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# Algebra

### The rate of the boat in still water and rate of the wind

19. A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water? 20. A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?

### Six dozen equally priced oranges cost a total of n dollars.

Six dozen equally priced oranges cost a total of n dollars. In terms of n, what is the cost, in cents, of one orange. a. 25n/18 b. 18n/25 c. n/72 d. 72/n

### Average Annual Return

Henry invested \$12,000 in a new restaurant. When the restaurant was sold two years later, he received \$27,000. Find his average annual return by solving the equation 12,000(1+r)^2 = 27,000.

### Car's Collision Detector and Distance

A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

### High School Based Mathematics

Question 1: Write the word name for the number: 6,703,900,090. Question 2: Write this whole number in standard form: One hundred million, six thousand Question 3: Tammy wanted to determine the gas mileage she was getting on her car. She filled the gas tank on her car when the odometer read 49,420 miles.

### The sun has M = 2x10 30 . What is the Schwarzschild radius for the sun? [Note its true radius is 700,000.]

The Schwarzschild radius describes the critical value to which the radius of a massive body must be reduced for it to become a black hole. R = 2 G M / c 2 where G = gravitational constant 6.7x10 -11 M= mass of the object C = speed of light 3x10 8 The sun has M = 2x10 30 . What is the Schwarzschild radius for th

### Total Cost Equations

1. Allen bought 20 stamps at the post office in 37¢ and 20¢ denominations. If the total cost of the stamps was \$7.06, how many 37¢ stamps did Allen buy? 2. The profit on a watch is given by P = x2 - 5x - 9 and where x is the number of watches sold per day. How many watches were sold on a day when there was a \$15 loss?

### Solve by the Substitution Method

1) Solve by the substitution method 7x+5y=-12 -8x+y=54 What is the solution of the system? ( use an ordered pair. Use N if there is no solution) 2) Soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed to gather in order to get 360 lb mixture that is 11% protein? a. How many pounds

### Completing the Square Method with Conics

Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. 1) x2 + 12x - y + 30 = 0 Find the equation of the parabola determined by the given information. 2) Vertex at the origin, focus at (0, 3) Find the equation of the hyperbola. 3) Vertices at (0, 8) and (0, -8), fo

### Quick Mix Boxer Food Company

The Quick Mix Boxer Food Company wishes to introduce a package of dog treats which contains two new flavors of dog biscuits; liver and chicken which must meet certain nutritional requirements. The liver flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken flavored biscuits contain 1 unit

### Describe transformations on graph

State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or rotated about the y-axis are descriptions. a) g(x)=e^x-5 description of transformation: equation(s) for the horizontal asymptote(s): y-intercept in (x,y) form: b) h(x)=-e^x description of transformation: equat

### Sound Intensity and Loudness

Part 1 "Loudness" is measured in decibels, DB. I = I0 * 10 DB/10 (also typed as I =I0*10^(DB/10)) gives the intensity, I, of sound, where I0 is the intensity of the threshold of sound, or the sound that can barely be perceived. Using the library, web resources, and/or other materials,find the measure, in decibels, of a sound

### Multiply out ( x + 6 )( x3 - x2 - 5x + 1 )

Multiply out ( x + 6 )( x3 - x2 - 5x + 1 )

### Maximizing the Area of a Rectangle

Part 1: The equation A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L. Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land. Choose any two lengths for a rectangle and find the corresponding area for each using the given equation. Include units and show all

### Annual Inflation Rate Calculation

Find the most recent report of the annual inflation rate of a country of your choice as well as the type of currency used in that country. The equation S=C(1+r/100)^5 is to find the inflated cost S, in 5 years, of an item, good or service, where C is the current price of that item in that country's currency and where the inflati

### Transformation of graphs

Please see an attachment. 1) Describe the transformations on the following graph of f(x) = e^x . State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or rotated about the y-axis are descriptions. a) g(x) = e^x - 2 b) h(x) = - e^x 2) Describe the transformations

### Approximation of Pi Using Inscribed Polygons: Archimedes

Archimedes found his approximation to Pi by inscribed polygons. Start with a circle of radius 1 and a suitable starting polygon and solve for an inscribed polygon of 96 sides. Next, start with a unit circle and appropriate inscribed regular polygon to approximate Pi using a regular inscribed n-gon with 4096 sides.

