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# Basic Algebra

### Completing the Square for the Quadratic Equation

For the quadratic equation x² + x - 1 = 0. i Use the technique completing the Square to Determine the solutions (roots) of the equation ii Verify each root by plugging the root back into the equation and performing the computation

### Rational expression for total traveling time

Cystal drove 110 miles at y miles per hour. She then increased her speed by 3 miles per hour and drove an additional 150 miles. Using the equation D=RT, a rational expression for her total traveling time is?

### The Domain of an Expression

For the rational expression (x^2-1) / (x+1)^2, the domain of this is expression is? all values of x all values of x satisfying x does not equal 1 all values of x satisfying x does not equal -1 all values of x satisfying x does not equal 0 none of the above.

### Vector Equation: Example Question

A golf ball is hit at an angle a with the horizontal and moves under gravity with air resistance kv per unit mass, where v is the velocity and k>0 is a constant. Show that the equation of the path can be written as z=x(tan(a)+g/ku)+(g/k^2) log(1-(kx/u)), where u is the initial horizontal component of v. If k is small enoug

### Inequality: Runner's Pulse Rate Example Question

After a race, a runner's pulse rate R in beats per minute decreases according to the function: R(t) = 145e^-0.092t, 0 ≤ t ≤ 15 Find the runner's pulse rate at the end of the race. Find the pulse rate 1 minute after the end of the race. How long, to the nearest minute, after the end of the race will the runner's pul

### Algebra: The rational expression

Please help with the following problem. I recently read an obituary of Paul MacCready, the father of human powered aircraft. He invented the Gossamer Albatross, an aircraft which successfully flew the English Channel under human power (a cyclist turning the propeller). The aircraft flew from Folkestone, England to Cap Griz

### Problems with quadratic equation

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100ft of fence? What should the dimensions of the garden be to give this area? Write a quadratic equation in the variable x having the given numbers as solutions. T

### Word problems with quadratic functions

1. The number of tickets sold each day for an upcoming performance of Handelâ??s Messiah is given by N(x)=-0.4^2+12x+10, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? 2.Write a quadratic equation in the variable x having th

### Binomial Theorem for Euler's Formula

(a)Express e-½iθ-e½iθ in trigonometric form, and show that (1-eiθ)2 = -4eiθsin2 ½θ. (b) For a positive integer n, series C and S are given by where is binomial coefficient. By considering the expansion of (1-y)2n show that C = (-4)n cos nθsin2n (½θ) , and find a similar expression for S.

### Algebra and velocity

When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where â??vâ? is the initial velocity (speed) in ft/sec and â??kâ? is the initial height in feet (as if you were on top of a tower or building). Make up a sc

### Assessment of integer roots

Note the polynomial form P(x) = x2 - a. And, note that the two linear factors ( x + a ) ( x - a ), when multiplied together, yield ( x + a ) ( x - a ) = x2 - a. Consequently, we note that an equation of the form x2 - a= 0 can be factored as ( x + a ) ( x - a ) = 0, giving the two zeros of our equation x = a, -

### Phone company charges are assessed.

A phone company charges a different rate for a local call than a long distance call. A local call costs \$0.15 per minute and a long distance call costs \$0.45 per minute. Last month a customer made 320 minutes of calls. If the total cost of the calls was \$99.00, how many minutes of each type of call did the customer make? See

### Determine the factorability of a trinomial.

How would you use this procedure (factoring a quadratic expression with leading coefficient a = 1) to determine if a given polynomial is prime, that is, determine that it cannot be factored into a product of two linear polynomials

### Algebra: Equations for Height of Buildings

The height of a building is 1411 ft. How long would it take an object to fall to the ground from the top? Use the formula s=16t^2, where s is the distance, in feet, traveled by an object falling freely from rest in t seconds.

### Algebra Problems

Part 1: find a record-breaking temperature (in degrees Celsius) for a town or city in a country other than the United States. Include the name of the town and country along with the temperature, and what record was broken. Give the formula for converting degrees Celsius to degrees Fahrenheit. Using the formula, show how to conve

### Rate per hour

2 mechanics worked on a car. the 1st mechanic worked for 10 hours. the second mechanic worked 15. the total they charged was \$1525. What was the rate charged per mechanic if their total rates combined = \$130?

