Algebra Questions

with a truth table 1 Z A B C BC 2 Z A AB A B 3 F XY Z XY Z 4 F X YZ X YZ XZ

4 3

How do I find the GCD of the complex numbers a 24 3i b 7 i

Assignment 1 point Calculate the acute angles rounded to the nearest degree formed by the plane z 2y z 14 and a the zz plane Answer b the z axis Answer Note You can earn partial credit on this problem 4

Given the lines 1 x 7 4t y 3t z t 4 and 1 x 2 t y 3t Z 6 5t a find equations in general form for the parallel planes containing l and 2 containing 12 T1 2 b determine the geometric relation between the lines they are skew

If possible find the measure of angle X A Not enough information to solve B 2X 52 C X 128 X 32 20 32

modeled by the function P x 3x 3 90x What do the zeros of the function tell you about the number of paddleboards that Waterworks should produce Waterworks is a company that manufactures and sells paddleboards Its profit P in hundreds of dollars earned is a function of the number of paddleboards sold x measured in thousands Profit is 39x In order to make a profit Waterworks must produce more than and fewer than paddleboards

Find an nth degree polynomial function with real coefficients a leading coefficient of 1 and satisfying the given conditions n 3 3 and 4i are zeros f x Simplify your answer

Form a polynomial f x with real coefficients having the given degree and zeros Degree 4 zeros 4 2 2 multiplicity 2 Let a represent the leading coefficient The polynomial is f x a Type an expression using x as the variable Use integers or fractions for any numbers in the expression Simplify your answer S

A polynomial function P x with rational coefficients has the given roots Find two additional roots of P x 0 13 7 and 8i Two additional roots of P x 0 are Express complex numbers in terms of i Type exact answers using radicals as needed Use a comma to separate answers as needed

Write a polynomial function of least degree with rational coefficients so that P x 0 has the given root 2 7i P x x x COLLE

Is 4 a root of the polynomial f z 2z4 11z 14z 9z 18 4 va root of f x because We can also confirm this because 4 a possible rational solution

Mr Smith is opening up a new business selling bell bottom jeans One of his employees who understands math determined that the weekly profit for the company would be modeled by the equation P z r 50 z 10 z 90 If Mr Smith wants to make a positive profit and not go out of business how many jeans should he sell per week He should sell between and jeans

Which of the following are possible rational roots for the given polynomial f x 2 82 2 146 15 000 05 2 3 15 3 73 8 146 146 000 2 5 000 73 4 15 000 8 1

Find all of the real solutions to the following equation Write your answers in order from least to greatest 5x x 4x X X X

2 Sketch the graph of f x 9x 4x 1 4 2x x 1 8 On the graph show the zeros and the behavior of the function near by as well as the long run behavior

Let P 1 3 5 6 u 4 2 1 0 V 1 W W 43 U3 2 W3 3 5 V2 a Find a basis U U U3 for R such that P is the change of coordinates matrix from u U U3 to the basis V V2 V3 Hint What do the columns of P C B 6 1 6 4 and V3 U b Find a basis w W W3 for R such that P is the change of coordinates matrix from V V2 V3 to W W W3 1 3 Complete parts a and b 6 Con repr

1 point Simplify the rational expression 2x 1 2x 3

Use technology to find points and graph the line 4y 5x 8 following instructions below Plot at least two points that fit on the axes below Click a point to delete it 10 9 15 done plotting points 4 3 10 25 9 9 10

Find the indicated side x Use either the Law of Sines or the Law of Cosines as appropriate Assume B 22 and C 98 Ros X A C 1000 1 point Simplify the rational expression 2x 1 2x 3

Suppose that G is a finite Abelian group that has exactly one subgroup for each divisor of IGI Show that G is cyclic

For the triangle shown find the length AD Assume u 19 v 19 2x 10 and y 10 Round your answer to two decimal places AD B The area is V Find the area of the triangle ABC C 131 2 a 45 3 ft and b 35 7 ft square ft D A C

A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain cable car is to be installed running to the top of the mountain from a point 800 ft out in the plain from the base of the mountain Find the shortest length of cable needed Your answer is 3271 Preview ft

3 Maximum mark 5 with GDC In an arithmetic series the first term is 7 and the sum of the first 20 terms is 620 a Find the common difference b Find the value of the 78th term

Maximum mark 4 without GDC The second term of an arithmetic sequence is 7 The sum of the first four terms of the arithmetic sequence is 12 Find the first term w and the common difference d

Determine which of the rational functions given below has the following feature There is a hole in its graph at x 5 OA f x OC f x X 9 x 5 OB f x OD f x x 5 x 9 x 5 x 5 5x 1 x 9 x 5 x 9 x 5

Find all complex zeros of the polynomial function Give exact values List multiple zeros as necessary f x 3x4 20x3 44x 80x 128 8 OA 4 i i 8 OB 4 2i 2i 3 OC 13 4 4 4i 4i 8 D 3 4 21 2i

