The expression on (3+i)(4+5i) can be written in form a+bi, where a and b are integers. What are the values of a and b? (Show your work please)

Answers

Answer 1

\((3 + i)(4 + 5i) \\ 12 + 15i + 4i + 5 {i }^{2} \\ 12 + 19i - 5 \\ 7 + 19i\)

Therefore, a is 7 aka real part and b is 19 which is imaginary part.


Related Questions

If you started the problem by converting 1 pound to 16 ounces, would you get the same results?

Answers

Answer:

yes

Step-by-step explanation:

you would get results bc results are results

What is 4/3•3.14•1.5^3?

Answers

I think the answer to your question is going to be 14.13
 What is 4/33.141.5^3?

(d+2) (-7) simplified form

Answers

d-5 is the answerrrrrr

Answer:

-7d -14

Step-by-step explanation:

(-7)(d+2)= (-7 *d) +(-7*2)

-7d -14

Please help someone

Please help someone

Answers

Answer:

A.

Step-by-step explanation:

because a right angle was the same legnth as that figure and also you can make a L so its A

Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 8 , − 1 ) (8,−1) and ( 4 , − 9 ) (4,−9).

Answers

The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.

What is the equation of the perpendicular bisector of a line segment?

In this problem we find a line segment whose endpoints are known and we need to determine the equation of the line perpendicular such that the segment is partitioned into two segments of equal length. Now we present the procedure. First, determine the coordinates of the midpoint:

M(x, y) = 0.5 · (8, - 1) + 0.5 · (4, - 9)

M(x, y) = (6, - 5)

Second, determine the slope of the line segment:

m = [- 9 - (- 1)] / (4 - 8)

m = (- 8) / (- 4)

m = 2

Third, calculate the slope of the bisector:

m' = - 1 / m

m' = - 1 / 2

Fourth, determine the intercept of the bisector:

b = y - m' · x

b = - 5 - (- 1 / 2) · 6

b = - 5 + 3

b = - 2

The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.

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Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 8 , 1 ) (8,1)

Identify the coordinates of point E. Responses (–2, –3) (–2, –3) (3, –2) (3, –2) (–2, 3)

Answers

(-2,-3) it located at the Quadrant lll on a Cartesian plane.

What are coordinates?

Coordinates are a set of numbers or values that represent the position of a point or object in a coordinate system. A coordinate system typically consists of two or more axes, such as the x-axis and y-axis in a Cartesian coordinate system, that intersect at a point called the origin. Coordinates are often written as ordered pairs (x, y) or as triplets (x, y, z) in three-dimensional space.

According to the question:
A cartesian plane has four quadrant. Each quadrant is represents as I,II,III,IV with different signs.
For example: quadrant one, quadrant two, quadrant three, and quadrant four. X-axis is a horizontal axis. Y-axis is a vertical axis X-coordinate is a horizontal position. Y-coordinate is a vertical position. Origin is a point of intersection of the two axes.

So the point E located in 3rd quadrant which is (-,-) it implies (-2,-3)

point E has value of -2,-3 at the x and y axis respectively.
Therefore, correct answer is (-2,-3).  

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Q) Identify the coordinates of point E by observing the figure below.

a. ( 3, -2 )

b. ( -3, -2 )

c. ( -2, -3 )

d. ( -2, 3 )

Identify the coordinates of point E. Responses (2, 3) (2, 3) (3, 2) (3, 2) (2, 3)

Helppppppppppppppppppppp

Helppppppppppppppppppppp

Answers

Answer:

5,7,9

Step-by-step explanation:

(5,7,9)-4<8

Stop drop hit the folks don’t stop

A circle with a radius of 9 millimeters.

Answers

Answer:

You didnt give us a question to answer, just a statement.

Step-by-step explanation:

I’ll give brainlest so pls help ;-;

Ill give brainlest so pls help ;-;

Answers

Answer:

-3

Step-by-step explanation:

1+-3= -2

5-4= 1

-2+1= -3 i think

Answer:

7

Step-by-step explanation:

Hello There!

For this one all we have to do is plug in the values

Remember l l means absolute value

l -5 - 4 l - l 1 + (-3)l

-5-4=-9

l-9l the absolute value of -9 is 9

1-(-3)=-2

l-2l the absolute value of -2 is 2

we´re left with

9-2

9-2=7

so the answer to the problem is 7

If Lindsay was serious about winning the competition of who can think of the most symmetrical words, which strategy would be best?​

Answers

With a little bit of effort and persistence, she should be able to come up with a strong list of symmetrical words and be well on her way to winning the competition.

What is number?

Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used in various fields such as science, engineering, finance, and many others. Number is an abstract concept that can be represented using symbols, such as digits (1, 2, 3) or letters (A, B, C). Number can be used to represent a quantity, an amount, or a certain order. It can also represent relationships between objects, such as combinations, sequences, and patterns.

The best strategy for Lindsay to use to win the competition of who can think of the most symmetrical words is to focus on words that have the same letters in the same positions at the beginning and end of the words. Examples of such words are "civic", "level", and "radar". Lindsay can also focus on words that have the same letters in the reverse order, such as "mom", "noon", and "racecar". Additionally, Lindsay can look for words that have the same letter pattern, but with different combinations of letters, such as "deed" and "feed".

Lindsay can also try to look for words with multiple pairs of symmetrical letters, such as "coconut" or "bobcat". She can also look for words with symmetrical letters in the middle, such as "potato" or "banana". Finally, Lindsay can look for palindromes, which are words that read the same backwards and forwards, such as "racecar" and "kayak".

