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# Algebra

### Vertical Pole Supports and Anchors

1st one- One leg of an isosceles right triangle measures 12 meters long. Find the length of the hypotenuse of the triangle.? Would it be 12 over the sq rt of 2 2nd one A wire is needed to support a vertical pole 18ft tall. A cable will be anchored to a stake and it forms a 30 degree with the ground. nearest tenth... How fa

### Find the LCD for a given rational expression; reduce to the lowest terms

Find the LCD for the given rational expression, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. Page 345 # 47. x y 1 ----, ------, ------ 9y^5 12x^3 6x^2y # 48 5 3b 1 -------, -------,

### Find two positive numbers that satisfy the given requirements

Find two positive numbers that satisfy the given requirements The product is 192 and the sum is a minimum

### A Fence Three Sides of a Rectangular Yard

Justin wants a fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. Justin has 80 feet of fencing available. (recall: area of a rectangle =length *width). One side is x and another is 80-2x - Write an equation to represent the area of the exercise yard

### Revenue Equation and Maximum Revenue Determination

A company that manufactures typewriter ribbons knows that the number of ribbons, x, it can sell each week is related to the price, p, of each ribbon by the equation x=1200-100p. the amount of revenue earned each week would be R(X)= 1200P-100P^2. - Graph the revenue equation and label the x- and y-intercepts. - Find the max

### Determine the equation needed to find the height of the dock. Find the height of the dock.

A boat is being pulled into a dock with a rope attached to the boat at water level. when the boat is 12 feet from the dock, the length of the rope from the boat to the dock is 3 feet longer than twice the height of the dock above the water. - Determine the equation needed to find the height of the dock. - Find the height

### Application Word Problem : Distance, Time and Speed - Object thrown Upward

An object is projected vertically upward from the top of a building with an initial velocity of 144 ft/second. It's distance, s(t) in feet above the ground after t seconds is given by the equation: s(t)=-16^2+144t+100 - find the maximum height, s(t), of the object above the ground. - find the height of the building, th

### Fields Extensions/Algebraic

Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K. Let S be the subspace of F. Hint for the "-->" of proof. If S is a field and u is not equal to 0, then 1/u is in S. What d

### Countable Subsets and Dense Sequences

Give a example of countable subset l^2 ( it is the class of all sequences which are bounded ) which is dense in l^2 ?

### Help with solution

Solve each system by the addition method # 9 x - y = 12 2x + y = 3 # 10 x - 2y = 1 -- x + 5y = 4 # 11 2x - y = 5 3x + 2y = 3 # 12 3x + 5y = 11 x - 2y = 11 # 18 x + y= 13 22x + 36y = 356 Solve each system by the addition method. D

### Parabola Application Word Problem : Suspension Bridge

A suspension bridge is built with its cable hanging between two vertical towers in the form of a parabola. The towers are 400 feet apart and rise 100 feet above the horizontal roadway, while the center points of the cable is 10 feet above the roadway. (a) Find the equations of the parabola (b) Find the height above the roadway

### Finding the Equation of a Line Given a Slope and a Point

The line with the slope -6 that goes through (-1,-7) The line with the slope -8 that goes through (-1,-5) A developer prices condominiums in Florida at 20,000 plus \$40 per square foot of living area. Express the cost C as a function of the number of square feet of living area s. The threshold weight for an individual is

### A stationary car A is passed by a car B moving

A stationary car A is passed by a car B moving with a constant velocity of 15m/s. Two seconds later, car A starts moving with a constant acceleration of 1m/s^2 in the same direction.(If car has constant velocity acceleration must be zero) a) Using the formula s=ut + 1/2at^2,where s is the distance from the starting point in m

### Velocity, Time and Distance of a Rock After it has been Thrown

If a rock is thrown into the air on small planet with a velocity of 25 meters/second, its height in meters after t seconds is given by V = 25t ? 4.9t2. Find the velocity of the rock when t=3 A particle moves along a straight line and its position at time t is given by s(t) = 2t3 ? 27t2 + 108t where s is measured in meters and t

### Algebra Concepts Check

Week two DQ 1 1) How can you differentiate between a formula and an equation? For example. Week two DQ 2 2) What are some "Pitfalls" to watch out for in? A. Using the addition property in solving for X? B. Using the multiplication property in solving for? For example. Week two DQ 3 3) how do you remember

### Let T be a Mobius transformation, T doesn't equal to identity. Show that a Mobius transformation S commutes with T if S and T have the same fixed points.