### Alternate ways to solve a problem

Read the problem below. Then, describe two or more alternate ways to solve this problem. A farmer sends his daughter and son out into the barnyard to count the number of chickens and pigs. When they return the son says that he counted 200 legs and the daughter says she counted 70 heads. How many pigs and chickens does the f

### Pythagorean theorem is utilized.

1.The formula r=2sqrt(5L) can be used to approximate the speed r, in miles per hour, of a car that has left skid marks of length L, in feet. How far will a car skid at 30mph? 2.What does it mean to refer to a 20 inch TV set or a 25 inch TV set? Such units refer to the diagonal of the screen. A 25 inch TV set also has a wid

### Evaluating as Linear Equations or Not Linear Equations

1. Determine which of the following are linear equations and which are not linear equations. State the reason for your answer. (a) x + y = 1000 (b) 3xy + 2y + 15z - 20 = 0 (c) 2xy + 4yz = 8 (d) 2x + 3y 4z = 6.

### Algebra: Equations

1. How can you determine whether a system has no solution by graphing? 2. Solve by graphing: y=x-3 y=-x+1 3. Solve by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. 3y-x=0 x-4y=-2 4. Ticket sales. Tickets for a concert were sold to adults for \$3 and

### Assessing the Area of a Rectangle

1. A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x. S=_______ 2. The diameter of a spherical balloon is 8 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the

### How fast does each bicyclist travel?

1. Kathy bicycles 5 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Kathy can bicycle 72 km. How fast does each bicyclist travel? 2. The office jet printer can copy Lisa's dissertation in 8 min. The laser jet printer can copy the same document in 10 min. If the two machines work together, how

### Unit Price for Product Sale

DQ 3.1 - Unit Price Find a product for sale that comes packaged in different sizes. Compute the unit price (e.g. dollars per ounce, dollars per foot, dollars per megabyte, etc.) for two of the available sizes. Which is the better bargain? Write an equation describing the relationship between price, P, size S, and unit pric

### Algebra

1. Graph y=x-1 List at least five points on the line 2. Graph 2x+y=6 Find the x and y intercepts. 3. Find the slope of the line through (1/3, 2) (-1/3, 1) 4. Graph the line through (2,3) with slope 1/2 . 5. Write an equation for the line in the following graph. Use slope and intercept form if possible. (

### Need Assistance with Algebra

Show all work, and use Equation Editor or MathType to format all equations. 2.1-56 Solve 2.2-36 Solve 2.3-86 Solve 2.4-30 Solve for x. 2.4-84 Finding the list price. Find the list price if there is a 12% discount and the sale price is \$4400. 2.5-20 Write an algebraic expression for two numbers that d

### Inventing a word problem

I need to better understand - how to invent a word problem calling for an algebraic solution (i.e. variables instead of numbers). Please provide one or two examples with solutions. Thanks.

### Additional and Multiplication Principles Solving

I need help with the problems in the attached document. Please provide step-by-step instructions so that I can check my problems to make sure I did them correctly. 1. Solve x - 3 = -7 2. Solve x - 5 = 25 3. Using the addition principle solve 15 = n - 2. Be sure to check. 4. Solve using the multiplication principle. Be sur

### Investment: portfolio fraction

Helen has 1/5 of her portfolio in US stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds. What fraction of her portfolio is invested in municipal bonds? Please show work in reach the solution. Thanks.

### Give an example of a logarithmic equation that can not be solved and explain why it can not be solved.

1. Solve for x in the following equations. a. log-base-3(x - 5) + log-base-3(x + 3) = 2 b. log-base-7(x) + log-base-7(x - 1) = log-base-7(2x) 2. Show that the following statement is true. Please refer to the attachment for the statement. 3. A quantity of oxygen gas had 16.32g of the radioactive isotope oxygen-19 i

### Steps to Solve Linear Equations

Discuss the following: I. Given a 1-variable linear equation 10z-4=86. Explain the techniques, and show the steps used for solving this equation. Check if the solution is correct. II. Using the same 1-variable linear equation in I above, change the linear equation to a linear inequality (Use either < or >). Explain the tec