Complex numbers Questions and Answers

Select all that are True. The Law of Sines works for most triangles but not for right triangles. The Law of Cosines works for most triangles but not for right triangles. The Law of Sines works for all triangles, including right triangles. The Law of Cosines works for all triangles, including right triangles.

Give the slope and the y-intercept of the line y = x + 7. Make sure the y-intercept is written as an ordered pair. Slope = y-intercept =

Use the graph below to help you answer the questions. a. Show use of division to find the remaining roots of y = x³ - 4x² - x + 4. b. Use the roots to rewrite the function in factored form. c. Classify the original polynomial by its degree and number of terms. d. Describe end behavior, turning points, and increasing/decreasing intervals of the graph.

Maurice says: "Every linear function has exactly one zero. It follows from the Fundamental Theorem of Algebra." Cheryl disagrees. "What about the linear function y = 2?" she asks. Whose reasoning is correct? Select one: a. Maurice b. Cheryl c. not enough information

Choose the property illustrated by the following statement. 0 +6=6 A. additive inverse property B. associative property of addition C. commutative property of addition D. identity element of addition

Simplify the expression. 2r-4r+7+r

Find all points having a y-coordinate of - 6 whose distance from the point 11, 22 is 17. (a) By using the Pythagorean Theorem. (b) By using the distance formula.

Which value is NOT a solution to the equation? Choose all that apply. 27= -x4 - 12x² Select one or more: a. 0 b. 3i c. İ√3 d. 3

Padraig is a financial advisor. He earned a salary of $80,000 last year and sold stocks for $5,000. Which of the following types of income did Padraig have? I earned income Il passive income III capital gains income a. I and II b. I and III c. II and III d. III

Use a calculator to identify the following for the parabola: y = x² + 2x + 1 a. vertex b. axis of symmetery c. maximum or minimum value d. domain e. range

Enter the appropriate word or phrase in each blank. (Use^ to denote an exponent. Do not enter spaces in your answer. Enter the simplified expressions in parts b and d.) a. The expression (a + b)² is called the Write your response here... of a binomial. b. When simplified, (a + b)² is equivalent to the expression c. This resulting trinomial is called a d. For example, (x+4)²-

Find the inverse for each of the following one-to-one functions. (a) f(x) = 2x + 7 f-¹(x) = (b) f(x) = -x-4/4x + 1 f-¹(x) = (c) f(x)=√x-1, x ≥ 1. f-¹(x) = x ≥

To measure the area of a quadrangle, two students decided to walk along two sides of the rectangular lot, starting at the same corner at the same time. If student A walks at 2 paces per second and student B walks at 3 paces per 2 seconds, how far are they separating from each other after 8 seconds?

Consider sec(-(2 + 3x)) = √2. The principle solution is x = We now determine all solutions for this problem. What is the period of secant? List all values of 0 in the interval [0, 2x) such that sec(0) = √2. (Notice the relationship between the period and the interval here.) (List all values in this answer box separated by a comma. Depending on the trig function and value, it is possible that there will only be one entry.) Thus, using the above work, all solutions are given by x=_ where k € Z. (There will be a separate formula for each value you listed in the previous answer box. List each formula in this answer box separated by a comma. Remember to use k as appropriate.)

Give all transformations that occur to the function y=x that produce the function y=2|x|-3. Give both the transformations and the order in which they occur.

Divide and simplify to the form a + bi. 20 i/3+ i

Write the expression in the standard form a + b i. (5+3i)-(9-8i) (5+3i)-(9-8i) = (Simplify your answer.)

Write the expression in the standard form a + bi. (4-8 i) + (9+3i) (4-8 i) + (9 +3i) = (Simplify your answer.)

Divide and express the result in standard form. 2/6-i

Plot the complex number -3i and find its absolute value.

Explain why i23 must be equal to -i

Plot the complex number and find its absolute value. 5+4i

Let L1 be the line passing through the point P1=(-10, 5, 11) with direction vector →d1= [−2, 3, 2]T, and let L2 be the line passing through the point P2=(-34, 13, -3) with direction vector →d2=[2, -5, 0]T. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2) = d. Use the square root symbol 'V' where needed to give an exact value for your answer. d= Q1= Q2= d = 4√33 Q₁=(-4,-4, 5) Q2 = (-24, -12, -3) Above is the answer, however, I am not sure how to get to these solutions.

Financial Markets. The tock and bond markets are not the only financial markets. Give two or three additional examples.

Solve cos^2(x) = 3 sin(x) for all solutions x ∈ [0,2π].

Which of the following explains why f(x) = log4x does not have a y-intercept? Check all that apply. There is no power of 4 that is equal to 0. There is no power of 4 that is equal to 1. Its inverse does not have any x-intercepts. Its inverse does not have any y-intercepts.

