Algebra question and answers for December 21, 2023
- Q a) Write down two examples of polynomials.b) Identify the constant term, degree, and leading coefficient of your polynomials.
- Q 1. Find the GCF of the following:a) xy, yx, xyb) x, x, xc) y(2y - 1), 3(2y - 1)2. Identify the missing factors:d) 20 = (4) (?)e) -14x = (7)(?)f)...
- Q Perform the operations and simplify.a) 5x(x+3)? 4(x - 7x)b) (3x - 2y) (5x + y)c) (2a - b)
- Q 1. Write the following real numbers in ascending order {i.e. from least to greatest}|-10.1| , |-21/2| , 9.8, |10|, 10, |-9,9|, |9+7/8|, 9
- Q Explain in your own words how to divide a polynomial by a monomial. Perform the operation and simplify: {(12x)-(21x)/(3x)}
- Q Use the half-angle formulas to simplify the expression.?1-cos 10x/2Solve the equation. (Find all solutions of the equation in the interval [0, 2?). Enter your answers as a comma-separatedlist.)3 sin(4x) =...
- Q A farmer picks 242 apples on Monday and 118 apples on Tuesday. On Wednesday, she sells 109 of the apples at the market. Which equation can be used to find...
- Q g(x) = 78-7xFind x when g(x) = 43. (Just type the number).________
- Q (Restrictions, linear equations, interval notation, domain) To find the domain of a function we need to find restrictions on x by solving an equation and write our answer in interval...
- Q If a(3, 4) - b(2, 4) = (8, 10), determine a and b. Just enter the answers for a and b. NO NEED TO SHOW WORK!
- Q Let n be an odd integer ? 25.(1) Find the number of pairs (x, y) of positive integers which satisfy theequation x + 2y = n.(2) Find the number of...
- Q Which of the following graphs is the correct plot of y = - 3 cos(x)?
- Q 1 2 3a=2 3 4 1 5 8a)If the matrix of cofactors from A is 4 -12 7 ...
- Q Find the variation constant and an equation of variation where y varies directly as x and y = 18 when x = 3.The variation constant is k = ______.
- Q Determine if a graph is a function.Is this the graph of a function?NoYes
- Q Sketch a graph of the function f(x) = 0.5 sin(4x).
- Q An object was dropped off the top of a building. The function f(x) = -16x +484represents the height of the object above the ground, in feet, a seconds after being...
- Q Find an equation of variation where y varies inversely as the square of x, and where y = 0.76 when x = 0.1.The equation of variation is y =
- Q Convert the angle 477 to radians. Give the exact value. This means there should be a ? in your answer. Also, any fraction in your answer should be fully reduced.
- Q Graph the trigonometric function. y = -3 cosec(2/3x)Start by drawing three consecutive asymptotes. Then plot two points, one on each side of the second asymptote. Finally, click on the graph-a-function...
- Q Write the series using summation notation.1/3+1/9+1/27+1/81....
- Q For y = 3 sin 8x,its amplitude isits period is
- Q The maximum number of grams of fat (F) that should be in a diet varies directly as a person's weight (W). A person weighing 144 lb should have no more...
- Q If ? =-1?/6, thensin (?) =?cos(?) =?Give exact values. No decimals allowed!Example: Enter sqrt(2)/2 for ?2/2. With functions like sqrt, be sure to use function notation(parentheses). sqrt(2)/2 will work, but...
- Q For f(x) = a*sin(bx), use: Amplitude = |a|;Period T = 2.?/|b|Section Width a.k.a. Distance between Critical Points = T/4Without graphing the function y= -3sin(6x), determine its amplitude, period, and the...
- Q Find an equation for the line perpendicular to 2x + 4y = 24 and goes through the point (3, -3). Write your answer in the form y = mx +...
- Q 14. Determine whether the series ? ? (-1)?/{n^[(n+1)]} n=1is conditional convergent, absolute convergent,...
- Q Suppose that there are weather patterns in a city. If it is sunny, there is a 20% chance that it will be rainy the next day. If it is raining,...
- Q Let ABC be triangle and I its incenter. Denote D the midpoint of BC and E a the midpoint of arc BC containing vertex A. Prove angle IDB = angle...
- Q The position(m)-time(sec) data for a moving body is given: 0 0.25 0.5 0.75 1.25 1.5 13 10.2 17.2 26.2 33.1 39.1 Approximate the velocity at time t = 1.25 sec...
- Q Without graphing the function y = 10 cos (5x), determine its amplitude and period. Leave answersin exact form; type pi for .amplitude =period =
- Q Without graphing the function y = 6 sin(10x), determine its amplitude and period. Leave answersin exact form; type pi for ?.amplitude =period=
- Q You want to purchase an automobile for $25,865. The dealer offers you 0% financing for 60 months or a $3,260 rebate. You can obtain 6% financing for 60 months at...
- Q Solve the system of linear equations by graphing.y = 2x6x + y = 8
- Q 2a. The doubling time for dorkism is 4 weeks. That is, with a given amount of dorkism in your system, it will double every 4 weeks, so you'll be twice...
- Q Find the first four terms of the sequence.f(n)=5n-2a? =
- Q Find the next 3 terms of the arithmetic sequence 5, 15, 25, 35,The next 3 terms are
- Q Write 4 additional terms of the geometric sequence 5, 10, 20, ... .The next 4 terms in the geometric sequence are
- Q Write the first four terms of the sequence.an = an-1 +4, a? = 6What is the first term? a?=
- Q Find the first four terms of the sequence with first term 9 and nth term an = 4an-1 +5.a? =(Simplify your answer.)
