### Adding and Subtracting Functions

Simplify (f(x+h)-f(x))/h, where a.) f(x)=2x+3 b.) f(x)=1/(x+1) c.) f(x)=x^2

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Simplify (f(x+h)-f(x))/h, where a.) f(x)=2x+3 b.) f(x)=1/(x+1) c.) f(x)=x^2

Graph each quadratic function and state its domain and range. h(x) = -3x^2

Find all real or imaginary solutions to each equation. 19x + 25 6x= ----------- x+1

How do you solve the following expression: 4t^2 + 25 = 20t Make sure to show all work.

Solve the rational inequality. State and graph the solution set. a -------->0 a+2

2y^2 - 3y - 6=0

Derive rules to test whether a number is divisible by N, where N ranges from 2 to 13. E.g. A number is divisible by 3 if the sum of the digits is divisible by 3. Show that a palindromic number which has an even number of digits is always divisible by 11.

In a family there are two cars. In a given week, the first car gets an average of 25 miles per gallon, and the second car gets 40 miles per gallon. The two cars combined drive a total of 2100 miles in that week, for a total gas consumption of 60 gallons. How many gallons were consumed by each of the two cars that week?

4m^2 + 20m + 25 =

An aquarium tank can hold 7700 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 77 minutes. The second pipe can fill the tank in 44 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Simplify. Assume a and b are positive real numbers and m and n are rational numbers. ( a^-3/mb^6/n)^-1/3 ------------------ (a^-6/mb^9/n)

How do you simplify the expression: (-27x^9)^1/3? Please help me understand this.

Perform the operation. Reduce each answer to the lowest terms: 3/2y - 3/ 2y + 4

Find the LCD for the following rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. 4/x -y , 5x/ 2y - 2x

-2a^2/3a^2 * 20a/15a^3

Find the exact coordinates of the inflection points and critical points of the function f(x)= on the interval (-10, 10). (See attached file for full problem description)

I need to find the maximum and minimum surface areas for 2 cubes with a total volume of 432 in^3. No other perameters are specified. I've been able to use common sense to find the max is 432 sq/inches (two 6"^3 cubes) and min is 343.051 sq (one 7.5595"^3 cube and one cube of 0.171"^3). I need help with the equations for the maxi

Please see the attached file for the fully formatted problems.

Use distributive property to remove parenthesis. (3 - 5 u + 2y) (-9)

6x^2 + 11x - 10

The following trinomial is in the form ax^2 + bx + c. Find two integers that have a product of ac and a sum of b. There is no need to factor the trinomial 15t^2 - 17t -4

Factor the following polynomial completely, given that the binomial following it is a factor of the polynomial. x^3 + 2x^2 - 5x - 6, x + 3

Factor each difference or sum of cubes. u^3 - 125y^3

Factor the following polynomial completely. -36a^2b + 21ab^2 - 3b^3

X>-2y and x-3y<6

X + 8y > 8 and x - 2y < 10

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

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

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)

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.