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# Basic Algebra

### Real or imaginary solutions

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

### Word Problems : Surface Area of an Open Top Box

Thomas is going to make an open top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner? keywords: open-top

2y^2 - 3y - 6=0

### Find Divisibility Rules for the Numbers from 2 to 13

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.

### Algebra word problems: miles per gallon

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?

### Factoring Polynomials

4m^2 + 20m + 25 =

### Filling an aquarium tank

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?

### Surface area of a cube

The formula A=6V^2/3 gives the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet.

### Algebra Word Problems : Sailboat Speed

The sail area displacement ration S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet. S= 16AD^-2/3 A) Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds.

### Finding the Area of a Triangle

What is the exact area of a triangle with a base of square root 30 meters and a height of square root 6 meters.

### Simplifying Expressions

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)

### Algebra Word Problems : Comparing Wind Chills

Use this formula for the following word problem. W= 91.4 - (10.5 + 6.7 principal square root v - 0.45v) ( 457 - 5t) --------------------------------------------------------------- 110 Who will feel colder: a person in Minneapolis at 10 degrees F with a

### How fast was each one traveling?

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one half hour longer than smith's. How fast was each one traveling?

### Use a proportion to estimate the size of the bear population on the Keweenaw Peninsula

To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population.

### Reduce to lowest terms

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

### Find the LCD for the rational expressions

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

### Perform the indicated operation

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

### Find the exact coordinates of the inflection points

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)

### Minimum and maximum surface areas of a cube are found.

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

### Differentiating Functions with Fractal Exponents

Please see the attached file for the fully formatted problems.

### Distributive Property

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

6x^2 + 11x - 10

### Cube Roots of 27 and Vector Operations

14. Find the three cube roots of 27. Write roots in rectangular form. 15. If P = (?2.3). P7 = (?1,5),and is the vector from P1 to P2, a. Write v in terms of i and j. b. Find ||v|| In Exercises 16?19, let v=?5i+2j and w=21?4j. Find the specified vector, scalar, or angle. 16.3v?4w 17.v.w 18. the angle between v and w, to

### Finding two integers that have a product of ac

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

### Use factoring to solve the problem.

Use factoring to solve the problem. Demand for pools. Tropical pools sells an aboveground model for p dollars each. The monthly revenue from the sale of this model is given by..R= -0.08p^2 + 300p Revenue is the product of the price p and the demand. a) Factor out the price on the right hand side of the formula b) Wha

### The amount of an investment of P dollars for t years at simple interest rate r is given by A = P+Prt.

The amount of an investment of P dollars for t years at simple interest rate r is given by A = P+Prt. a) Rewrite this formula by factoring out the greatest common factor on the right hand side. b) Find A if \$8300 is invested for 3 years at a simple interest rate of 15%

### Factor polynomial completely.

Factor the following polynomial completely. If a polynomial is prime, say so. 9bn^3 + 15bn^2 - 14bn