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mathematics
linear algebra

Questions and Answers of Linear Algebra

Suppose that $4100 is invested at 2.3%, compounded quarterly. How much is in the account at the end of 6 years?
Kathryn deposits $250 in a retirement account each month beginning at age 40. If the investment earns 5% interest, compounded monthly, how much will have accumulated in the account when she retires
Charles deposits $100 in a retirement account each month beginning at age 25. If the investment earns 4% interest, compounded monthly, how much will have accumulated in the account when he retires at
Sue and Richard want to establish a college fund for their daughter that will have accumulated $120,000 at the end of 18 years. If they can count on an interest rate of 3%, compounded monthly, how
Determine the terms and the degree of the polynomial. (a) 7x3 - 4x2 + 8x + 5 (b) -3n4 - 6n3 + n2 + 2n - 1 (c) 3a4b - 7a3b3 + 5ab - 2
Multiply. Assume that all exponents are natural numbers. (a) (an + bn) (an - bn) (b) (ta + 4) (ta - 7) (c) (an + bn)2
Perform the indicated operations. (a) 13ab2 - 4a2b - 2ab + 62 + (-ab2 - 5a2b + 8ab + 4) (b) (-6m2n + 3mn2 - 5mn + 2) + (4m2n + 2mn2 - 6mn - 9) (c) (2x + 3y + z - 7) + (4x - 2y - z + 8) + (-3x + y -
Factor out the largest common factor. (a) 3x + 18 (b) 5y - 20 (c) 2z3 - 8z2
Assume that variables in exponents represent natural numbers. (a) x2n + 5xn - 24 (b) 4x2n - 4xn - 3 (c) x2 + ax + bx + ab
Factor the trinomial. (a) w2 - 7w + 10 (b) p2 + 6p + 8 (c) x2 + 6x + 5
Factor the difference of squares. (a) z2 - 81 (b) m2 - 4 (c) 16x2 - 9
Factor the square of the binomial. (a) x2 + 12x + 36 (b) y2 - 6y + 9 (c) 9z2 - 12z + 4
Factor the sum or the difference of cubes. (a) x3 + 64 (b) y3 - 8 (c) m3 - 216
Factor completely. (a) 18a2b - 15ab2 (b) 4x2y + 12xy2 (c) x3 - 4x2 + 5x - 20
Factor by grouping. (a) x3 - 3x2 + 18x - 6 (b) x3 + 3x2 + 6x + 18 (c) y3 - y2 + 2y - 2
(a) x - 5 = 7 (b) y + 3 = 4 (c) 3x + 4 = - 8
(a) A = 1/2bh, for b(Area of triangle)(b) A = Ï€ r2, for Ï€ (Area of a circle) (c) P = 2l + 2w, for w (Perimeter of a rectangle)
Find the domain of the rational expression. (a) - 5/3 (b) 4/7 - x (c) 3x - 3/x(x -1)
Multiply or divide and, if possible, simplify.(a) r - s / r + s ∙ r2 - s2 / (r - s)2(b) x2 - y2 / (x - y)2 ∙ 1 / x + y(c) x2 + 2x - 35 / 2x3 - 3x2 ∙ 4x3 - 93x / 7x - 49
Add or subtract and, if possible, simplify.(a) 7 / 5x + 3 / 5x(b) 7 / 12y - 1 / 12y(c) 4 / 3a + 4 + 3a / 3a + 4
Perform the indicated operations and, if possible, simplify. (a) n(n + 1) (n + 2) / 2 ∙ 3 - (n + 1) (n + 2) / 2 (b) n(n + 1) (n + 2) (n + 3) / 2 ∙ 3 ∙ 4 (n + 1) (n + 2) (n + 3) / 2 ∙ 3 (c) x2
Simplify. Assume that variables can represent any real number. (a) √ (- 21)2 (b) √ (-7)2 (c) √(9y2)
Simplify and then, if appropriate, write radical notation. (a) (2a3/2) (4a1/2) (b) (3a5/6) (8a2/3) (c) (x6/9b-4)1/2
Write an expression containing a single radical and simplify. (a) 3√6√2 (b) √2 4√8 (c) 4√xy 3√x2y
Simplify. Assume that no radicands were formed by raising negative quantities to even powers. (a) √15 √35 (b) √21 √6 (c) √8 √10
A surveyor places poles at points A, B, and C in order to measure the distance across a pond. The distances AC and BC are measured as shown. Find the distance AB across the pond.
An airplane is flying at an altitude of 3700 ft. The slanted distance directly to the airport is 14,200 ft. How far horizontally is the airplane from the airport?
An equilateral triangle is shown below.(a) Find an expression for its height h in terms of a. (b) Find an expression for its area A in terms of a.
The diagonal of a square has length 8√2. Find the length of a side of the square.
