Algebra question and answers for October 13, 2023
- Q Decide if the following is rational or irrational: ?64
- Q Add or subtract as indicated and write the result in standard form.(5 - 6i) + (9 +91)14-3i-14-3i14 + 3i-4 + 15i
- Q Find the product and write the result in standard form.(-6 +9i)(5 + i)-21 +39i-21-51i-39 + 39i-39 - 51
- Q Suppose a is a non-zero algebric number and 3 is a transcendental number. Show that a +3 and a are transcendental numbers.
- Q Divide and express the result in standard form.4+5i / 5-4i-1 1i-i
- Q Multiply.[x-(6-2i)][x-(6+2i)]Note that these expressions contain complex numbers. Simplify your answer as much as possible.
- Q Find all zeros of f(x) = x + 4x + x + 4. Enter the zeros separated by commas, using exact values, not decimal approximations.
- Q Let z be a complex number, and let n be a positive integer such that z" = (z + 1)" = 1.a) Prove that |z| = |z + 1| =...
- Q Solve the inequality: -25> x - 27Enter your answer as an interval, such as [a, ?).
- Q Let Po, P?, and p? be the orthogonal polynomials described below, where the inner product on P4, is given by evaluation at -2, -1,0, 1, and 2. Find the orthogonal...
- Q For each subfield S of Q[i, z], determine Auts (Q[i, z]).
- Q Use the given transformation to evaluate the integral.where R is the triangular region with vertices (0, 0), (7, 1), and (1, 7).x = 7u + v, y = u +7v
- Q If z = x + iy and z+3/z-3 lies on the y-axis of complex plane, where z ?3, then which of the following options is correct? (a) y = 0(b)...
- Q A 100 acre plot of land has a concentration time of 80 minutes. The area is residential single family homes with a C-0.40. What is the percent increase in stormwater...
- Q Find the angle ? between v=cos 7?/4i+sin7?/4j and z= cos4?/3i+sin 4?/3j.
- Q Evaluate ?/3 using a double angle indetity
- Q Evaluate T/3 using a double angle indetity
- Q Find all solutions to 2 cos (0) = -1 on the interval 0 ? 0 < 2m.Solve 7 sin(26) +5 sin(o)= 0 for all solutions 0 < < 2.Give your...
- Q ABCD is a parallelogram with coordinates A(4, 2), B(3,-1), C(-1,-1),and D(-1, 2). To prove that ABCD is a rhombus, you would plot the parallelogramon a coordinate plane and then find...
- Q Verify the identity:cos (2A)/ 1 + sin (24)= cot A-1/cot A + 1
- Q The population in a certain city was 58,000 in 2000, and its future size is predicted to be P(t) = 58,000 e 0.014t, where t is the number of years...
- Q What is the linen valuation of bath towels in a property that has 2,500 pieces in stock purchased at $14.95 each and 288 just bought at $16.50 each?a $43,92350b $39,423.50C...
- Q Find all the zeros of the polynomial f(x)=x-x+2x - 4x-8 given that -2i is a root.
- Q 1. Cooking temperature for chicken should be between 165 and 175 degrees F.Inequality; 165 ?x? 175Interval notation; [165 F,175 F]2. The number of shipments should not exceed 10.Inequality; x <...
- Q Which of the following statements is FALSE?f(z)=z + 1/z+1 is a fractional linear transformationf(z) = z is a conformal map from the right half-plane {z : Re(z)>0} onto its imageIf...
- Q Let a, b, c be complex numbers satisfyingb-a /c - a=a-c/b-cConsidering the triangle with vertices a, b, c. Prove |b-a| = |c-a| = |b-c|.
- Q The half-life of radium-226 is 1600 years. Suppose you have a 20-mg sample. How long will it take to decay to 7-mg? Round to 4 decimal places.
- Q ln (3, 5) secret sharing scheme, the dealer selects K=15, h(x)=5x^2+6x+15 mod 19. show how three shadow holders x-=1,3 and 5 can construct the master secret K
- Q Find all the complex fourth roots in rectangular form of w = 81( cos 4?/3 + i sin 4?/3 ) z0z1z2z3
- Q Consider the set of real numbers and the set of complex numbers. Is every real number also a complex number? Is every complex number also a real number? Explain.
- Q If cos ? = 3/4 and ? terminates in Quadrant IV, find the exact value of each of the following. Caution: The triangle is not a 3-4-5 since the hypotenuse...
- Q If function h has an inverse and h-(1) = -4, find h(-4).h(-4)=
- Q A Chevrolet Sonic Hatchback costs $14,785.00. With a 11% down payment, you can have an amortized loan for 8 years at a rate of 4.5%.What will the monthly payment be?How...
- Q State the intervals of the domain where the given function is increasing or decreasing. You may want to create a graph of the function, using your knowledge of transformations, in...
- Q One of your tenants has ten years remaining on a lease at $3,500 per month. The space is now worth $4,000 per month. An adjacent tenant wants to expand their...
- Q For the function given below, set up and then completely simplify the expression forf(x+h)-f(x)f(x)=7x - 4xFor partial credit, enter the first step, just the meaning of the calculation in its...
- Q A rental car company charges $35 plus 40 cents per each mile driven.Part1. Which of the following could be used to model the total cost of the rental where m...
- Q Use the "Five-Point Method" for graphing one period of the following function:y = -3 sin[2(x - ?)]
