Mathematics College

HELP!!!!
Which addition expression has the sum 8 – 3i ?
(9 + 2i) + (1 – i)
(9 + 4i) + (–1 – 7i)
(7 + 2i) + (1 – i)
(7 + 4i) + (–1 – 7i)

Answers

Answer 1

The expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i) which correct option(B).

What is complex number?

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

(B) (9 + 4i) + (–1 – 7i)

⇒ (9 + 4i) + (–1 – 7i)

⇒ 9 + 4i –1 – 7i

Rearrange the terms like wise and apply arithmetic operations

⇒ 9 - 1 + 4i - 7i

⇒ 8 – 3i

Hence, the expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i).

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Answer 2

Answer: the first part is option B

the second part is option C

Step-by-step explanation:

Related Questions

If two lines are perpendicular, which statement must be true? A.The slopes of the two lines are equal. B.The slopes of the two lines are undefined. C.The slopes of the two lines are zero. D.The slopes of the two lines are negative reciprocals.

Answers

Answer:

Option D is correct that is The Slopes of two lines are negative reciprocals.

Step-by-step explanation:

Perpendicular lines are the lines which intersect each other at right angle or make 90° angle with each other.

we that the Slope of perpendicular lines are equal to -1

Therefore, Option D is correct that is The Slopes of two lines are negative reciprocals.

Answer:

The answer to your question is D. The slopes of the two lines are negative reciprocals.

Step-by-step explanation:

Hope this helps have a great day :D

A group of friends is collecting aluminum for a recycling drive.Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.The weight of each person's donation is shown in the table.

A. order the weights of the donations from greatest to least.

B. Which of the friends will receive a free movie coupon? Which will not?

C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum? Explain

Brenda. Claire Jim. Micah

4.3. 5.5. 6 1/6. 15/4

Peter
4 3/8

Answers

Answer:

Brenda      Claire      Jim     Micah        Peter

 4.3             5.5       6 1/6     15/4           4 3/8

 4.3             5.5       6.17      3.75        4.375   (all values in decimal)

A. order the weights of the donations from greatest to least.

6.17 , 5.5 , 4.375 , 4.3 , 3.75

B. Which of the friends will receive a free movie coupon? Which will not?

As given - Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.

So, Brenda, Claire, Jim and Peter will receive coupons and Micah will not receive.

C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum?

Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have;

[tex]3.75+0.5=4.25[/tex] pounds

Then he would have got the coupon as a minimum of 4.25 pounds is required.

There are two less nickels than dimes, and as many quarters, as nickels and dimes together. The total amount of money is $5.25. How many quarters, dimes, and nickels are there?

Answers

n=d-2
q=n+d =>q=(d-2)=q=2d-2
25q+5n+10d=525
replace q and n with d
25(2d-2) +5(d-2)+10d=525
50d-50+5d-10+10d=525
65d=585
d=9
n=7
q=16

A business bought a lot of 2,500 lamps for fifty thousand dollars and wants to to sell them at 15% prfit. How much should each lamp cost?

Answers

Let L = how much is lamp should cost

L = [(50,000)(0.15) + 50,000]/(2500)

Calculate the right side of the equation to find your answer.
So 15% of 50000=7500 The answer is 7500

Express the decimal number 100 in all radices from 2 to 9

Answers

A decimal number can be converted into diffrent radices by continuos division and recording the remainders.


Part 1

To convert the decimal number 100 to radix 2, we have:

[tex] \frac{100}{2} =50 \ remainder \ 0 \\ \\ \frac{50}{2} =25 \ remainder \ 0 \\ \\ \frac{25}{2} =12 \ remainder \ 1 \\ \\ \frac{12}{2} =6 \ remainder \ 0 \\ \\ \frac{6}{2} =3 \ remainder \ 0 \\ \\ \frac{3}{2} =1 \ remainder \ 1 \\ \\ \frac{1}{2} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 2 is 1100100



Part 2:

To convert the decimal number 100 to radix 3, we have:

[tex]\frac{100}{3} =33 \ remainder \ 1 \\ \\ \frac{33}{3} =11 \ remainder \ 0 \\ \\ \frac{11}{3} =3 \ remainder \ 2 \\ \\ \frac{3}{3} =1 \ remainder \ 0 \\ \\ \frac{1}{3} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 3 is 10201