The area of square PQRS is 100 ft2, and A, B, C, and D are the midpoints of the sides. Find the area of square ABCD.
Rationalize the denominator. (a) √3/7 (b) √2/3 (c) 3√7 / 3√25
Rationalize the numerator. (a) √50 / 3 (b) √12 / 5 (c) 3√(2 / 5)
Convert to radical notation and, if possible, simplify. (a) y5/6 (b) x2/3 (c) 163/4 (d) 47/2
Convert to exponential notation. (a) 5√(173) (b) (4√13)5 (c) (5√12)4 (d) 3√(202)
Convert to decimal notation. (a) 8.3 × 10-5 (b) 2.07 × 107
Convert to scientific notation. (a) 405,000 (b) 0.00000039
Write the answer using scientific notation. (a) (3.1 × 105) (4.5 × 10-3) (b) 2.5 × 10-8 / 3.2 × 1013
-7, 43, - 4/9, √17, 0, 2.191191119, 3√64, -22, - √2, 4 ¾, 12/7, 5√5. (a) Which are rational numbers? (b) Which are whole numbers? (c) Which are integers? (d) Which are real numbers?
Divide and simplify:3x2 - 12 / x2 + 4x + 4 ÷ x - 2 / x + 2
Subtract and simplify: x / x2 +9x + 20 - 4 / x2 + 7x + 12
Write an expression containing a single radical. (a) √y5 3√y2 (b) √(a + b)3 3√a + b / 6√(a + b)7
How long is a guy wire that reaches from the top of a 17-ft pole to a point on the ground 8 ft from the bottom of the pole?
The formulagives the monthly mortgage payment M on a home loan of P dollars at interest rate r, where n is the total number of payments (12 times the number of years). The cost of a house is $98,000.
The formulagives the monthly mortgage payment M on a home loan of P dollars at interest rate r, where n is the total number of payments (12 times the number of years). The cost of a house is
Multiply. Assume that all exponents are integers. (a) (ta + t-a)2 (b) (an - bn)3
Consider the numbers 6 6/7, √12, 0, -13/4, 3√8, - 1.2, 29, -5 (a) Which are whole numbers? (b) Which are irrational numbers? (c) Which are integers but not natural numbers? (d) Which are rational
Compute and write scientific notation for the answer: 2.7 × 104 / 3.6 × 10-3
Multiply and simplify: x2 + x - 6 / x2 + 8x + 15 ∙ x2 - 25 / x2 - 4x + 4.
Subtract and simplify: x / x2 - 1 - 3 / x2 + 4x - 5.
How long is a guy wire that reaches from the top of a 12-ft pole to a point on the ground 5 ft from the bottom of the pole?
Multiply: (x - y - 1)2.
Convert to scientific notation: 4,509,000.
The top x shareholders in a corporation each own y shares of a certain stock. The corporation's ownership is represented by a total of w shares of stock. Express the percent of the corporation owned
A corporation is having a shareholders' meeting. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by 2,351,000 shares of stock
A partnership owned equally by 13 partners is worth $1.3 million. The partnership loses a lawsuit worth $3 million. What is the value of any personal property each partner must forfeit to pay the
A sole proprietorship is worth w dollars. The owner loses a lawsuit against him for y dollars where y is greater than w. Express algebraically the value of the personal property the owner must
Six equal partners own a local pizzeria. The partners have made a tremendous profit and bought many personal items such as cars, boats, new homes, and so on. In order to protect their personal
Three people invest in a business. The first two invest in the ratio 2:3, and the third person invests twice as much as the other two combined. The total invested is $30 million. a. How much did the
Ten years ago, Lisa bought a hair salon for x dollars. She built up the business and it is now worth nine times what she paid for it. She decides to sell half of the business to a friend, and they
Four people invested in a restaurant. One person invested $100,000. Two others invested in the ratio x:2x, and the fourth person invested an amount equal to the other three investors combined. The
Tomika owns 3/5 of a law partnership. What percent of the partnership does she own?
Ryan owns three-eighths of a florist shop worth $76,000. What is the value of Ryan's share of the business?
A corporation issues 1,200,000 shares of stock at its beginning to shareholders. How many shares must a shareholder own to have a majority of the shares?
Elisa owns 28% of the Grudman Corporation. The rest of the shares are owned equally by the remaining six shareholders. What percent of the corporation does each of the other shareholders own?
Julie and Kristen are the partners in a local sporting goods shop. They needed $51,000 to start the business. They invested in the ratio 5:12, respectively. a. How much money did each invest? b.
Joe, Thea, and Taylor invested in a partnership in the ratio 1:4:7, respectively. Years later, when the partnership was worth $1.6 mil- lion, Thea decides to go to graduate school and sells her part
Why might the buyer and seller of the same stock both think that their trading price was an "astute" decision? How might those words apply to what you have learned?