- Q A soap manufacturing company was distributing a particular brand of soap through a large number of retail shops. Before a heavy advertisement campaign, the mean sales per week was 140...
- Q A movie theater has a seating capacity of 203. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there...
- Q What was transferred from the hydrochloric acid to the water molecule?Click on the background to slide down the LabPad and have a look again.a) A hydrogen atomb) An electronc) H+d)...
- Q In Electrical Engineering, complex numbers are used to describe current, voltage, and impedance in a circuit, and these three quantities are related by the equation E = IZ. Find Z...
- Q For f(x) = x + 2 and g(x) = 5x + 5, find the following functions.a. (fog)(x); b. (gof)(x); c. (fog)(0); d. (gof)(0)a. (fog)(x) = (Simplify your answer.)
- Q The accessories buyer sold a group of pearl earrings very well. 1150 pairs were sold at $10.00 each. To clear the remaining stock the buyer reduced the remaining 50 pairs...
- Q Determine whether the set W is a subspace of R with the standard operations. Justify your answerW = {(a,a-3b,b): a and b are real numbers}
- Q Find the inverse of the function.y = 8x 6Select one:a. 3x/4b. 4x/3c. x+6/8d. X-6/8
- Q A real estate license holder may do all of the following EXCEPTA) explain business details.B) explain the general content.C) explain factual statements.D) give legal advice.
- Q When a legally enforceable promise is exchanged for a legally enforceable promise,A) an offer is made.B) a contract is created.C) an executed note is made.D) an acceptance and counteroffer is...
- Q How many back-up contracts can be created using the TREC-promulgated addendum for that purpose?A) As many as the seller wantsB) No more than twoC) OneD) Equipment
- Q The government-sanctioned website that allows consumers to obtain a free copy of their credit report from each of the three agencies isA) www.fico.com.B) www.creditbureau.com.C) www.freecreditscore.com.D) www.annualcreditscore.com.
- Q What type of trust would be used by an investor to earn money from apartments, houses, offices, and shopping centers?A) REMTB) Banking trustC) REITD) Auditor's trust
- Q (2x - 5)What is the value of the leading coefficient?What is the coefficient for x?What is the constant value (term with no variable)?
- Q The best way to graph a line from data points is to graph the points and then pick two of those points (that seem to fit the trend) to build...
- Q cube roots of 125( cos(5?/6) + / sin(5?/6))(a) Find the roots of the given complex number in trigonometric form. (Let 0 ? ? < 2?.)smallest -value Zolargest -valueZ1Z2(b) Write each...
- Q The graph of y=f(x) is shown in blue. Draw the graph of y = 3f(x), shown in red, by determining how a stretch or compression will transform the location of...
- Q The function f(x) = 7x + 1 is one-to-one.Find an equation for f-1(x), the inverse function.
- Q Let a, b, c be three positive integers. Show that abc(a - b)(b ? c)(c ? a) is divisible by 6. (Hint: Use the pigeonhole principle)
- Q Rewrite the equation in logarithmic form.4x = y
- Q Find the sumS = cos(2x) + cos(4x) + cos(6x) + ... + cos(2nx),where n is a positive integer. Express your answer as a product and quotient of trigonometric functions.
- Q Identify the numerical coefficient, the bases, and the exponents.6xy9
- Q A hospital records the number of floral deliveries its patients receive each day. For a two-week period, the records show15, 27, 26, 24, 18, 21, 26, 19, 15, 28, 25,...
- Q 1 Write down the first 10 terms of the Fibonacci sequence. 2 Give a recursive definition for this sequence.
- Q Completely factor P(x)=x^4 + 3x^3 + 12x^2 +48x-64 into linear factors, given that - 4i is a zero.P(x) =(Type your answer in factored form. Express complex numbers in terms of...
- Q Find an nith-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to grach the function and verify the real zeros...
- Q Suppose a brand of light bulbs is normally distributed, with a mean life of 1500 hr and a standard deviation of 100 hr.Find the probability that a light bulb of...
- Q Consider the following autonomous DE.y' = 4(y - 1)^2(y - 3)Choose all correct answers.There are two critical points.If y(1) = 4, then the solution is an increasing function.One critical point...
- Q Penninsula Hardware buys cabinet doors for $24.00 less 39%, 10 %, and 4%. The store's overheadexpenses are 34% of cost and the required profit is 14% of cost.Find the Cost.Find...
- Q A small craft in Lake Ontario sends out a distress signal. The coordinates of the boat in trouble are (8, 10). The Coast Guard's Moonlight II (rescue boat) is at...
- Q A ship leaves its port and sails on a bearing of N3620'E, at speed 25.4 mph. Another ship leaves the same port at the same time and sails on a...
- Q Convert to an exponential equation.log 0.1 = -1The equivalent equation is.(Type in exponential form.)
- Q Find the product of the complex numbers. Leave the answer in polar form.Z? = cos3?/4 +i sin 3?/4 Z? = cos 2?/3 +isin 2?/3
- Q Find a polynomial with real coefficients of the specified degree that has the given zeros.Degree 3; zeros: -2, and -4-i
- Q This question is about the fox and rabbit population in a forest. If the fox population increases the rabbit populatio starts to decrease since each fox eats 0.075 rabbits in...
- Q Find the cosine of the angle between the vectors with respect to the standard inner product on P2.p= x - x, and q = 8 + 4x + 5x.NOTE: Enter...
- Q In a mathematical statement 1 + 2 = 3,which is a connective?1N +2I
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