Part 3:

To convert the decimal number 100 to radix 4, we have:

[tex]\frac{100}{4} =25 \ remainder \ 0 \\ \\ \frac{25}{4} =6 \ remainder \ 1 \\ \\ \frac{6}{4} =1 \ remainder \ 2 \\ \\ \frac{1}{4} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 4 is 1210



Part 4:

To convert the decimal number 100 to radix 5, we have:

[tex]\frac{100}{5} =20 \ remainder \ 0 \\ \\ \frac{20}{5} =4 \ remainder \ 0 \\ \\ \frac{4}{5} =0 \ remainder \ 4[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 400



Part 5:

To convert the decimal number 100 to radix 6, we have:

[tex]\frac{100}{6} =16 \ remainder \ 4 \\ \\ \frac{16}{6} =2 \ remainder \ 4 \\ \\ \frac{2}{6} =0 \ remainder \ 2[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 244



Part 6:

To convert the decimal number 100 to radix 7, we have:

[tex]\frac{100}{7} =14 \ remainder \ 2 \\ \\ \frac{14}{7} =2 \ remainder \ 0 \\ \\ \frac{2}{7} =0 \ remainder \ 2[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 202



Part 7:

To convert the decimal number 100 to radix 8, we have:

[tex]\frac{100}{8} =12 \ remainder \ 4 \\ \\ \frac{12}{8} =1 \ remainder \ 4 \\ \\ \frac{1}{8} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 144



Part 8:

To convert the decimal number 100 to radix 9, we have:

[tex]\frac{100}{9} =11 \ remainder \ 1 \\ \\ \frac{11}{9} =1 \ remainder \ 2 \\ \\ \frac{1}{9} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 121

Help me look at pics

Answers

Divide 45 by 9.  This leaves you with 5 in the denominator of your fraction.  Next, cancel out the x^5 factors completely.  They disappear.  Next, divide y^16 by y^4.  You'll get y^12.  The first answer is the correct one.

Answer:

It's the first one

Step-by-step explanation:

Which is another way to name UST? TSR TSU USR UTS

Answers

Another was to name it is <TSU.
TSU is the correct answer

jeff finds some bugs. he finds 10 fewer grasshoppers than crickets. he finds 5 few crickets than ladybugs. if jeff finds 5 grasshoppers. how many ladybugs does jeff find? how many crickets does he finds?

Answers

Answer:
Jeff finds 15 crickets
Jeff finds 20 ladybugs

Explanation:
Assume that the number of grasshoppers is x, the number of crickets is y and the number of ladybugs is z

We are given that:
1- Number of grasshoppers is 10 less than number of crickets.
This means that:
x = y - 10 .............> equation I

2- Number of crickets is 5 less than number of ladybugs.
This means that:
y = z - 5 ..............> equation II

3- Jeff found 5 grasshoppers.

Substitute with value of grasshoppers in equation I to get the number of crickets as follows:
x = y - 10
5 = y - 10
y = 10 + 5
y = 15 crickets

4- Now we know that the number of crickets is 15, substitute with that value in equation II to get the number of ladybugs as follows:
y = z - 5
15 = z - 5
z = 15 + 5
z = 20 ladybugs

Based on the above:
number of crickets is 15
number of ladybugs is 20

Hope this helps :)

Jeff found 15 crickets and 20 ladybugs

Let the number of grasshoppers be x

Let the number of crickets be y

Let the number of ladybugs be z

If Jeff finds 10 fewer grasshoppers than crickets, hence x = y - 10

If he finds 5 few crickets than ladybugs, hence y = z - 5

If jeff finds 5 grasshoppers, hence x = 5

Since x = y - 10

5 = y - 10

y = 5 + 10

y = 15

Similarly since y = z - 5

15 = z - 5

z = 15 + 5

z = 20

This shows that Jeff found 15 crickets and 20 ladybugs

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The coordinates of A, B, and C in the diagram are A(p, 4), B(6, 1), and C(9, q). Which equation correctly relates p and q?

Answers

Refer to the diagram shown below.

