Algebra question and answers for December 24, 2023
- Q A jar contains 30 black marbles and 15 white marbles. You draw one marble at random. If you draw a black, you win $6. If you draw a white, you...
- Q In Exercises 13-14, find the dimension n of the solution space W of Ax = 0, and then construct an isomorphism between W and R" 1 1...
- Q Use the like bases property to solve the equation5? -=125n =
- Q Find the distance between the skew lines P(t) = (4, 3,0) + t (?2, ?3, 2) and Q(t) = (?3,?1, 5) + t (1, 3, -1). Hint: Take the cross...
- Q Find an equation of the circle that has center (-1, 4) and passes through (5,-2).
- Q Let the subspace V C R is given byv={ x? x? x?) : x?+3x?+2x?=0}Find a basis of V
- Q Joseph invested $89,000 in an account paying an interest rate of 6.6% compounded how long would it take, to withdrawals are made, quarterly. Assuming no deposits or the nearest tenth...
- Q Your employer automatically puts 15 percent of your salary into a 401(k) retirement account at the beginning of each year. The account earns 9% interest (compounded continuously). Suppose you just...
- Q Elijah is going to invest in an account paying an interest rate of 5.5% compoundedcontinuously. How much would Elijah need to invest, to the nearest hundred dollars, for the value...
- Q Charlie reads quickly. He reads 1(3/7) pages every 2/3 minutes. Charlie reads at a constant rate.How many pages does he read per minute?____________pages per minute
- Q Solve.3?(x+1) - 2 = 0Do not include x = in your answer. If there is no solution, the answer is the empty set
- Q Find a vector that has the same direction as <-2, 4, 2> but has length 6.
- Q A person invests 10000 dollars in a bank. The bank pays 6.5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money...
- Q Solve ?2x-5+ ?2x = 5If there are multiple answers, list them separated by a comma. For example 1, 2. If there is no solution, indicate this with the empty set...
- Q Which of the following points are on the graph of y = -2x - x -8?Select all that apply.A) (14, -414)B) (-13, -333)C) (-8, -128)D) (-4,-35)E) (15,- 473)F) (-12, -283)
- Q Express using rational exponents. ?aProvide your answer below:
- Q Provide a possible/general partial fraction decomposition of the rational expressionf(x)/x(x - 1)(x + 5)?(x + 2x + 9), where f(x) is a polynomial without common factors and is degree 6.
- Q Evaluate each sum.(a) 2+5+8+-+98=(b) 5 - 10/3 + 20/9 - 40/27 + .... =
- Q Caleb bought groceries and paid $1.60 in sales tax. The sales tax rate is 2.5%. What was the price of Caleb's groceries, before tax?
- Q In triangle ABC, m?A = 38 degrees, m?C 101 degrees, and the length of AB = 8.Find the measures of the other sides and angles.m?B = ___________ degreeslength of AC=...
- Q A person invested $7, 400 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 4...
- Q Perform the operation. Give your answer in radical form. You may leave the radicand in exponential form.[(5)^1/2]. [(25)^1/5]
- Q Write out your answer in order of the variable indices to receive full points!1 0 0 2 -10 1 0 1 30 0 0 0 0Write the solution in (a)...
- Q Evaluate each expression.9) log?? 410) log?? 1/311) log? 1/81
- Q A school choir needs to make T-shirts for its 75 members and has set aside some money in their budget to pay for them. The members of the choir decided...
- Q Simplify. (Assume all variables are nonnegative.) (3?2x - ?3x) - (?2x - 7?3x)Provide your answer below:
- Q Select the factors that multiply to create a polynomial.with this description:(1) Leading term is 5x?(2) Has four real roots(3) Has zeros at x = 1 and x = -2(Select all...
- Q Consider the difference equation yt+1(a+byt) = cyt, t = 0,1, .... , where a, b, and c are positive constants, and yo > 0. Show that yt > 0 for...
- Q Given that g(x)=x-2x-6, find (g o g)(-3).
- Q A parabola can be drawn given a focus of (-8,-5) and a directrix of x = -2. What can be said about the parabola?
- Q Let A be a 7 x 6 matrix such that Ax = 0 has only the trivialsolution. Find the rank and nullity of A.Let A be a 5 x 7...
- Q Write a cosine function that has a midline of 2, an amplitude of 5 and a period of 4/3.
- Q Zombies lose limbs. Mutants grow limbs. Mutant-zombies do both. Today, a certain mutant-zombie grew 5 limbs, lost 12 limbs, and grew another 2 limbs.What is the change in number of...
- Q Solve tan(x)=-?5 on 0?x<2?There are two solutions, A and B, with A<BA = B = Give your answers accurate to 4 decimal places
- Q State the amplitude, period, and increment for each function. Then graph.y=-3 sin 2xAmplitude:Period:Increment:y = 2 cos 2xAmplitude:Period:Increment:
- Q Jerome will be buying a used car for $10,000 in 2 years. How much money should be ask his parents for now so that if he invests it at 10%...
