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# Basic Algebra

### Simplify rational expressions, solve rational equations, solve word problems

See attached file for full problem description. Add/subtract and simplify: 1. 5 -4 ___ + ________ c2d3 7cd2 36. 3x + 2 x - 2 _______ + ______ 3x + 6 x2 - 4 50. 3(x - 2) 5(2x + 1) 3(x + 1) _______ +

### Rational Expressions & Equations Series

See attached file for full problem description. Solve by factoring and using the principle of zero products. Remember to check. 2 30. - 9x + 14 = 0 2 34. x + 16x = 0 2 46. 3x - 7x = 20 2. The length of a rectangle garden is 4m greater than the width. The a

### Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: Solve by factoring.

1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the

### Vertical motion of a baseball under quadratic drag friction

Problem 1: Consider a two-dimensional problem in the xy-plane. There are two points in space, labeled as P and Q, as shown in the figure to the right a) Using polar coordinates, sketch on the figure at points P and Q the radial and azimuthal unit vectors. b) Write down a general expression for the radial and azimuthal unit

### Derive the Sackur-Tetrode equation using the microcanonical ensemble

Derive the formula for the entropy of an ideal monoatomic gas using the microcanonical ensemble. This formula is known as the Sackur-Tetrode equation.

### Algebra Word Problems

Jenny purchased a prepaid phone card for \$20. The long distance calls cost 10 cents a minute using this card. Jenny used her card only once to make a long distance phone call. If her remaining credit on the card is \$18.90. How many minutes did her call last?

### Customers of a phone company can choose between two service plans for long distance calls. The first plan has a \$24 one-time activation fee and charges 14 cents a minute. The second plan has no activation fee and charges 18 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a \$24 one-time activation fee and charges 14 cents a minute. The second plan has no activation fee and charges 18 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

### Evaluate the expression: 2t-1

Evaluate the expression: 2t-1 given that -3t+9 = 6 See attached file for full problem description.

### Algebra Help

Solve by graphing. Indicate whether each system is independent, dependent or inconsistent. 1. y= 2x-1 x+y= 2 2. 2x-3y=12 3y-2x= -12 3. 3x-y=4 3x-y=0 Solve each system by the substitution method. Indicate whether each system is independent, dependent or inconsistent 4. x-y=3 3x-2y=3 5. 3y=x+5 3x-9y= -10 6

### Algebra Questions

See attached file for full problem description. 1. Solve. 6x - 0.37 = 5(x - 0.28) 2. Identify the base in the statment "50% of 300 is 150." 3. Identify the rate in the statment " 260 is 52% of 500." 4. The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base.

### Business Math: Which is the better method for calculating overtime?

(1) Sally worked 48 hours this week . Her overtime rate is 1.5 times the regular rate. When calculating gross pay with overtime, there are two options: Option 1. ( total regular hours X hourly rate ) + ( overtime hours X overtime rate ) = gross pay OR Option 2. ( total number of hours worked X the ho

### Prediction to Produce Market Demand

Your company produces a product in a market that has grown by 10% per year for the past 15 years. According to your estimate, the market is currently at 30% of saturation. Predict sales for the next 20 years.

### Important information About Solving Equations and Word Problems

7(3x+4) = 8(2x+5) + 13 2(x-3) - 3(x+5) = 3(x-2) - 7 3x - 5(3x-7) = 2(x+9) + 45 Geometry: The length of a rectangular playing field is 5 ft less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field. Science and medicine: A bicyclist rode into the country for 5

### Algebra Questions: parabolas, graphing, quadratic equations, etc.

***See attached file for full problem description.*** For questions 18, 20, 22, 24, complete the table by matching each graph with the correct equation from (a) - (h). For each equation in exercises 25 to 28, identify the axis of symmetry, create a suitable table of values, and sketch the graph (including the axis of symme

### Solve and graph compound inequality

Solve each compound inequality. State the solution set using interval notation and graph it. x<= 0 and x + 6 > 3

### Important information about Capacitive Reactance

Capacitive reactance X_c in an electrical circuit to an alternating current is given by: (Please see attached) where f is frequency of the current and C is capacitance of the circuit. Solve for f.

### GRAPHS & SLOPES of line

1.Graph x+4Y=5 2. Graph x-2y=6 3. How do I find the slope of the line with points (0,0) (2,4) 4. How do I find the slope of the line with points (-3,1) (2,-2) 5. How do I graph the line with points & slope (-2,5) slope -1 6. How do I draw l1 (L sub 1) through (-4,0) (0,6) What is the slope of any line paral

### Growth rate of an exponential function

In everyday language, exponential growth means very fasy growth. In this problem, you will see that any exponentially growing function eventually grows faster than any power function. (a) Show that the relative growth rate of the function f(x) = x^n, for fixed n>0 and for x>0, decreases as x increases. (b) Assume k>0 is f

### Writing Equations from Word Problems

74. An algebraic equation is a complete sentence. It has a subject, a verb, and a predicate. For example, x + 2 = 5 can be written in English as "Two more than a number is five." Or. "A number added to two is five." Write an English version of the following equations. Be sure you write complete sentences and that the sentences e

### Algebra : Solving Equations, Word Problems and Base of Trapezoid

Please see the attached file for the fully formatted problems. 1.12x-6=11x 2. 5x+8+3x--x+5=6x-3 3. -3x=27 4. 5. Business and finance-Jose has savings accounts for each of his five children. They contain \$215, \$156, \$318, \$75, and \$25. Find the median and the mean amount of money per account. 6. 9x+7=5x-3

### Algebra Word Problems: Student/Non-Students Tickets for Soccer

There were 1000 more students at the soccer game than non-students. Student tickets were \$8.50 and non-students were \$13.25. If the total revenue for the game was \$75,925, then how many tickets of each type were sold?

### Slope-Intercept Form

Write the equation in slope-intercept form. 42. y + 2 = -6 (x-1)

### Proofs by induction

I'm having a hard time comprehending how to write proofs by induction. I'm looking for answers to these problems so that I may have a better understanding of how they are done. --- All problems need to be proved using induction in proofs. 1. Consider n infinitely long straight lines, none of which are parallel and no th

### Lagrangian for an Harmonic Oscillator

Write the Lagrangian for a one-dimensional particle moving along the x-axis and subject to a force F=-kx (with k possitive). Find the lagrange eqn of the motion and solve it. lagrange eqn 0=mX+Kx where X is the second erv with respect to T

### Can you give a real-world example when the solution of a system of inequalities must be in the first quadrant?

Can you give a real-world example when the solution of a system of inequalities must be in the first quadrant?

### What is the situation when two linear inequalities have no solution?

What is the situation when two linear inequalities have no solution?

### Graph inequality

Graph inequality. Using the test point method. 4x + 3y > 24

### Microsoft Word Equation

(See attached file for full problem description) --- 1. Access Microsoft Word. 2. To start the Equation Editor, use the menu choice Insert / Object; under the Create New tab, select Microsoft Equation 3.0. ? If you have Word's Equation Editor loaded, you will get a toolbar that has the graphics templates needed to create

### Find log 10000 to the base of 10. Find log 10000 to the base of 2.

A) Using a calculator, find log 10000 where log means log to the base of 10. b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer

E^x e^2