Let T be a Mobius transformation, T doesn't equal to identity. Show that a Mobius transformation S commutes with T if S and T have the same fixed points.

### Whole number and polygon

Task1 some whole numbers can be written as the sum of consecutive whole numbers. for example: 5=2+3 12=3+4+5 some whole numbers can be written as the sum of consecutive whole numbers in more than one way. for example: 9=4+5=2+3+5 which whole numbers can be written as the sum of consecutive whole numbers? can they

### Equality

In a basketball game scrimmage, the Toros scored a total of 103 points and made three times as many field goals (2 points each) as free throws (1 point each). They also made eleven 3 point baskets. How many field goals and free throws were made?

### Simple Statistics word problem - 100 soldiers are required...

As a test 100 soldiers are required to complete 9 weeks of training 18 percent of them fail due to the short period of 9 weeks. If 2 more weeks are added, what would be the percentage of failures? Feel free to answer in an attachment if needed. I need to see how to solve this type problem in a statistical manner. You may a

### Application Problems: Velocity, Distance and Cost of Production

A 40,000 lb. rocket is launched from sea level straight up, then falls back to earth. The total flight time was 160 seconds. The rocket reached it's apex in 1 minute and 20 seconds. What altitude did the rocket reach before falling back to earth....in miles? The assembly operation takes two minutes for an operator to perform

### Arithmetic sequence

How do I find the 40th term of the arithmetic sequence knowing the general term An=(Asubscript n -1)n-3? The first term in A1=9

### Exponential form

How would I write (log subscript b) 219 = 3 in exponetial form?

### Solving a quartic equation

I can not factor or group this to set it equal to zero to determine the solution. Can you help me? 4x^4-65x^2+16=0

### Fixing a Budget

This is a sample budget prepared by Dick and Jane who are both employed. Dick is paid weekly and brings home a check for \$350.00 each week. Jane is paid every two weeks and brings home a check for \$500.00 each pay day. Jane sometimes receives an additional amount for paid overtime and Dick receives a bonus from time to time.

### Solve by the elimination method

Solve by the elimination method. -------------------------------------------------------------------------------- Solution 2x+3y=4 10x-6y=3 than I multiplying the first equation by 10 and the second equation by -2. 20x+30y=4 <= should be 40 -20x+12y=-6 =>42y=34 => y=17/21, x=11/14 how do I solve for (x

### Elimination method and substitution methods

Elimination method 1) 5r-6s=-10 6r+5s=49 2) 1/3x + 1/1y=2/3 2/3x + 3/5y=1/5 3) 5x+3y=-12 6x-3y=-54 4) p=47+q 8p=6q+404 Substitution method 1) x+y=5 y=x-3 2) r-45=0 6r-5s=133 3) 6x+3y=-36 -7x+y=60 System of equation by graphing: 1) y-2x=0 y=4x-1

### Word problem

I've attached the file. I need to know if I'm going in the right direction (in the red font), if not could you explain? (See attached file for full problem description) --- A person has 14 close friends. (a) How many ways can she invite 8 of her 14 close friends to a holiday get-together. Explain. (b) Suppose tha

### Finding Products and Simplifying Exponents

Please help with the following problems. I need more detail on each problem how the solution was achieved using these steps. Thanks for your help. 2. Find the product: (x - 2)(x + 3)(x - 4) (x - 2)(x + 3)(x - 4) = 3. Simplify without having negative exponents: (- 3s-3t2)-2 (- 3s-3t2)-2 4. Conve

### Word problem

Value Rent-A Car rents a luxury car at a daily rate of \$43.81 plus 5 cents per mile. A business person is allotted \$100 a day. How many miles can the business person travel for \$100.