is smaller than Q. 3. P = R + U. 4. In one of the diagonals, all 3 numbers are perfect squares. 5. In one of the two diagonals, (P, T, X or R, T, V) the 3 numbers are in ascending orde

### Quadratic Equations (Solve by Factoring and Square Root)

Quadratic Equations: Please show how arrived at answer. Thank you. 1.) Solve quadratic equation by factoring. Solve: 2y^2 - 3y - 2 = 0 2) Solve quadratic equation by taking square root. Solve: (2 x + 2)^2 = 64

### Question about Quadratic Equations: Completing the Square

Solve quadratic equation by completing the square. 4x^2 + 8x + 1 = 0

### Solve Inequalities

1.) |5-x|<= 4, Solution=??? 2.) 48 >= 4x(x-1), Solution=???

### Removing the Demonimator by Multiplying Both Sides By LCD

When we solve a rational equation, why is it OK to remove the denominator by multiplying both sides by the LCD? Why can you not remove the denominator when simplifying a rational expression? Provide examples to support your discussion. 2. What are extraneous solutions of an equation? Why do they sometimes occur when we solve

### Quadratic equation standard form

Consider the quadratic equation m(x)=0.20x^2-1.6x-1. Write the equation in standard form m(x)=a(x-h)^2+k, then find each of the following (to four decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range

### Function/algebra

1.SOLVE A=1/2H(b1+b2) for b2 2. write 3-square root-36 in standard form Linear Functions 3.Find the slope of the line passing through the points (-2, 4) and (-3, 5). a.1 b.-1 c.-9/5 d.-5/9 Zeros of Polynomial Functions 4.Find the zeros of P(x) = (

### Exponential and Logarithmic Functions

1. Solve for x: ln(7x-1)=6 Answer: a.57.4898 b.403.572 c.403.286 d.57.7755 2. Solve for x: ln x = 3+ln(x-1) answer: a.3.95257 b.0.952574 c.1.0524 d.5.0524 3. The half-life of carbon-14 is 5730 years. Find the percent of a sample present after 5370 years. Answer: a.101.25% b.

### Mass and radius of three of the nine solar planets

I need the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters. I chose Pluto, Venus, and Mars. Using your data, calculate the gravitational acceleration on each of the three planets you selected. The masses should be measure

### Exponential and Logarithmic Functions and Compound Interest

1. Graph: f(x)=e cubic x 2. Are the following functions inverses of each other? Yes or no a. F(x)=x-1/3 b. G(x)=3x-1 3. Solve for x: ln(7x-1)=6 4. Identify the graph of the function: f(x)=2-4^x 5. Solve for x: in x = 3+in(x-1) 6. The half-life of carbon 14 is 5730 years. F

SOLVE FOR 'X' 9X^2 - 12X - 12 > 0 QUESTION :- SOLVE FOR X 1. 9X^2 -12X -12 >0 SOLUTION: The above given inequality is an quadratic which has two factors 9x^2 -12x-12 > 0 = 9x^2 &#8211;18x + 16x &#8211;12 > 0 = 9x(x-2) + 6(x-2) > 0 = (x -2) (9x + 6)>0 which implies the product of (x -2) & (9x + 6

### Polynomial Rational Function Zeros Calculation

1.LIST THE ZERO OF THE CUBIC FUNCTION AND TELL WHICH, IF ANY, ARE DOUBLE OR TRIPLE ZEROS y = x squared (x-1) 2. USE THE RATIONAL ZERO THEOREM TO FIND ALL POSSIBLE RATIONAL ZEROS OF THE POLYNOMIAL: g(x) = -3x cubic -8x squared +x+ 14 3.USE SYNTHETIC DIVISION TO FIND UPPER AND LOWER BOUNDS OF THE REAL ZEROS OF f. f(x) =

