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# Algebra

### Area Word Problems : Effect of Changing Length and Width of a Square - Effect on Area

Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had?

### Substitution

(See attached file for full problem description) Could someone please help me with the problem and show me ALL the steps.

### Solve for X and Y : sqrt(6x+2y)-1=sqrt(7-2y)

Sqrt(6x+2y)-1=sqrt(7-2y)

### Simplify : (x-y)-z=x-(y-z)

Simplify (x-y)-z=x-(y-z)

### L'Hospital's Rule, Asymptotes, Global Extrema, Inflection Points

F(x) = x^2 e^(17x) 1. Find an equation for each horizontal asymptote to the graph of f. 2. Find an equation for each vertical asymptote to the graph of f. 3. Determine all critical numbers. 4. Determine the global maximum of the function. 5. Determine the global minimum of the function. 6. Find inflection points. 7. Fin

### Real and Non-Real Affine Intersection Points and Their Multiplicities

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let

### Solving a Word Problem Subject to Constraints

Joe has to take a test which consists of short-answer questions worth 9 points each and essay questions worth 25 points each. He must do at least 9 short-answer questions, but won't have time to do more than 10. He has to answer at least 3 essay questions, but can't spend time to do more than 10. If no more than 19 questions can

### The absolute value of 1/2n +2 = the absolute value of 3/4n-2

The absolute value of 1/2n +2 = the absolute value of 3/4n-2, how do I solve when it isn't equal to anything but themselves?

### Solving Equations with Absolute Values : |b+7| +5=13

|b+7| +5=13 solve the equation. I am not sure how to do that some of the answers are {-1, 15} or I come up with {1}...I don't think I am doing this correctly.

### Application Word Problems : Mile Race

Sally runs 2 mph faster than Paul throughout a 10 mile race. If Sally finishes 25 minutes ahead of Paul, what was Sally's time for the race?

### 9 Math problems: Solve each proportion from pages

Page 371 & 372 Solve each proportion # 28. 9 3 --- = --- X 2 # 31. 5 3 --- = ---- 9 x # 39. a a + 3 ------ = -------- A + 1 a # 41. m - 1 m - 3 ----------- = ---------

### Hyperbolas and Completing the Square : Vertices, Foci and Asymptotes

Completing the square problems: HYPERBOLAS- Find the center, vertices, foci, and asymptotes of the hyperbola. Please give the equation in standard form, i.e. (x-h)^2/a^2 - (y-k)^2/b^2=1 or other way around. 15) ? 9x^2-y^2-36x-6y+18=0 Answer: Center (2,-3) Vertices (3,-3), (1,-3) Foci: (2+ or &#8730;10, -3)

### Splitting Fields : Find the splitting fields over Q for x^3+3x^2+3x-4.

Find the splitting fields over Q for x^3+3x^2+3x-4. Recall a splitting field is as follows: Let K be a field and let f(x)=a_0+a_1*x+...+a_n*x^n be a polynomial in K[x] of degree n>0. An extension field F of K is called a splitting field for f(x) over K if there exist elements r_1,r_2,...,r_n elements of F such that (i) f(x

### Rectangular Kitchen Measured Cost

1st one: A family has a rectangular kitchen which measures 12 by 18 feet. They want to put diagonal heating coils in the floor of the room. How much will it cost them to put in the coils if they cost \$25 foot? 12 x18 =216= Area 216x25= 5400 but since they want to put diagonals would I take half of this? 2nd one: A wi

### 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

### Reducing Speed Limit Requirements

The 42 kilometer drive from Oakdale to Ridgemont usually takes 28 minutes. Because highway construction requires reduced speed limit, the trip now takes 14 minutes longer. Find the reduced speed limit in km/hr.

### Square roots in a system of equations.

An explanation of the steps to use in a problem involving square roots in a system of equations using the sample problem given. Thank You. Please see attached.

### Modern Algebra Question

Modern Algebra Question If G is a group in which (a.b)^i =a^i.b^i for three consecutive integers i for all a,b belongs to G, show that G is abelian. The fully formatted problem is in the attached file.

### Inflection points calculations

What are the inflection points? (a) f(x) = 12x^5 +15x^4 -240x^3+19 (One of the inflections is 0. Find the rest. Results cannot be -2.82 and 2.07) (b) f(x) = (x^2 - 8x + 32)(x-4)

### 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

### Solving the logarithmic equation

(1-3v) s=1.59t solve for V

### 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

### THE DEPTH OF CUT OFF {d} FOR A SHEET

THE DEPTH OF CUT OFF {d} FOR A SHEET PILED RETAINING WALL IS GIVEN BY ONE OF THE SOLUTIONS OF THE FOLLOWING EQUATION; 27.402d3+223.518d2=364.7 FIND THE REQUIRED VALUE OF d TO THE NEAREST 0.1 METRE

### 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

### 176 passengers going from Boston to Denver on an Amtrak...

There are 176 passengers going from Boston to Denver on an Amtrak. The regular coach seat are \$103 and sleeper coach seat are \$199 . The receipt total was 24,080.00 . How do I find out many passenger purchase what type of ticket?

### Factorizing Functions Solved

Need help learn all the steps to solve these problems. Solve 3x^2 GE - 4x - 1 X^2-3x-3 +2 = 0 find all solutions