Calculate the slope of line segment AB as m₁.
[tex]m_{1} = \frac{4-1}{p-6}= \frac{3}{p-6} [/tex]

Calculate the slope of line segment BC as m₂.
[tex]m_{2} = \frac{q-1}{9-6} = \frac{q-1}{3} [/tex]

The product of the slopes of perpendicular lines is equal to -1.
Therefore
[tex]( \frac{3}{p-6})( \frac{q-1}{3})=-1 \\\\ \frac{q-1}{p-6}=-1 \\\\ q-1 = 6-q \\\\ p+q = 7 [/tex]

The equation that relates p and q is p+q = 7

Answer:  p + q = 7

Use the graph of y = tan x to find all values of x, 0 ≤ x ≤ 2π, for which the following is true.

tan x is undefined

Answers

check the picture below, notice the red asymptotic lines.

now, recall that 

[tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \\\\\\ tan\left( \frac{\pi }{2} \right)=\cfrac{sin\left( \frac{\pi }{2} \right)}{cos\left( \frac{\pi }{2} \right)}\implies \stackrel{und efined}{tan\left( \frac{\pi }{2} \right)=\cfrac{1}{0}} \\\\\\ tan\left( \frac{3\pi }{2} \right)=\cfrac{sin\left( \frac{3\pi }{2} \right)}{cos\left( \frac{3\pi }{2} \right)}\implies \stackrel{und efined}{tan\left( \frac{\pi }{2} \right)=\cfrac{-1}{0}}[/tex]

all real numbers that are less than or equal to -27?in interval notation.

Answers

All real numbers that are less than or equal to -27?in interval notation.

(-∞, -27]
Final answer:

The set of all real numbers less than or equal to -27 in interval notation is (-∞, -27].

Explanation:

The set of all real numbers that are less than or equal to -27 can be represented in interval notation as (-∞, -27]. In interval notation, a square bracket indicates that the endpoint is included in the set. In this case, -27 is included because the question states 'less than or equal to.' The symbol '-∞' represents negative infinity, indicating that there is no lower bound on the set.

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I need help fast!! Having trouble with this!!

Answers

THE ANSWER TO THIS PROMBLEM IS A



d = 8t

if t = 0 then d =0
if t =1 then d =8x1 = 8
if t = 2 then d = 8x2 = 16

answer is C.
d = 8t

What is the difference between the sample average y and the population​ mean?

Answers

When a finite number of samples are drawn from a larger population, the sample mean of that sample, while usually close to the population mean, is not the same thing.  A population mean, on the other hand, is a description of pretty much ALL of whatever is being examined.

Example of population:  Everyone in the USA
Example of a sample:    One person, chosen at random, from each of the 50 states


Use integers to represent the values in the statement.The hightest elevation in a country is Mt.Snowy with an altitude of 15178 feet.The lowest elevation in the country is Green Valley with an altitude of 237 feet below sea level

Answers

the lowest elevation can be represented in integers like this: -237 feet
because it is below sea level, it is negative
the highest elevation can be expressed like so: 15178 feet

Answer:

Integers include positive Natural Numbers and Negative Natural numbers along with number which has no value called Zero.

Positive Integer=1,2,3,4.........Infinity

Negative Integer= -1,-2,-3,-4,...... -Infinity

Height of Mt.Snowy which is above sea level can be represented in terms of Integers = + 15,718 feet

Height of Green Valley which is above sea level can be represented in terms of Integers = + 237 feet

As, both Mountain snowy and Green valley are above sea level , so it will be represented by positve Integers.

Calculate the quotient and remainder of 19 divided by 7.

Answers

If you want the remainder then it will look like this: 2R5. But if you want the decimals then it is 2.71428571, to be exact. Hope this helps.

!!!!PLEASE HELP!!!!

Joe purchased a tray of 48 petunias to plant in his garden. The graph shows points representing the number of flowers left to plant at several different times while Joe is planting.

Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of petunias left to plant, y, and the time, x, Joe has spent planting.

Answers

Required equation is y - 36 = (24 - 36)/(2 - 1) (x - 1)

y - 36 = -12(x - 1)

y - 36 = -12x + 12

12x + y = 12 + 36

12x + y = 48

Answer:

12x + y = 48

Step-by-step explanation:

How do I answer question #9

Answers

add 6,3, and 5 together to get. 14. subtract 14 and 26. you get 12 left over. 12 mm less rain is the answer
Hello ItzJibblez!

STEPS
1. First you will add 6 mm+ 3 mm + 5 mm = 14
2. Then you subtract 26 - 14 = 12.

