Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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Question 1139573: please explain:
Determine whether there is a maximum or minimum value for f(x) = -2x^2 + 3x + 4 and find that value
Click here to see answer by rothauserc(4718)

Question 1139653: Use the Gauss-Jordan elimination method to solve the system of linear Equations:
2x+3y-2z=10
3x-2y+2z=0
4x-y+3z=-1
Click here to see answer by Edwin McCravy(20054)

Question 1139652: Show that P³= span {x²+x³, x, 2x²+1,3}
Click here to see answer by ikleyn(52772)

Question 1139652: Show that P³= span {x²+x³, x, 2x²+1,3}
Click here to see answer by greenestamps(13198)

Question 1139686: Jesse's car gets 30 miles per gallon of gas.
(a) If Las Vegas is 240 miles away, how many gallons of gas are needed to get there and then home?
(b If gas is $3.04 per gallon, what is the total cost (in dollars) of the gas for the trip?
Click here to see answer by ikleyn(52772)

Question 1139684: Maurice is traveling to Mexico and needs to exchange $430 into Mexican pesos. If each dollar is worth 12.29 pesos, how many pesos will he get for his trip?
Click here to see answer by ikleyn(52772)

Question 1139685: An oatmeal cookie recipe calls for
1/2 cup of butter to make 6 dozen cookies. Hilda needs to make 15 dozen cookies for the bake sale. How many cups of butter will she need?
Click here to see answer by jim_thompson5910(35256)

Question 1139721: Hudson travels 1,350 miles in a jet and then 300 miles by car to get to a business meeting. The jet goes 375 mph faster than the rate of the car, and the car ride takes 1 hour longer than the jet. What is the speed, in miles per hour, of the car?
Click here to see answer by josgarithmetic(39615)

Question 1139729: Mike, an experienced bricklayer, can build a wall in 6 hours, while his son, who is learning, can do the job in 12 hours. How long, in hours and minutes, does it take for them to build a wall together?
Click here to see answer by ikleyn(52772)

Question 1139733: If y varies directly as x and y = 14 when x = 3, find the equation that relates x and y.
Click here to see answer by josgarithmetic(39615)

Question 1139734: If v varies directly as w and v = 5 when w = 1/2,find the equation that relates v and w.

Click here to see answer by josgarithmetic(39615)

Question 1139732: Ronald can shovel the driveway in 6 hours, but if his brother Donald helps it would take 3 hours. How long, in hours and minutes, would it take Donald to shovel the driveway alone?
Click here to see answer by josgarithmetic(39615)

Question 1139736: The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10 pound watermelon on a hanging scale, the spring stretched 5 inches.
(a) Write the equation that relates the length of the spring in inches, L, to the weight in pounds, p.
(b) What weight of watermelon (in pounds) would stretch the spring 6 inches?
Click here to see answer by josgarithmetic(39615)

Question 1139739: If v varies inversely with w and v = 6 when w = 1/3,find the equation that relates v and w.
Click here to see answer by josgarithmetic(39615)

Question 1139738: The area of a circle varies directly as the square of the radius. A circular pizza with a radius of 6 inches has an area of 113.04 square inches.
(a) Write the equation that relates the area in square inches, A, to the radius in inches, r.
(b) What is the area (in square inches) of a personal pizza with a radius 5 inches
Click here to see answer by josgarithmetic(39615)

Question 1139735: Joseph is traveling on a road trip. The distance in miles, d, he travels before stopping for lunch varies directly with the speed in mph, v, he travels. He travels 100 miles at a speed of 50 mph.
(a) Write the equation that relates d and v.
(b) How far would he travel (in miles) before stopping for lunch at a rate of 55 mph?
Click here to see answer by josgarithmetic(39615)

Question 1139728: When driving the 9 hour trip home, Sharon drove 420 miles on the interstate and 135 miles on country roads. Her speed on the interstate was 25 more than on country roads. What was her speed, in miles per hour, on country roads?
Click here to see answer by josgarithmetic(39615)

Question 1139737: The distance an object falls varies directly to the square of the time it falls. A ball falls 144 feet in 3 seconds.
(a) Write the equation that relates the distance in feet, d, to the time in seconds, t.
(b) How far (in feet) will the ball fall in 6 seconds?
Click here to see answer by Theo(13342)

Question 1139720: Byron wanted to try out different water craft. He went 124 miles downstream in a motor boat and 45 miles downstream on a jet ski. His speed on the jet ski was 10 mph faster than in the motor boat. Byron spent a total of 4 hours on the water. What was his rate of speed, in miles per hour, in the motor boat?
Click here to see answer by Theo(13342)

Question 1139839: I want to start a lemonade stand and need to determine how much lemonade I need to sell to break even each day.
If I know I spend $5 on supplies and sell the lemonade at $0.50 per glass determine the number of glasses I must sell to break even. After you find the number of glasses tell me what the x-intercept, y-intercept and slope represent in the function. Answer should include:
1. Number of glasses
2. x-intercept
3. y-intercept
4. slope
Thank you very much.
Click here to see answer by josgarithmetic(39615)

Question 1140055: Profit made by a company when 60 units are sold is R1600. When 150 units are sold profit increases to R5,200. Assume that profit function is linear and of the form - P(u)= a + b(u) where P is profit in Rands and 'u 'is the number of units sold. Determine 1. the Values of a and b. 2. The breakeven level and 3 how many units will yield R12,000 profit?
andoh@cjassociates.co.za
Click here to see answer by josgarithmetic(39615)