- Q A new car is purchased for $18, 000 and over time its value depreciates by every 4 years. What is the value of the car 17 years after it was...
- Q Determine the order of each of the following quotient groups.1. (a) Z? /([4])2. (a) Z?/([3])
- Q Express the equation in exponential form(a) log? 4 = 2.That is, write your answer in the form 2 ? =B thenA =___ and B =____(b) log?125 = 3.That is, write...
- Q Determine all possible exact values of ? between 0 degrees and 360 degrees that satisfy the equation sin? =cos150.
- Q Simplify 1 + cot(t)/(1 + tan(t)) to a single trig function.a) Use Reciprocal Identities to rewrite the expression to only have sine, cosine or tangent funciton.b) Times an appropriate trig...
- Q Prove that limx?0 sin(1/x) does not exist in R.
- Q Anna invested $28,000 in an account paying an interest rate of 6.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to thenearest tenth of...
- Q Write the sum without sigma notation and find its sum.k=0?10 1/(k + 1)(k + 2)
- Q Given that sin(a) = 1/3 and cos(b)= -2/6 with a and b both in the interval [?/2, ?]find the exact values of sin(a + b) and cos(a ? b).Step 1:...
- Q A plane has an airspeed of 127 km/h. It is flying on a bearing of 71 while there is a 20 km/h wind out of the northeast (bearing 225) What...
- Q Evaluate the following expression. DNE if the expression is undefined.a) arcsin ( sin(( 38?/8 )) =_____b) arccos(cos(3?/8 ))=___c) cos?( sin(5?/3)=___
- Q Decide whether it would be more convenient to solve the system of equations by substitution or elimination.3x+8y=-1314x +3y/5 = -10Select the correct answer below:O eliminationO substitution
- Q sin(?) =-9/41 where 3?/2< ? < 2?.Use the given information about to find the exact value of cos(2?).
- Q Express the equation in logarithmic form:(a) 4 = 16 is equivalent to log? A = B.A =andB=(b) 10^(-4) = 0.0001 is equivalent to log?? C = D.C =andD =
- Q Simplify (-8?3+6?15) - (?3-?15).Provide your answer below:
- Q Calculate the perimeter of the triangle formed by the following set of vertices. {(-2,-2), (2, 2), (3,-7)}
- Q Determine the parametric equation of a line that goes throughA(3,5,7) and is perpendicular to the line (3,-5,2) +t(3,-3,3)
- Q Let f(x) = 2x - 1 and g(x) = x 4.Find (f o g)(-2).Then (f o g)(-2) = ______
- Q In (r, q) coordinates A = (83.0, 344 degrees) and B = (69.0, 2.90E2 degrees). Given R = A - B(a) In polar coordinates the resultant vector is R =)Rr,...
- Q Simplify ?ab
- Q Simplify the expressions below as much as possible. Leave no negative numbers under radicals.?(-27)/?(-9) = ?(-20).?(-5) =
- Q Simplify: ?(48a?b). Present the answer in the simplest way.Provide your answer below:
- Q Find how much money needs to be deposited now into an account to obtain $3,700 in 5 years, if the interest rate is 3.5% per year compounded continuously.
- Q What is tan 11?6 ?A.)-?3/3B )?3/3C.)-?3D.)?3
- Q Determine the amplitude and period of the function y = 3 sin(2x). Then, graph the function over its single period using five key points.
- Q Use the equation = 16.665 -0.21x to find the value of ? given x = 48. Round the result to the nearest tenth. ?=____
- Q Find the equation of the tangent line to the curve y = 3 sec x - 6 cos x at the point (?/3, 3). The equation of this tangent line...
- Q The observed bunny rabbit population on an island is given by thefunctionp=-0.4t + 130t + 1200where t is the time in months since they began observing the rabbits.1. When is...
- Q Evaluate: - ??(243).Provide your answer below:
- Q Write the expression log?(x ?y) as a sum of logarithms with no exponents or radical.
- Q Calculate the distance between (-1/2,2) and (5/3,-2/3).
- Q Number of Brokers Who Sold x Houses in June. x 1 2 3...
- Q Find the point that is symmetric to the point (4, -2) with respect to the x-axis, the y-axis, and the origin.The point symmetric to (4, -2) with respect to the...
- Q Solve the system by graphing: y<3x +2 ...
- Q Steve wants to grow his $45000 savings to $59000 before his travels around the world. How long will this take if the bank is offering 6.1% annual interest compounded monthly?...
- Q Drag each tile to the correct box.Arrange the complex numbers in order according to the quadrant in which they appear, starting with the first quadrant.3-4i -1-3i ...
- Q Graph polynomial function f(x)=x+5x-x-5 by finding zeros, y intercept, end behavior, and other pertinent information. All work must be shown algebraically.
- Q A heavy log is dragged across the ground by two horses pulling on ropes (see the figure below). The magnitudes of the tension forces in the direction of the ropes...
- Q graph g(x) = x^2 - 2x - 8what are the x and y intercepts?
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