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Basic Algebra

Solving Equations

Show me an example of how this problem is solved. 7r ________ = -14 12

Quadratic Equations

Explain and show each step in solving the following quadratic equation: 4b^2 - 15= -7b

Solve the equation y = x2 - 6x + 8 = 0

Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a)Solve by factoring, b)solve by completing the square, c)solve by using the quadratic formula

Algebra and Trigonometry (16 Problems)

1. Write an equation for the circle that passes through the points: (1, -1), (-5, 7), and (-6, 0). 2. Express the polar equation in rectangular form. 3. Find the total area enclosed by the graph of the polar equation r = 1 + cos 2θ. 4. Write the equation of the line tangent to the parametric curve x = tcos t, y

Algebra - Sequence Questions

Brackets [ ] are used to indicate a subscript, so a[n] means the nth term of a sequence. 1. Write the first four terms of the sequence defined by a[n] = 2n + 3. 2. Write the first four terms of the arithmetic sequence with a[1] = -6 and d = 4. 3. What is the common ration in the geometric sequence 4, -12, 36, -108, . .

Opposite, Odd and Even Numbers

1. The Greeks believed matter and energy were opposites. So is Einstein right in saying opposites are equivalent? 2. Can you add opposites? 3. You can add odd numbers and even numbers. Could they represent opposite theories like Plank and Maxwell? Can even and odd numbers be used as algebra in equations.

Logarithms and Exponents Applications Word Problems

1. Complete table for savings in which interest is compounded continously. Initial investment Annual rate Time to double total $1000 ? ? $2281.88 2. Complete table for radioactive isotope Isotope Half-life(years) Initial quantity Amt after 1000 years 5715 ? 3.5g 3. The population of P of a city is given by P=

Graphing and Solving Systems of Inequalities

1. Graph the inequality. y  1 2. Graph the inequality. y  3x 3. Given f(x) = 4x + 1, find f(3). 4. Given f(x) = 5x2 - 3x + 1, find f(-2). A) -13 B) 15 C) -25 D) 27 5. Given f(x) = x2 + 5x + 3, find f(0). 6. Rewrite the equation 4x - 10y = 11 as a function of x. A) B) C)

Logarithms

Please answer the following questions: 1. Find the domain of the function f(x) = ln(x - 7). 2. Simplify: log 1000 3. Write as a single logarithm (DO NOT find approximations): 2 log 4 + log x - log2. 4. Expand and simplify: ln(e^x). 5. Solve for x: log(x - 4) + log 2 = 1.

Radicals and Rational Exponents

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign. ADDITIONAL INSTRUCTOR COMMENTS/REQUIREMENTS For unit

Arithmetic Sequences

A. what is d, the difference between any 2 terms? answer: show work in this space. b. using the formuls for the nth term of a arithmetic sequence, what is 101st term? answer: show work in this space. c. using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? answer: show work in

Algebra Problems

Solve for x in the following equations: 1. 2 + 4(x + 2) = 3x - 2(x + 1) 2. |5x - 3| + 4 = 11 3. Solve for x: 3/x - 1/(x+2) = -2/(3x + 6) 4. Solve for y by completing the square: y^2 + 8y + 5 = 0 5. Use the quadratic formula to solve for x: x^2 - 4x + 2 = 0 6. Solve for x by factoring. x^3 + x^2 - 6x =

Simple math

(See attached file for full problem description) 1. Which of the ordered pairs (3, 1), (0, -4), (-4, 0), (-3, -7) are solutions for the equation x - y = 4? A) (0, -4), (-4, 0), and (-3, -7) B) (-4, 0) and (-3, -7) C) (0, -4) and (-3, -7) D) (3, 1) and (-4, 0) 2. Give the coordinates of the point graphed below.

Important Information About Fixed Rate

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P [1+r/n}^nt, let r = 10%, P=1, and n= 1 and give the coordinates (t,a) for the points where t= 0,1,2,3,4. Round the A value to the tenth's place. a. show coordinates in this space.

Abstract Algebra: Groups

(See attached file for full problem description with all symbols) --- 2.34 (I) How many elements of order 2 are there in and in ? Show work. (Answer: 25, 75 respectively) (II) How many elements of order 2 are there in ?

Abstract Algebra: Groups

(See attached file for full problem description) 2.22 Define f: {0,1,2,...,10} {0,1,2,...,10} by f(n)= the remainder after dividing by 11. (I) Show that f is a permutation. (II) Compute the parity of f. (III) Compute the inverse of f.

Algebra Word Problems : Maximizing Volumes, Compounding Interest and Logarithms

1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer b) Graph this fun

Discriminants

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. How do I create three unique equations where the discriminant is positive, zero, or negative. For each case, Please help me explain what this value means to th

Radicals (16 Problems)

Solve the formula for the indicated variable. 1. I = E __ for R R + r Find the root. All variables represent nonnegative real numbers. 2. √m6 Use the product rule for radicals to simplify the expression. All variables represent nonnegative real numbers. 3. 3√5b9 Simplify

Binomial Coefficients Formula Proof

n Prove that if n>=2, then Σ (-1)^(r-1) r n!/(r!n-r!) = 0 r=1 I think it should be done by mathematical induction. From the examples, I'm assuming that mathematical induction should be used. If you are able, please use this method.