Solve for x and check for extranepus roots. (a) √x-1=1 x = (b) √x - 2 = x - 2 X = (c) √x + 6 = x X = (d) √3x + 16 = −8+√4x + 116 x =

2. Show your work. a. Simplify using i: -144 b. Find the absolute value: -1 + 3/ c. Simplify: (1-21)-(-2-i) d. Simplify: (4- i)(2 + 5i) e. Simplify: -2-3i/6i

Newton's Law of Cooling states that for a cooling substance with initial temperature To, the temperature T after t minutes can be modeled 0' by T = (To-T)e+T, where T is the surrounding temperature and r is the cooling rate of the substance. You remove a baked potato from a 400°F oven and place it on the counter in your 67°F kitchen. After 20 minutes, you measure the temperature of the potato to be 128°F. What will the temperature of the potato be after 26 minutes? about 104°F about 69°F about 113°F about 37°F

Write the quotient as a complex number. Show your work. -2i/1 + i

What does the notation Ry-3x+1(DAB) mean? Reflection Rotation Clockwise Counter-clockwise Around the origin to the axis Over the x-axis Over the y-axis Over y-3x+1 180° 90° 270°

Divide and express the result in standard form. 5i/2-7i 5i/2-7i (Simplify your answer. Type your answer in the form a +bi. Use integers or fractions for any numbers in the expression.)

.Find a general solution to y" - 2y + 1y =12.5elt/t² + 1 Use a and b for the constants of integration associated with the homogeneous solution. y =

Perform the indicated multiplication. - 4i(-3+7i)

Given the function h(x)=x²-7x³ +14x² -38x-60 has a zero of 1+3i, find the remaining zeros of the function (using algebra!). Write the function in factored form over the complex number system. Zeros:__________________ Factored:______________

Enter the expression or number that is required to solve the equation. Do not enter any blank spaces in your answers. 2(1 – 5x) = 72 a. Apply the distributive property: Write your response here... b. When the constant term is moved to the right side, the resulting equation is: c. Solve: X = d. Solution set:

The property of equality states that we can add or the same number from each side of an equation and obtain an equivalent equation. The property of equality states that we can or divide each side of an equation by the same nonzero number and obtain an equivalent equation.

Solve the equation. Enter the solution set below. Recall that solution set notation is written in the form {p}, where P is the solution of the equation. (For example, if 2 is a solution, the solution set is {2}.) -4 = 38 + 6x

Question 36 (1 point) At a sandwich shop, 42% of customers buy a drink with their sandwich. Only 28% of customers buy a drink and chips with their sandwich. What is the probability that a customer who buys a drink also buys chips? a)70% b)about 66.7% c)14% d)1.5%

Andy and Cheyenne are planning to have their wedding and reception at a local venue. The venue charges a rental fee of $2030. The menu they have selected costs $36.75 per person. a. If they have $7,500 saved for their reception, what is the maximum number of guests that can attend the reception without going over budget? b. If, in addition to the meal, the couple wants to provide a beer and wine selection at the reception, there is an additional charge of $19.50 per person. In this case, what is the maximum number of guests that can attend the reception without going over budget?

If a linear equation is an identity, what is its solution set? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.

Let f(x) = - 3x + 7. Find each of the following: f(a) = 2f(a) = f(2a) = f(a + 2) = f(a) + f(2)=

Perform the indicated operation. (4 + 2i)(4-2i)

Write the equation of the line in standard form. slope = 3; (-1, 4) Select one: a. 3x=y-7 b. x-3y = -7 c. 3x-y = -7 d. y = 3x +7

Darnell invested a total of $52,000 in two accounts. The first account earned 13% after one year. However, the second account suffered a 5% loss in the same time. At the end of one year, the total amount of money gained was $2,620. LA at 13% at 5%

Graph the function f(x)=4/ x+2 -1 State the domain and the range (2)

Subtract and simplify. (13+5i)-(4+3i) (13+5i)-(4+3i) = (Simplify your answer. Type your answer in the form a + bi.)

Express 9[cos(60°) —isin(60°)] in the form a+ bi

Determine whether each of the following mapping is a homomorphism (justify your answer). If yes, find its kernel. i. Define : Z → R by p(x) = x. (where Z and R are both groups under addition). ii. Let(G,*) be a group under a binary operation and let y: GG be defined by y(m) = m² for all meg.

Using Euler's equation (eixes) eix e¹g) prove (1) sini+sing = 2 Sin (x+y). cos (x-4) sin(x+y)+sin(x-y) (2) Sinx cosy (3) cost cosy = = cos(x+y) - cos(x-y)