So the answer to your amazing question is 14 mm! 

Have an awesome day!!!

What is the constant of proportionality I. The equation y=5x?

Answers

Answer:

The value of the constant of proportionality is [tex]k=5[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

The value of the constant k is equal to the value of the slope

In this problem we have

[tex]y=5x[/tex] ------> is a linear direct variation

The slope is [tex]m=5[/tex]

therefore

The value of the constant of proportionality is [tex]k=5[/tex]

The constant of proportionality on the equation is 5.

To obtain the constant of proportionality ;

We compare the general direct proportionality relation with the equation given.

The equation given : y = 5x

The direct relationship between y and x is :

y α x

y = kx - - - (1)

Where, y and x are variables and k is the constant of proportionality.

Comparing equation (1) with the equation given :

y = kx

y = 5x

We can observe that, k in the equation (1) equals to 5 in the given equation.

Hence, the constant of proportionality is 5

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Consider the function h(x) = arcsin x) considering the input of h... i) ...which is a valid unit of measure for the input quantity

Answers

Given the function [tex]h(x)=\arcsin(x) [/tex]

Part a:

Considering the input of h

i.) A valid unit of measure for the input quantity is Seconds

ii.) The possible input values, i.e. the domain of h are -1 ≤ x ≤ 1



Part B:

i.) A valid unit of measure for the output quantity is the Radians.

ii.) The possible output values, i.e. the range of h is 0 ≤ h ≤ 2π



Part C:

i.) [tex]\arcsin\left(\sin\frac{\pi}{3}\right)=\frac{\pi}{3}[/tex]

ii.) [tex]\arcsin\left(\sin\frac{2\pi}{3}\right)=\frac{2\pi}{3}[/tex]

iii.) [tex]\arcsin\left(\sin\frac{7\pi}{6}\right)=\frac{7\pi}{6}[/tex]

iv.) [tex]\arcsin\left(\sin\frac{7\pi}{4}\right)=\frac{7\pi}{4}[/tex]

A number added to 12 and then subtracted by 18 equals 26. What is the number

Answers

the answer would be 32. take your 26 and add 18 then subtract 12. then rework it forward if you don't understand.
32? you would add 
hope this helps

Two vectors are given by a with arrow = 3 î + 6 ĵ and b with arrow = -1 î + ĵ. (a) find a with arrow ✕ b with arrow.

Answers

Given that vectors are  [tex]\vec a = (3, 6, 0)[/tex] and [tex]\vec b = (- 1, 1, 0)[/tex], the cross product of the two vectors are [tex]\vec a \times \vec b = (0, 0, 9)[/tex].

How to determine the cross product of two vectors

Vectorially speaking, cross product is a operation between two 3-dimension vectors to generate a third vector perpendicular to the two former. If we know that [tex]\vec a = (3, 6, 0)[/tex] and [tex]\vec b = (- 1, 1, 0)[/tex], then the cross product is:

[tex]\vec a \times \vec b = \left|\begin{array}{ccc}\hat{i}&\hat {j}&\hat{k}\\3&6&0\\-1&1&0\end{array}\right|[/tex]

[tex]\vec a \times \vec b = (0, 0, 3 + 6)[/tex]

[tex]\vec a \times \vec b = (0, 0, 9)[/tex]

Remark

The statement is incomplete and there is no possibility to complete it. Hence, we decided to consider the given statement as complete.

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Final answer:

The cross product of vectors a and b is found by creating a matrix with the vectors' components and calculating its determinant. The result in this case is -3î.

Explanation:

To find the cross product of vectors a = 3 î + 6 ĵ and b = -1 î + ĵ, you have to follow the matrix method. We list the unit vectors î, ĵ at the top of our matrix, and then add the components of vectors a and b underneath.

⟮ î ĵ ⟯
⟮ 3 6 ⟯ (from vector a)
⟮ -1 1 ⟯ (from vector b)

We calculate the determinant of this matrix using the rule of Sarrus. The resulting vector will be î(y1*z2 – z1*y2) - ĵ(x1*z2 – z1*x2) which, when plugging in our values, gives 3î - 6î. Therefore, a✕b equals -3î.

