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Find the product of these complex numbers.(8 + 5)(-7 + 9) =
A. -101 +37i
B.-11-107/
C. -11 +37/
D. -101-107/

Answers

Answer 1
Answer:

Final answer:

To find the product of two complex numbers, you can use the distributive property. First, multiply the real parts and then multiply the imaginary parts. The correct answer is A. -101 + 37i.


Explanation:

To find the product of two complex numbers, you can use the distributive property. First, multiply the real parts of the complex numbers together, and then multiply the imaginary parts together. For the given complex numbers (8 + 5) and (-7 + 9):

Real part: (8 * -7) + (8 * 9) = -56 + 72 = 16

Imaginary part: (5 * -7) + (5 * 9) = -35 + 45 = 10

So, the product is 16 + 10i. Therefore, the correct answer is A. -101 + 37i.


Learn more about Complex numbers here:

brainly.com/question/20566728

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6. How many solutions does the given system have?y = 3x - 1
6x - 2y = -2
A. one solution
B. two solutions
C. infinite solutions
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Answers

Answer:

C. Infinite, I think.

Step-by-step explanation:

Because if you plug in y=3x-1 the equation would be: 6x-2(3x-1)=-2 and when you distribute the 2, the equation becomes: 6x-6x-2=-2. Then you do 6x-6x which =0 and then subtract another 2 and you get -2=-2
2 is the answer because 20 -2 equals to 2

Show that W is a subspace of R^3.

Answers

Answer:

Check the two conditions of Subspace.

Step-by-step explanation:

If W is a Subspace of a vector space, V then it should satisft the following conditions.

1) The zero element should be in W.

Zero element can be different for different vector spaces. For examples, zero vector in $ \math{R^2} $ is (0, 0) whereas, zero element in $ \math{R^3} $ is (0, 0 ,0).

2) For any two vectors, $ w_1 $ and $ w_2 $ in W, $ w_1 + w_2 $ should also be in W.

That is, it should be closed under addition.

3) For any vector $ w_1 $ in W and for any scalar, $ k $ in V, $ kw_1 $ should be in W.

That is it should be closed in scalar multiplication.

The conditions are mathematically represented as follows:

1) 0$ \in $ W.

2) If $ w_1 \in W; w_2 \in W $ then $ w_1 + w_2 \in W $.

3) $ \forall k \in V, and \hspace{2mm} \forall w_1 \in W \implies kw_1 \in W

Here V = $ \math{R^3} $ and W = Set of all (x, y, z) such that $ x - 2y + 5z = 0 $

We check for the conditions one by one.

1) The zero vector belongs to the subspace, W. Because (0, 0, 0) satisfies the given equation.

i.e., 0 - 2(0) + 5(0) = 0

2) Let us assume $ w_1 = (x_1, y_1, z_1) $ and $ w_2 = (x_2, y_2, z_2) $ are in W.

That means: $ x_1 - 2y_1 + 5z_1 = 0 $ and

$ x_2 - 2y_2 + 5z_2 = 0 $

We should check if the vectors are closed under addition.

Adding the two vectors we get:

$ w_1 + w_2 = x_1 + x_2 - 2(y_1 + y_2) + 5(z_1 + z_2) $

$ = x_1 + x_2 - 2y_1 - 2y_2 + 5z_1 + 5z_2 $

Rearranging these terms we get:

$ x_1 - 2y_1 + 5z_1 + x_2 - 2y_2 + 5z_2 $

So, the equation becomes, 0 + 0 = 0

So, it s closed under addition.

3) Let k be any scalar in V. And $ w_1 = (x, y, z) \in W $

This means $ x - 2y + 5z = 0 $

$ kw_1 = kx - 2ky + 5kz $

Taking k common outside, we get:

$ kw_1 = k(x - 2y + 5z) = 0 $

The equation becomes k(0) = 0.

So, it is closed under scalar multiplication.

Hence, W is a subspace of $ \math{R^3} $.

An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=103+30x. Predict the weight of luggage for a flight with 86 passengers.

Answers

Answer:

2683

Step-by-step explanation:

Using the linear regression equation that predict the relationship between the weight of the luggage and the total number of passenger y = 103 + 30x, we can plug in the number of passenger x = 86 to predict the weight of the luggage on a flight:

y = 103 + 30*86 =  2683

A king company requires 20 hours of labor to produce a standard table, and a chair requires 12 hours of labor. The labor available is 565 hours per week. The company can produce at most 35 chairs per week.The goal is to find the region that shows the number of tables and chairs that the company can produce in a week, based on the given restrictions. The first step is to represent the situation with a system of inequalities.

Let x be the number of tables and y be the number of chairs.

Which system of inequalities best represents this situation?

please help and thank you!!

Answers

Since x represents tables, and tables require 20 hours, 20x is the number of hours spent on tables. The total hours must not exceed 565, so must be less than or equal to that value. The first selection is appropriate.

Consider this composite figure that is made of two half spheres a cylinder. A composite figure is comprised of one cylinder and two half spheres. The cylinder has a height of 9 millimeters and radius of 5 millimeters. The volumes of each figure that make the composite figure have been determined. Sphere V = 500 3 π mm3 Cylinder V = 225π mm3 What is the volume of the composite figure?

Answers

Answer:

the answer is c

1,175/3mm3

Step-by-step explanation:

I got it right

Answer:

Actually:

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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized below:Selling Time Frequency
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Find the proportion of selling times in the sample that are less than 20 days claims that it can sell a detached, residential house faster than any other realty company.

Answers

Answer:

0.35

Step-by-step explanation:

Given the data:

Selling Time___ Frequency

0 10____________3

10 20__________ 4

20 30__________ 6

30 40__________ 4

40 50__________ 3

Proportion of selling time in sample above that are less Than 20 days :

Taking the sum of the frequency :

Hence, total frequency = (3 + 4 + 6 + 4 + 3) = 20

Selling time which is less Than 20 days :

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