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# Basic Algebra

### Proof by Math Induction

Prove 1^3 + 2^3 + ......+ n^3 = (1 + 2 + ..... n)^2 for all natural numbers n. I have not done ones where the right hand side looks like this one does.

### concrete counter-example

Suppose A is a 3 × 5-matrix of rank 3. Is the linear system AX = B consistent for every B &#8712; R3 ? --- If yes, explain why. ----If no, provide a concrete counter-example (concrete = with numbers).

### Algebriac mixed word problems

For the systems of linear equations in questions 1-3 - Determine how many solutions exist - Use either elimination or substitution to find the solutions (if any) - Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection 1. 4x = 8 and 5y = 15 2. 0.2x + 0.4y = 1.7 and 8.3x - 6.3y

### Algebra - System of equations can be solved by graphing or by substitution or elimination.

System of equations can be solved by graphing or by substitution or elimination 1. What are the pros and cons of each method? Which method do you like best? Why? 2. What circumstances would cause you to use a different method?

### Questions on rational expressions, quadratic formula

In this exercise, four questions are answered. They involve the simplification of rational expressions, solving for x in a quadratic and a cubic function. 1) (a^3 b^4 / 125)^(1/3) 2) (2 r^5)^(1/2) * (10 t^4)^(1/2) 3) (x + 4)^3 = 7.51 4) x^2 + 8x + 17 = 0

### Decreasing cube.

Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by..... V(s)=s3 - 13s2 + 54s -72 a) Find V(10). b) If the new width is s -6 centimeters, then what are the new length and height? c) Find t

### Equation Square Root

A student claims that the equation square root of (-x) = 3 has no solution, since the square root of a negative number does not exist. Why is this argument wrong? (hint: you do not need to use imaginary numbers to do this)

### Demand for pools assignment

Demand for pools. Tropical Pools sells an aboveground model for p dollars each. The monthly revenue for this model is given by the formula R(p) = -0.08 p2 + 300p. Revenue is the product of the price p and the demand (quantity sold). a) Factor out the price on the right-hand side of the formula. b) Write a formula D

### Factoring Techniques Employed

See attached (1)Did you feel techniques employed in "factoring" are useful in daily life? (2)The two configurations were a circle and a rectangle with 100 feet of fence.  Discuss the possibility of utilizing other shapes for this fenced in area. Could you create a figure with a larger area than the circle? In particular,

### Exponential and Logarithmic Functions for Interest

See Attached. Showing work not required. 1.Suppose \$2000 is invested at an annual interest rate of 5%. Compute the balance after 10 years if the interest is compounded monthly.

### Solving Algebra Math Problems

1. Solve using the five-step problem solving process. Show all steps necessary to arrive at your solution. Express the answer in scientific notation to three decimal places. If the distance from the earth to the sun were 92,900,000 miles, how long would it take a rocket, traveling at 2.8×10^3 miles per hour, to reach the su

### Introductory and Intermediate Algebra Problems

1. The mass of Earth is about 6 x 10^21 metric tons. The mass of the sun is about 1.998 x 10^27 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation. 2. The perimeter P of a square of side x is given by the polynomial equation: P=4x. A baseball diamond is a squ

### Estimating The Income

1. Use inductive reasoning to predict the next line in the pattern. 4 × 9 = 36 4 × 10 = 40 4 × 11 = 44 4 × 12 = 48 2. Estimate the income earned for 27 hours at \$9.20 an hour. 3. At a given time of day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 5 ft post

### Language arts literacy skills

Can someone help me to find a quick 5 to 10 page passage from a textbook that has to do with the language arts. Then please help me to create one out of three pre-reading activities. If someone can show me how to create the first pre-reading activity then I can come up with an idea for the other 2. Please provide any references

### Computing Return on Assets

In January 1999, a company was formed. Total assets were \$500,000, of which \$300,000 consisted of depreciable fixed assets. The company uses straight-line depreciation, and in 1999 it estimated its fixed assets to have useful lives of 10 years. After tax, income has been \$26,000 per year each of the last 10 years. Other assets h