At the end of the trading day on April 25, Texas Instruments Inc closed at $28.84, which was a + 5.22% net change from the previous day's close. What was the approximate close on the previous day?
On April 25, Berkshire Hathaway Inc closed at $126,875 per share. One year earlier, one share closed at $108,750. What was an approximate one-year percent change?
Write a formula that will convert the volume given in 1,000s into a volume given in 100s. Use the left side of the equation to indicate in which cell to store the formula.a. Intel Corpb. Yahoo! Inc
Write a formula to determine the percent change for each of the following. Use the left side of the equation to indicate in which cell to store the formula.a. Apple Incb. Cooper Tire & Rubber Co
Write a formula to determine the net change for each. Use the left side of the equation to indicate in which cell to store the formula.a. Microsoft Corpb. Cooper Tire & Rubber Co
Determine the volume for each of the following stocks.a. Berkshire Hathaway Incb. McDonald's Corporationc. Texas Instruments Incd. Westpac Banking Corporation
Determine the closing price on April 21 for each of the following stocks.a. Texas Instruments Incb. Freeport-McMoRan Copper & Gold Inc
Use the information from Exercise 5 to determine the percent of net change from April 21 to April 22 for each of the corporations listed in that question. Round answers to the nearest tenth of a
Which of the following is a true statement? Explain your reasoning. The 52-week high can never be higher than the day's high. The day's high can never be higher than the 52-week high.
How might those words apply to what you have learned? Why is the author warning readers that a share is not a lottery ticket?
Use the following data to construct a stock bar chart for the 5-day period.
Use the following data to construct a stock bar chart for the 5-day period.
Use the candlestick chart to answer the questions.a. On which days were opening prices higher than the closing prices? b. On which days were the closing prices higher than the opening prices? c.
Construct a candlestick chart for the information presented in Exercise 12.In Exercise 12
Construct a candlestick chart for the information presented in Exercise 13.In Exercise 13.
What was the day's opening price on the following days?April 28April 29April 30May 1May 2
What was the approximate net change from April 29 to April 30? Express that net change as a monetary amount and as a percent to the nearest tenth.
What was the approximate net change from April 30 to May 1? Express that net change as a monetary amount and as a percent to the nearest tenth.
Why might the author be warning readers to be cautious of averages? How might these words apply to what you have learned?
Use a spreadsheet to determine the 7-day SMA for Citigroup Inc.
Use a spreadsheet to determine the 10-day SMA for Dell Inc.
Use a spreadsheet to determine the 2-day, 3-day, and 5-day SMA.
The stock chart shows the 3-day and 10-day SMA for 20 consecutive trading days of Sony Corp stock. Identify the crossovers and discuss the implications.
The stock chart shows the 3-day, 5-day, and 10-day SMA for 16 consecutive trading days of General Electric Co stock. Examine days 6-16. Identify the crossovers and discuss the implications.
Use a spreadsheet to calculate the 2-day and 5-day SMA for ten consecutive day closing prices of Yahoo! Inc. Graph the closing prices and averages.
Determine the 3-day SMA for the ten consecutive day closing prices of Sprint Nextel Corp listed below. $7.78, $8.08, $7.99, $8.02, $7.89, $8.72, $9.19, $9.16, $8.98, $9.38
Determine the 5-day SMA for the ten consecutive day closing prices for MasterCard Inc listed below. $242.50, $273.98, $278.16, $293.94, $285.04 $290.80, $296.02, $291.01, $293.41, $286.85
Determine the 4-day SMA for the ten consecutive day closing prices for Wal-Mart Stores Inc listed below. $57.35, $58.61, $57.98, $58.07, $57.50 $56.97, $56.35, $56.83, $57.16, $57.18
Determine the 6-day SMA for the twelve consecutive day closing prices for Exxon Mobil Corp listed below. $92.60, $92.46, $92.45, $91.79, $93.07, $89.70 $89.61, $89.51, $90.07, $88.82, $89.93, $88.82
Determine the 2-day SMA for the ten consecutive day closing prices for Toyota Motor Corp listed below. $101.96, $101.80, $101.50, $103.07, $104.94 $105.12, $105.66, $104.76, $100.56, $101.31
Determine the 3-day SMA for the ten consecutive day closing prices for Procter & Gamble Co listed below. $66.21, $65.90, $67.05, $67.03, $66.80 $66.65, $66.65, $65.80, $65.92, $65.21
Determine the 4-day SMA for the ten consecutive trading day closing prices for International Business Machines Corp listed below. $121.69, $122.85, $120.70, $123.61, $123.18 $122.03, $122.82,
Determine the 6-day SMA for the ten consecutive trading day closing prices for Rite Aid Corp listed below. $2.65, $2.63, $2.70, $2.63, $2.50, $2.65, $2.66, $2.56, $2.52, $2.37

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