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Basic Algebra

Applied Math Skill Check 15 Bases and Exponents

Applied Math Skill Check Bases and Exponents 1. Structural Analysis - the equation used to find the cross-sectional area of a cylindrical column (area of a circle): Answer: Show your work: 2. Physics - The equation used to find the amount of centripetal force on a mass moving in a circle:

Many questions -- Substitute method, slope, graph lines.

1. Determine the x- and y-intercepts of the given equation. Show your work. Then plot the intercepts, and graph the line. -5x + y = 0 2. Determine the x- and y-intercepts (if any) of the given equation. Show your work. Then plot the intercepts, and graph the line 7x + 56y = 0 3. Select the line that has the given slope

Logarithmic/asymptote

In exercise 53-56, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. 56. h(x) = 2 + log2 x The figure show the graph of f(x) = log x. In exercises 59-64, use transformations o

Simplying rational expressions

I would like help understanding How doing operations- adding, subtracting, multiplying, and dividing - with rational expressions similar to or different from doing operations wit้ fractions? Also can understanding how to work with one kind of problem help understand how to work another type? when might you use this skill i

Factorization of Polynomials.

I sent my problems via attachment word document. Please read the instructions and fill out all problems that show any extension of work. please. 1.Factor completely. If the polynomial is prime, state this. 75x2 - 3 2. Factor completely. If the polynomial is prime, state this. 48x2 +

Exponential and Logarithmic Functions

Solve for solutions: The exponential models describe the population of the indicated country, A, in millions, t years after 2003. Use these models to solve 2,4 and 6. India A = 1049.7e^0.015t Iraq A = 24.7e^0.028t Japan A = 127.2e^0.001t Russia A = 144.5e^- O.004t 2. What was the population

How to factor out a polynomial

I have a polynomial x^4 - 16x^2 + 40x - 25. I need to know the technique in how to factor it out. Not just the answer. For example, this answer: (x +5)*(x -1)*(x^2 -4*x +5) What steps do I need to take to get to that? Or any other factored out answer? Thank you for your time.

Evaluate logarithmic expressions

In Exercises 1?40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 7. log(7) 15. logb x^3 x 8. log9(9) 16.

Exponential and Logarithmic Equations.

Solve each exponential equation. Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 24. 10^x = 8.07 26. e^x = 0.83 28. 19^x = 143 30. 9e^x = 107 32. 4e^7x = 10,273 34. e^(1-8x) = 7957 36.

Solution of Exponential Equations

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. 2. 3^x=81 4. 5^x =625 6. 3^(2x+1) =27 8. 5^(3x-1) =125 10. 4^x =32 12. 125^x =625 14. 5^(2-x) = 1 125 16. x-2 = sqrt 7 7

Algebra - Developing and Solving Problems

Harry has $2.25 in Nickels, Dimes and quarters. If he had twice as many nicels, half as many dimes .... The sume of the digits of a three digit number is 11. If the digits are reversed ... Find the Vertex, Focus and ... Find the equation of the parabola .... Write each equation in the form ... Find the Vertex, Foc

Mathematics

The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was approximately 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio?

Algebra word problems

Supplementary angles are angles whose measures have a sum of 180degrees. Complementary angles are angles whose measures have the sum of 90 degrees. Find the measure of an angle whose supplement is 10 degrees more than twice it's complement. Let 90- x equal the degree measure of it's complement and 180 -x equal the degree measure

Polynomial -- word problem.

If a ball is thrown downwards from a height of 128 feet with an initial velocity of 32 feet per second and its height above the ground is given by the formula S = - 16t2 - 32 t + 128. How long will it take the ball to reach the ground?

Algebra: Example Word Problem

At 10:00 a.m., train A leaves the station heading east at 40 m.p.h. At 11:00 a.m., train B leaves the same station heading North 30 degrees W (theta = 120 degrees) at 70 m.p.h. How fast is the distance changing at 12:00 noon. Give both the exact answer and a one decimal place approximation. You may find it helpful to plot th

Math

showing your work 1. Convert the following equations into logarithmic form: a. 6 = 2x b. 9 = 6y c. 7 = 3y d. X = 5y 2. Convert the following equations into exponential form: a. X = log38 b. -9 = log5Y c. X= log6Y d. 100 = log2Z 3. Simplify the follow

Algebra Express Terms

1. Express in terms of i: -sqrt(-297) 2. Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. 8-1/3ax-7/8z^8 3. Simplify. Assume that no radicals were formed by raising negative numbers to even powers. sqrt(20)k^7q^8 4. Simplify: (-3a^2)^3

Algebra

1. A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 15. Find the length of a side. 2. One side of a rectangle is 12 inches and the other side is x inches. What values of x will make the perimeter at most 44? 3. The equation y = 0.004x - 0.40 can be used to determine the approx

Algebra: Order of Operations

1.Apply the Order of Operations to simplify the following expression: 9x[(2x2 - 3x + 7) - (9x3 - 3x2)/3x2] 2.Subtract. 3x4 + 4x3 + 7 - (x4 - 2x3 - x2 - 9x) 3.Simplify the expression, and identify the constants, coefficients, and variables in the simplified expression. (8w^4 - 6wz + 6wz^2) - (2w^4 + 7wz -

Algebra - Understanding Functions

Determine whether each relation is a function. In addition, provide reasons for identifying a relation as a function.1. {(3, 4), (5, 9), (9, 9), (2, 3)}2. {(0, 0), (0, 1), (1, 4), (2, 4)} 3. {(2, 1), (4, 5), (8, 4), (1, 0)} 4. {(8, 3), (8, 0), (7, 7), (4, 7)}

Algebra Word Problem of Speed Time and Distance

A family makes a 43.25 km trip in 5.5 hours. On the first part of the trip they crossed a lake in a canoe paddling at 12 km/h. For the rest of the trip, they hiked on a scenic trail. If their average walking speed was 5 km/h, how far did they walk?

Percent: How Many Questions Were on the Test

A student got 50% of the questions on an algebra test correct. If he answered 10 out of the first 12 questions asked correctly but missed 3/4 of the remaining questions, how many questions were on the test?

Algebra - Finding dimensions of a shape

A rectangular swimming pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.

Solving Simultaneous Equations by Substitution Method

Solve each system of equations by substitution method. Show work by step by step solutions. 1) x + 3y = 2 3x + 9y = 6 2) 4x - 2y = 2 2x - y = 1 3) x/4 - y/4 = -1 x + 4y = -9 4) x/6 - y/2 = 1/3 x + 2y = -3 5) 2x = 3y + 4 4x = 3 - 5y 6) 4x = 3y + 8 2x = -

Barn Painting Rational Expression

Barn painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x = 5.

Rational expression for his average speed

Driving Marathon. Felix drove 800 miles in x hours on Monday. 1) write a rational expression for his average speed. 2) On Tuesday he drove for 6 hours at the same average speed. Write a rational expression for his distance on Tuesday.