Use the factor theorem to decide whether or not the second polynomial is a factor of the first 7x4 13x 2x2 x 4 x 2 Yes O No

Use a graphing calculator to approximate the real zeros Give each zero as a decimal to the nearest tenth f x 3x x2 15x 5 OA 0 3 2 2 2 2 OB 3 2 3 2 3 OC 0 3 2 2 2 2 OD 3 5 5

Describe the transformations and give the equation for the graph 10 PPA K 111 8 6 8 A 2 AIXS OA It is the graph of f x x shrunken vertically by a factor of 9 and translated 5 units down The equation is y xl 5 OB It is the graph of f x x stretched vertically by a factor of 9 and translated 5 units down The equation is y 9 x 5 OC It is the graph of f x x shrunken vertically by a factor of 9 and translated 5 units down The equation is y 9 x 5 OD It is the graph of f x x stretched vertically by a factor of 9 and translated 5 units down The equation is y x 5

A faucet is used to add water to a large bottle that already contained some water After it has been filling for 5 seconds the gauge on the bottle indicates that it contains 18 ounces of water After it has been filling for 13 seconds the gauge indicates the bottle contains 58 ounces of water Find and interpret the average rate of change in the volume of water per second OA The average rate of change is 6 This means that the volume of water is decreasing at a rate of 6 ounces per second OB The average rate of change is 6 This means that the volume of water is increasing at a rate of 6 ounces per second OC The average rate of change is 5 This means that the volume of water is increasing at a rate of 5 ounces per second OD The average rate of change is 5 This means that the volume of water is decreasing at a rate of 5 ounces per second

Determine whether fog x x and whether gof x x f x g x x X OA fog x x gof x x OB fog x gof x x OC fog x x gof x x OD fog x x gof x x

Graph the function f x A 2 if x21 1 x if x 1 19 O B 2 X Q 5 O C G O D

A triangular shaped lake front lot has a perimeter of 1100 ft One side is 200 ft longer than the shortest side while the third side is 300 ft longer than the shortest side Find the lengths of all three sides OA 100 ft 300 ft 300 ft OB 300 ft 300 ft 300 ft OC 300 ft 500 ft 600 ft OD 200 ft 400 ft 500 ft

Give a rule for the piecewise defined function Then give the domain and range OA O C f x 5 if x 2 6 if x 22 Domain 5 6 Range 0 00 5 if x 2 6 if x 2 Domain 00 00 Range 5 6 f x 81 B O D f x 4 f x 5 ifx 2 6 if x 2 Domain 5 6 Range 0 00 5 if x 2 6 if x 2 Domain 00 00 Range 5 6 X

Determine whether the equation has a graph that is symmetric with respect to the y axis the x axis the origin or none of these y x 4 x 2 OA x axis only OB x axis y axis origin OC y axis only OD none of these ALLEN

The graph of a linear function f is shown below Write the equation that defines f Write the equation in slope intercept form Ld Ay 8 6 4 di 2 9 O A y 5x 6 OB y 5x 6 OC y 5x 6 OD y 5x 6

Find the requested value 2x 1 if x 6 f 6 for f x 6x OA 11 OB 36 O C 48 if 6 x 9 6 7x if x 9

Give the domain and range of the relation Year 1993 1994 1995 1996 1997 Number of Companies 52 102 187 170 218 OA The domain is 1993 1994 1995 1996 1997 The range is 52 102 170 187 212 OB The domain is Year The range is Number of Companies OC The domain is 52 102 170 187 218 The range is 1993 1994 1995 1996 1997 OD None of these

Does the relation shown below define a function 8 2 8 8 0 6 6 3 7 4 O No Yes

Find the values of a b and c for which the quadratic equation ax bx c 0 has the given numbers as solutions Then use the values to write a quadratic equation 3 6 OA x 3x 18 0 OB x2 18x 3 0 O c x 3x 18 0 D x 18x 3 0

Solve the equation 4 0 5x x X 5 The solution set is 6 Simplify your answer

Solve the following equation for t t S 1 1191 Potions

Solve the equation by the square root property x 20 OA 20 OB 10 OC 2 5 O D 400

7x 4 6 x 1 2x 3 OA OB O C equation O D 13 1 7 9 13 15

Solve the equation 4 0 5x x x 5 3

How much should you invest into an account with 3 2 interest compounded quarterly if you want to receive a payment of 1000 each quarter for the next 5 years

f x x 5 5 6 41 9 X 8 subtract 5 then take square root subtract 5 then take square root Draw a machine diagram for the function f x subtract 5 then take square root subtract 8 take reciprocal multiply by 7 subtract 8 take reciprocal multiply by 7

Determine if each of the subset W is a subspace of the given vector space V a 1 0 a b eR V M22 with standards operations 0 b b W a b a b 2a a b eR V R with standards operations a W

Find an orthogonal matrix A where the first row is a multiple of 1 2 2 A