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Juanita works at a telemarketing company. She makes 12 sales calls per hour. Employees are encouraged to make more than 480 calls per week. Juanita has already made 144 calls this week. How many more hours, x, does Juanita need to work this week to reach the weekly goal of sales calls?

Answers

480 - 144 = 336
336 divided by 12 = 28

ANSWER: 28 Hours

Answer:

dswrfoASBGFUwy9uo

Step-by-step explanation:

fcfdscmskvnsk

what do Subway fraction and a whole number it is 5/6 x 36

Answers

The answer to this question is 221/6 I believe

The graph of the function f(x) = (x − 3)(x + 1) is shown.


Which describes all of the values for which the graph is positive and decreasing?

A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3

Answers

There's an error in the graph, but the answer is A.

Answer:

The correct option is A.

Step-by-step explanation:

The given function is

[tex]f(x)=(x-3)(x+1)[/tex]

Equate f(x)=0 to find the x-intercepts of the function.

[tex]0=(x-3)(x+1)[/tex]

[tex]x=3,-1[/tex]

The x-intercepts of the function are -1 and 3. From the below graph it is clear that,

In x<-1, the function is positive and decreasing.

In -1<x<1, the function is negative and decreasing.

In 1<x<3, the function is negative and increasing.

In x>3, the function is positive and increasing.

Therefore the correct option is A.

A given line has the equation 10x + 2y = −2.

Answers

what variable are u solving for?

      

Answer:

5x+y=12

Step-by-step explanation:

One pound of grapes costs $1.55. Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of 3.5 pounds of grapes?

A First one
B second one
C third one
D last one

Answers

1.55 / 1 = x / 3.5....$ 1.55 to 1 lb = $ x to 3.5 lbs

first one <==

it could have also been : 1 / 1.55 = 3.5 / x...but that is not an answer choice

Answer:

A

Step-by-step explanation:

One pound of grapes costs $1.55. To find the amount x of 3.5 pounds of grapes we would have to multiply 1.55 by 3.5. This would give us the amount x we would have to pay for them.

If we examine the 4 equivalent radios shown in the pictures, we will see that the first one correctly shows this equivalency.

[tex]\frac{1.55}{1} = \frac{x}{3.5}[/tex]

The other 3 pictures show radios that would give us x = 3.5 / 1.55 (second and third) or x = 1.55 / 3.5 (fourth picture).

Therefore, the correct answer would be a)

Which equation has a y-intercept of 0?

A) y = 7x + 1


B) y = -3x


C) y = 4x - 4


D) y = x + 5

Answers

The answer would be B because, unlike the others, it only shows the slope.
Compare all of these equations to y = mx + b.  The "b" represents the y-intercept.  The correct answer here is the equation that has no "b."  This means that b = 0.

240 square feet minus 100 square feet

Answers

240 - 100 = 140

your answer is 140 square feet

hope this helps
Your answer is 140 square feet

how do i figure out 3/4 of 640 fraction

Answers

640/4 x 3 = 480

answer
3/4 of 640 = 480

Fifty students were eating lunch in the school cafeteria. The ratio of boys to girls was 25:25. Mrs. White asked Kym to explain what that ratio meant. Kym said it meant that 25% of the students in the cafeteria were boys. Explain why Kym is incorrect.

Answers

Kym is wrong because the ratio means that 50% of the students in the cafeteria were boys.

What are ratios?

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value.

What percentage are boys?

Number of boys = (25 /50) x 50 = 25

Percentage of the number of boys = (25/50) x 100 = 50%

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Kym is incorrect because the ratio of boys to girls being 25:25 means there are equal numbers of boys and girls. Therefore, boys make up 50% of the students, not 25%.

Kym's explanation is incorrect because the ratio of boys to girls being 25:25 means that the number of boys is equal to the number of girls.
Specifically, this ratio can be simplified to 1:1. Since there are 50 students in total and the number of boys and girls is equal, there must be 25 boys and 25 girls.
Therefore, boys make up 25 out of the 50 students, which is actually 50%, not 25%.

The total number of students= 50.

Understand that a ratio of 25:25 means equal parts of boys and girls.

Simplify the ratio 25:25 to 1:1.

The number of boys: 50 students \/ 2 = 25 boys.

The percentage of boys,
(25 boys \/ 50 total students) * 100 = 50%.

Thus, boys constitute 50% of the student population, not 25%.

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