Question 1140155: using the linear programming we have startup arm at least 12%
In financial stock return has 3% and retail arm has 5% and the invested money is 100,000,000 so what is the correct answer?
Click here to see answer by ikleyn(52772)

Question 1140374: 2x + y ≤ 50
Click here to see answer by MathLover1(20849)

Question 1140385: please explain:
If f(x)=4/x and g(x)=3x^5, find (g ∘ f)(x)
thank you.
Click here to see answer by Alan3354(69443)

Question 1140385: please explain:
If f(x)=4/x and g(x)=3x^5, find (g ∘ f)(x)
thank you.
Click here to see answer by Theo(13342)

Question 1140385: please explain:
If f(x)=4/x and g(x)=3x^5, find (g ∘ f)(x)
thank you.
Click here to see answer by ikleyn(52772)

Question 1140384: please explain:
Determine whether f(x)=6/(x+5) is one-to-one. If it is one-to-one, find a formula for the inverse.
Click here to see answer by MathLover1(20849)

Question 1140383: please explain:
Find f(x) and g(x) such that h(x) = (f ∘ g)(x). h(x)=√(12x^2+21)
Thank you.
Click here to see answer by josgarithmetic(39615)

Question 1140518: Solve by any method
{5x-2y=31
{2x-y=-13
Click here to see answer by greenestamps(13198)

Question 1140516: A consistent dependent system of linear equations has how many solutions?.
Click here to see answer by ikleyn(52772)

Question 1140981: The Royal Fruit Company produces two types of fruit drinks. The first type is
70%
pure fruit juice, and the second type is
95%
pure fruit juice. The company is attempting to produce a fruit drink that contains
75%
pure fruit juice. How many pints of each of the two existing types of drink must be used to make
70
pints of a mixture that is
75%
pure fruit juice?

Click here to see answer by josgarithmetic(39615)

Question 1141287: f(x) = −x^2 + 8x − 16
Rewrite the function in
f(x) = a(x − h)2 + k
form.
Click here to see answer by Boreal(15235)

Question 1141287: f(x) = −x^2 + 8x − 16
Rewrite the function in
f(x) = a(x − h)2 + k
form.
Click here to see answer by josgarithmetic(39615)

Question 1141288: f(x) = 5x^2 − 10x + 7
Rewrite the function in
f(x) = a(x − h)2 + k
form.
Click here to see answer by josgarithmetic(39615)

Question 1141288: f(x) = 5x^2 − 10x + 7
Rewrite the function in
f(x) = a(x − h)2 + k
form.
Click here to see answer by greenestamps(13198)

Question 1141289: f(x) = 2x^2 + 12x + 15
Rewrite the function in
f(x) = a(x − h)2 + k form.
Click here to see answer by josgarithmetic(39615)

Question 1141273: The table shows the minimum wage rates for the United States during different years.
(a) Write the least squares regression equation that models the data. Let x = time in years since 1900 and let y = minimum hourly wage. Round to the nearest thousandths place.
(b) Use the equation to estimate the minimum hourly wage of a U.S. worker in 2028. Show your work.
Answer:
Year
1978
1979
1980
1990
1991
1996
1997
2007
2008
2009
Minimum hourly wage ($)
2.65
2.80
3.55
3.85
4.25
4.75
5.25
5.85
6.65
7.45
Click here to see answer by Boreal(15235)

Question 1141298: f(x) = 4x2 + 8x + 6
Rewrite the function in
f(x) = a(x − h)2 + k form.
Click here to see answer by josgarithmetic(39615)

Question 1141297: f(x) = 2x^2 + 12x + 15
Rewrite the function in
f(x) = a(x − h)2 + k form.
Click here to see answer by josgarithmetic(39615)

Question 1141304: f(x) = 2x^2 + 12x + 15
Rewrite in f(x) = a(x − h)^2 + k form.
Click here to see answer by josgarithmetic(39615)

Question 1141899: Formulate but do not solve the following exercise as a linear programming problem.
A hunger-relief organization has earmarked between $2 million and $3.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.75 million (inclusive), and Country B is to receive at least $0.25 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.70. How should the aid be allocated if the money, in millions, is to be utilized most effectively according to these criteria?
Hint: If x and y denote the amount of money, in millions of dollars, to be given to Country A and Country B, respectively, then the objective function to be maximized is
P = 0.4x + 0.7y.

max amount both countries receive collectively x + y ≤
min amount both countries receive collectively x + y ≥
max amount Country A receives x ≤
min amount Country A receives x ≥
min amount Country B receives y ≥

Click here to see answer by ikleyn(52772)

Question 1141898: Formulate but do not solve the following exercise as a linear programming problem.
A nutritionist at the Medical Center has been asked to prepare a special diet for certain patients. She has decided that the meals are to be prepared from Foods A and B and that the meals should contain a minimum of 380 mg of calcium, 10 mg of iron, and 40 mg of vitamin C. Each ounce of Food A contains 30 mg of calcium, 3 mg of iron, 5 mg of vitamin C, and 4 mg of cholesterol. Each ounce of Food B contains 25 mg of calcium, 0.5 mg of iron, 5 mg of vitamin C, and 5 mg of cholesterol. How many ounces of each type of food should be used in a meal so that the cholesterol content C (in mg) is minimized and the minimum requirements of calcium, iron, and vitamin C are met?
Minimize C = subject to the constraints
calcium=

iron =

vitamin C=

x ≥ 0
y ≥ 0
Click here to see answer by Theo(13342)

Question 1142505: Form a differential equation by eliminating the arbitrary constants y = Ae^x + Bcosx
Click here to see answer by ikleyn(52772)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760