### Mileage of Your Dream Car

My dream car is a Volkswagon Jetta (2008) MPG City 21, MPG Highway 29. Estimated Annual Fuel Cost \$1,751.00. Fuel tank capacity 14.5 gal. (55.0 L). Part 1: Using the Library, web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 50

### Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land.

Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land. Choose any two lengths for a rectangle and find the corresponding area for each using the given equation. Include units and show all calculations. Which of the two lengths that you chose gives a larger area? What is the corres

### Using the Karush-Kuhn Condition

1. Consider the LP Max z=c1x1+2x2+c3x3 Subject to x1 + 5x2+a1x3 &#8804; b1 X1-5x2+a2x3&#8804; b2 X1, x2, x3 &#8805; 0 The optimal tableau for this LP is 1 d1 2 1 0 30 0 d2 -8 -1 1 10 ------------------------------------ 0 d3 -7 d4 0 z - 150 Without u

### Writing Multi-Step Word Problems

I need to write 3 multi-step word problems with answers. One must use percentages, one must use exponents and the third can be any type. I have to include the process for solving each of the problems. The word problems don't have to be very difficult.

### Speed and distance word problems

1.The speed at which light travels is approximately 3.0 × 105 kilometers per second. How far will light travel in 1.5 × 101 seconds? 2. The distance from Earth to the planet Jupiter is approximately 4.5 × 108 miles. If a spaceship traveled at a speed of 2.5 × 104 miles per hour, how many hours would it take the spaceshi

### Some algebra questions involving rates

Gaining and losing weight are matters of caloric accounting: Calories in the food you eat minus Calories that you spend in activity. One pound of human body fat contains approximately 3,500 Calories. Based on information provided: Running 7 minute miles burns 979 calories per hour. Swimming at 2mph burns 408 calories per

### Factor completely

Factor completely: 4k2 + 12k + 9 a. ( 2k - 9 )( - 3k + 1) b. ( 2k + 3 )2 c. ( 2k - 3 )2 d. ( 2k + 3 )( 2k - 3) Question 2 Factor completely: x2 - 100 a. ( x + 10 )( x - 12 ) b. ( x + 10 )( x + 10 ) c. ( x - 10 )( x - 10 ) d. ( x + 10 )( x - 10 )

### An application of a rational function is Young's rule, which approximates the dosage of a drug prescribed for children.

Part 1: An application of a rational function is Young's rule, which approximates the dosage of a drug prescribed for children. a) Using the Library, web resources, and/or other materials, find the equation for Young's rule. State what each variable in the equation represents. Do not type the equation using the Equatio

### Horizontal and Vertical Asymptotes

1. How do you determine the vertical asymptotes, given the equation of a rational function? Illustrate with an example. Why can't the graph of that function cross the assymptote? Describe what happens to the graph of a function as the value of the independent variable approaches its vertical asymptote. 2. How do you determin

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?

### An art dealer sold two artworks for \$1520 thereby making a profit of 25% on the first work and 10% profit on the other

An art dealer sold two artworks for \$1520 thereby making a profit of 25% on the first work and 10% profit on the other, whereas if he had approached any exhibition he would have sold them together for \$1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork. A professor starte

### Population decline model

Population decline modeled by a rational equation P = P Suppose instead that the Population decline modeled by a rational equation P = P Suppose instead that the town experiences population decline that can be modeled by the following: P=P0/t+1 where t is the number of years from 2010.he town experiences population decline tha

### Linear Trend - Population growth

Choose the amount of population growth each year = example 350 (Hint: Choose a whole number for your growth rate, rather than a percent.) a) Fill in the following chart: Year (t) Population (P) t=0 P = 350 (2010) t=1 (2011) t=2 (2012) t=3 (2013) t=6 (2016) b) Find a linear equation in the form P