- Q Find the sum of the first 10 terms of the geometric sequence 2, 4, 8...(Type an integer or a decimal.)
- Q 4. Suppose the a function of two variables f(x, y) satisfiesf = af? + bfyProve that if there is a constant M >0 such that f(x, y)| < M for...
- Q Write an equation for a line perpendicular to y = -5x - 5 and passing through the point (-10, 0).y = ________
- Q Match each equation below to the curve it represents. Each answer should be A, B, C, D, E, F, or G.CURVESA. Circle,B. Ellipse,C. Point,D. Parabola,E. Empty Set,F. Intersecting lines,G. Hyperbola,EQUATIONSa)...
- Q Find the distance, d, between (-1,2) and (3,4), and find the midpoint, M, between these points.a) d=?20, M=(1,3)b) d=?52, M=(1,3)c) d=8, M=(3,2)d) d=1, M=(1,1)
- Q Find an equation for the line parallel to y = -x + 9 and goes through the point (4,- 9). Write your answer in the form y = mx +...
- Q Find the rules for the composite functions fo g and go f.f(x)=?(x+2); g(x) =1/(x-2)fog=_______gof=_______
- Q For the following differential equation, determine (without solving) an interval on which the solution of the equation is certain to exist and be unique. Justify youranswer.(Int)y' + y = e?...
- Q Factor out the greatest common factor in the expression.3x? - 33x + 15xSelect the correct choice below and fill in any answer boxes within your choice.A. 3x?-33x + 15x =...
- Q Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.(9,2), (8,-6)Choose the equation of the line in the form...
- Q A job placement agency advertised that last year its clients, on average, had a starting salary of $29,500. Assuming that average refers to the mean, which of the following claims...
- Q Factor out the greatest common factor in the expression.3x?-21x +33xSelect the correct choice below and fill in any answer boxes within your choice.A). 3x?-21x +33xB). The polynomial is prime.____
- Q Factor the difference of two squares.x - 121Select the correct choice below and fill in any answer boxes within your choice.A. x-121=_________B. The polynomial is prime.
- Q (a) Find the rational zeros and then the other zeros of the polynomial function f(x) = 2x + 7x + 98x + 343, that is, solve f(x) = 0.(b) Factor...
- Q A 26-ft ladder leans against a building so that the angle between the ground and the ladder is 80.How high does the ladder reach on the building? Round to the...
- Q Write-2-log? +log?(x + 1) + log, y as a single logarithm with coefficient 1.log?(x + 1)^1/(1/2)y/16x
- Q Simplify. Assume that all variables represent positive real numbers.-?180x?y?
- Q Mary invested her $45,000 bonus in an account earning 7.1% annual interest that is compounded continuously. How long will it take the account to triple in value? Round your answer...
- Q Graph the linear equation.x-3y = -9Use the graphing tool to graph the equation.
- Q Divide as indicated.y-64/yy+8/y-8Select the correct choice below and fill in the answer box(es) to complete your choice.(Simplify your answer. Use integers or fractions for any numbers in the expression. Use...
- Q Factor the given polynomial.x + 5x+6Select the correct choice below and, if necessary, fill in the answer box within your choice.A. x + 5x + 6 =_______B. The polynomial is...
- Q Can a triangle have sides with the given lengths? Explain.5.) 4 m, 8 m, 6 m.6.) 2.6 ft, 4.1 ft, 6.7 ft
- Q Given the definition of the main window of the periodic functiong(t) = t-t, -1 < t < 2, g(t + 3) = g(t)The window to the right of this window...
- Q The product of two consecutive room numbers is 110. Find the room numbers.The number of the first room, or the smaller room number, is ____The number of the second room...
- Q If tant =-5/12 and 3?/2< t < 2 ?, find sint, cost, sect, csct, cot t.Enter the exact answers.sin t =cos t =sec t =csc t=cot t =
- Q Three sequences are defined as follows:a?= 1 and an+1 = bn+cnb? = 2 and bn+1 = an + Cn,c?= 3 and Cn+1 = an + bn.(a) Use a spreadsheet to...
- Q Add or subtract.5?48 - 2?32 + ?275?48 - 2?32 + ?27 = ____
- Q Replace the radical with a fractional exponent. Do not simplify.(x?)/? = ________
- Q Chris can be paid in one of two ways. Plan A is a salary of $360 per month, plus a commission of 9% of gross sales. Plan B is a...
- Q A family has a $98,162, 30-year mortgage at 6.3% compounded monthly. Find the monthly payment. Also find the unpaid balance after the following periods of time..(A) 10 years (B) 20...
- Q Show that Z is integrally closed. and more generally, show that a UFD is integrally closed.
- Q Determine whether each sequence is arithmetic, geometric, or neither. (Write yourfinal answers down here and include your work in your File Upload to receive full credit.)(a) 4, 12, 16, 24,...
- Q Find the partial sum S12 for the arithmetic sequence with a = 6, d= 7.S12
- Q Let G be an abelian group acting on a set X. Suppose that there is only one orbit under this action. Assume that G||X|. Prove that there exists e?g ?...
- Q Find a power series for the function, centered at c.F(x) = 4/3-x, c=1Determine the interval of convergence. (Enter your answer using interval notation.)
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