### rational expression is undefined

1. List all numbers for which the rational expression is undefined 4/b+7 2. A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets the ground at a point 9.0 ft from the base of the pole. If the point is 65 ft from the base of the cliff, how high is the cliff? Round to the neare

### Range of a rational expression

What is the range of a rational expression? Be sure to limit your discussion to expressions only and keep in mind that functions, equations and graphs are not expressions. Give two examples of expressions and their respective range

### Finding and Using Rate

Please show all steps . Thank you. Write the unit rate for each situation. 1. travel 250 miles in 5 hours 2. earn 73.20 in 8 hours 3. read 80 pages in 2 hours Find each unit price. Then determine the better buy. Please explain thoroughly and show all steps. 1. paper : 100 sheets for \$0.99 500 shee

### Find the limits in states

Given that lim x-->a f(x)= 1 and lim x-->a g(x)= 0 and lim x-->a h(x)= -16 Find each of the limits (please show work). If the limit does not exist state why. a)lim x-->a f(x)g(x) b)lim x--->a (the square root of h(x)) c) lim x-->a f(x)/g(x) d) lim x-->a g(x)/(8f(x)+h(x))

### College Algebra Problem

I am not sure how to set the equations up in order to solve this problem? Hope you can help get me started. Last year you could get a hamburger, fries, and a cola at Zack's Drive In for \$2.80. Since the price of a hamburger has increased 20%, the price of fries has increased 50%, and the price of a cola has increased 60%, the

### A fireman stood on the middle step....

A fireman stood on the middle step of a ladder directing water into a burning building. As the smoke got less, he climbed 3 steps and continued his work. The fire got worse so he had to go down 5 steps. Later, he climbed up the last 6 steps and was at the top of the ladder. How many steps were there?

### Prove: TU and UT have the same characteristic polynomial

Prove: If T is a linear operator on the vector space V and T has an inverse and U is any other linear operator on V , then TU and UT have the same characteristic polynomial. (This will be like the proof that two similar matrices have the same characteristic polynomial. You can use the fact that if β is any basis for V , then [T

### Properties of inequalities/solving inequalities and equations

Topic 1: Properties of Inequalities We have two variables A and X. The value of X is less than the value of A Discuss without using any specific numbers, how we can prove that the value of ( -X) is greater than the value of( -A). Do not use any numerical examples. Keep in mind that A or X could be any numerical va

### Simplifying Rational Expression Factors

Week 4 Assignment 3: Mixed Problems By Day 4 complete and submit your answers to the facilitator; please show all necessary work. By Day 5 post your answers in the appropriate thread for review and comments from others. For the questions 1-7, simplify the following algebraic expressions: 1. (4 points) 2. (2 po

I am being asked to determine the type of quadrilateral defined by the point of intersection (using geometry & algebra) of the lines: x - 4y + 3 = 0 5x - y - 8 = 0 x - 4y -16 = 0 6x - 5y - 1 = 0

### how to factor a trinomial

Prepare a tutorial on how to factor a trinomial. I will need 3 examples so I can use this to assist with another assignment.

### Estimate the Mean of the Set of Data

13) A random sample of 91 employees of Eastern Electric Co. showed that the number of days missed by each worker last year due to illness was as follows: Days Missed Frequency 0 to 4 17 5 to 9 51 10 to 14 18 15 to 19 4 20 to 24

### Orbit of Venus. If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venus to complete one orbit of the sun?

Orbit of Venus. If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venus to complete one orbit of the sun? Here is the information to use: Kepler's third law. According to Kepler's third law of planetary motion, the ratio R T 2 3 has the same value for every planet in our solar sy

### Exploring Powers of Seven: Example Problem

If you calculate 7^90 on a TI-83+ calculator, you will get 1.145047759x10^76. This is misleading since it implies that the digit in the ones place is zero. Explore powers of seven and use what you learn to determine what digit is in the ones place in the expansion of 7^90. Note, this needs to be done without using a calcula

### Factoring formula

1. How would you apply a factoring formula to completely factor the expression "x4 - 1"? 2. i. What does the symbol "i" represent? ii. Is "12.5555..." a rational or irrational number? Explain. iii. Is "2.1273685..." a rational or irrational number? Explain. iv. Is "548/799" a rational or irrational number? Explain.