### Solve the Equation or Inequality

1. SOLVE (X-2)(9X+6)>0 2. SOLVE THE INEQUALITY X+43/X+3<6 3. SOLVE: SQUARED ROOT X+36-6=-X 4. 15X-SECOND POWER+2X-FIRST POWER+1=0 ANSWER: A.X=5,X=-3 B.X=5,X=1/3 C.X=-1/5,X=-1/3 D.NO SOLUTION

### Quadratic Equation, Maximum, Minimum and Types of Lines

1. Which set of ordered pairs(x,y) represents y as a function of x? Answer A. (2,-8),(1,6),(1,2),(6,1) B. 2,-8,1,6 C. (2,-8),(-8,2),(6,6) D.(2,-8),(-8,1),(2,6) 2. Evaluate the function at the specified value of the independent variable and simplify f(x)=3x squared-square root2x Answers a. 22.757 b. 24.551

### Quadratic Functions, Maxima, Minima, Even Function

1. Given f(x)=16-x squared,and g(x)=4-x, find f/g (x). 2. Find the maximum or minimum value of the quadratic function f(x)-x squared+10x-19. State whether this value is a maximum or minimum. 3. Evaluate the function at at specified value of the independent variable and simplify. F(x)=/x/-2; f(4) 4. Given f(x)=2/x-6

### Expression for period of pendulum

In the expression for the period of a simple pendulum, we do not take into account the mass that is hanging from the string. How is it possible that the mass does not affect the period of the pendulum? It was stated that the displacement that started the pendulum was small. What would happen if we started the pendulum with an ex

### Finance : Interest and the Fisher Effect

What is the nominal interest rate (i) in Canada if the real estate of return is 2.5% and the expected rate was 4.5%. (The Fisher Effect formula should be used in this problem).

### Quadratic Equations, Graphs, Rational Inequalities and Word Problems

Please see the attached file for the fully formatted problems. Includes the following Exercises: -Quadratic Functions and Their Graphs -Quadratic and Rational Inequalities; Equations, Functions and Inequalities -Quadratic Equations, Functions, and Inequalities Maximum height. If a baseball is projected upward from groun

### Differential equations - 2 Water tanks

Two identical water tanks labeled A and B are resting at the same elevation and are linked via a pipe with a valve. The cross sectional area of each of the tanks is 1m^2. The valve demonstrates linear behavior (volumetric flow is linear with pressure drop) and will allow a flow of 0.5 m^3/min under a pressure drop equivalent to

### Squaring Products and Factors

1 When we square a product, we square each factor in the product. For example (4b)2= 16b2. Explain why we cannot square a sum by simply squaring each term of the sum. For example, (a + b)2 is not equal to a2 + b2. Provide appropriate examples. 2 Take a number. Add 1. Square the result. Then subtract from that result

### Factor out the GCF in each expression. Factor each polynomial completely. Use grouping to factor each polynomial completely. Find the LCD for the given rational expressions

Factor out the GCF in each expression. 59. 2x^3-6x^2+8x 60. 6x^3+18x^2-24x *61. 12x^4t+30x^3t-24x^2t^2 *62. 15x^2y^2-9xy^2+6x^2y Factor each polynomial completely. 60. 32x^2y-2y^3 61. 3ab^2-18ab+27a Use grouping to factor each polynomial completely. 66. 3x+3z+ax+az 67. x^3+x^2-4x-4

### Let X be a nonnegative random variable

#20. Let X be a nonnegative random variable. Prove that... (see attachment)

### Exponential and logarithmic functions

A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3". a) 16 3/2 = 64 b) ex = 5 B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25". a) log 3 27 = 3 b) log e 1 = 0 c) log 125 25 = 2/3 C. Us

### Graphical representation of functions

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions and post to the discussion forum. Discuss these functions and their graphs with your classmates. 2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the follow

### Mathematical Definition of a Logarithm

Write the mathematical definition for a logarithm, i.e. for log (to base b) x.

### Change equation to exponential form

Change each equation to its exponential forms. Log 10 = 1