By focusing on words that have the same letters in the same positions at the beginning and end of the words, as well as words that have the same letters in reverse order, the same letter pattern, multiple pairs of symmetrical letters, and palindromes, Lindsay will be able to increase her chances of winning the competition of who can think of the most symmetrical words. With a little bit of effort and persistence, she should be able to come up with a strong list of symmetrical words and be well on her way to winning the competition.

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Priscilla’s grandmother’s fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry, and three parts grape. Priscilla uses the same measuring cup to measure all of the fruit, so one part is equal to one cup of diced fruit. In this exercise, you will compare the quantities in the recipe to understand ratios better.

Answers

Answer:

There are 11 parts of fruit: 4-strawberry, 3- grape, 2, cherry, 1- apple, 1-orange 4/11 from the entine quantity of fruits- strawberry

3/11-grapes

2/11- cherries

1/11- apples

1/11- oranges } ⇒ the quantity of oranges and apples are equal Hope it helps ;>

0.0047
What is 4.7 x 10'?
In the problem above, which direction does the decimal move (left or right)? How
many times does it move?

Answers

Answer:

4.7x10 equals 47, the decimal moves to the right one time

list the prime factor of

a) 104
d) 68​

Answers

Answer:

\(a) \: So, \: the \: prime \: factorization \\ of \: 104 \: is, \: 2 × 2 × 2 × 13 = 23 × 13. \\ \\ \\ \\b)2 × 2 × 17 or 22 × 17, \: where \: 2 \\ and \: 17 \: are \: the \: prime \\ numbers.\)

Two factory plants are making TV panels. Yesterday, Plant A produced 10,000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 5%

Answers

If the overall percentage of the defective panels from the two plants is 5% then plant B produced 4000 panels in total.

This question can be solved by formulating the problem into the form of a linear equation having two variables. Linear equation in two variables can be represented in the form of ax+by+c=0 where a, b and c are real numbers and x, y are variables or the coefficients, and a, b ≠ 0.

Let the production from plant A be x, and according to the question x=10000.

Also, let the production from plant B be y.

Now, as 3% of products are found defective from plant A and 10% of products are found defective from plant B and overall defective products is 5%.

Thus, 0.03x+0.1y=0.05(x+y)

As x=10000 then

0.03×10000+0.1y=0.05(10000+y)

300+0.1y=500+0.05y

0.05y=200

=>y=4000

Thus, the total number of panels produced by plant B is equal to 4000.

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36 apartments on 9 floors = apartments per floor

Answers

Answer:

4 apartments per floor

Answer: 4

Step-by-step explanation:

If there are 36 apartments in the building with 9 on each floor, you can find the answer by simply doing the equation 36/9=4.

Find m A. 10 B. 5 C.√53 D. 10√3/3

Find m A. 10 B. 5 C.53 D. 103/3

Answers

Answer:

\(m = 10\)

Step-by-step explanation:

Looking at the angles, we can see that this is a 30-60-90 triangle.

The side that is with the 30° angle and the 90° angle is represented by \(x\sqrt{3}\).

So let's find x.

\(x\sqrt{3} = 5\sqrt{3}\)

Divide both sides by \(\sqrt{3}\):

\(x = 5\).

Now the hypotenuse is always \(2x\) (the leg with the 90° and 60° is just x.) So,

\(2x = 2\cdot5 = 10\).

Hope this helped!

A school is organizing a cookout where hotdogs will be served. The hotdogs come in small packs and large packs. Each small pack has 10 hotdogs and each large pack has 18 hotdogs. The school bought 6 packs of hotdogs that have a total of 76 hotdogs. Write a system of equations that could be used to determine the number of small packs purchased and the number of large packs purchased. Define the variables that you use to write the system.

Answers

Answer:

10x+18y=76

x+y=6

Let x =  the number of small pack of hotdogs

Let y =  the number of large pack of hotdogs

Step-by-step explanation:

x = small hotdogs

y = large hotdogs

The total number of hotdogs is:

10x+18y=76

Since a total of 6 packs were purchased, we know x+y must equal 6

x+y=6

Write System of Equation

10x+18y=76

x+y=6

The system of equations is 10x+18y=76  and x+y=6 The variables are Let x =  the number of small pack of hotdogs

Let y =  the number of large pack of hotdogs.

The following information should be considered:

x be the small hotdogs

y be the large hotdogs

Now  

The total number of hotdogs is:

10x+18y=76

And

x+y=6

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A batted baseball leaves the bat at an angle of θ with the
horizontal and an initial velocity of v0 = 300 feet per second. The
ball is caught by an outfielder 530 feet from the home plate. The
range r of a projectile is given by sin  2
32
1 2
o r  v
.
What is the value of the angle of the bat from the ground?

Answers

Answer:

Sixty Baseball Physics Problems © page 1 ! ! Sixty Baseball Physics Problems (many with correct solutions!) Sixty Baseball Physics Problems

Step-by-step explanation:

which one is bigger 10/10 or 6/6

Answers

Answer:

Both are equal to each other.

Step-by-step explanation:

\( \frac{10}{10} = 1\)

\( \frac{6}{6} = 1\)

Answer:

None of them are bigger than the other, they are equal to each other.

\( \frac{10}{10 } = \frac{6}{6} \\ 1 = 1\)

Please see attached photo. The first word that is cut off is “find”. Thanks in advance!

Please see attached photo. The first word that is cut off is find. Thanks in advance!

Answers

Solution

For this case we have the following equation:

2x+ 5y= 10

We can solve for the following general form:

y= mx+b

And we have this:

5y = 10-2x

If we divide both sides by 5 we got:

y= 2- 2/5x

Then the answer is:

m= -2/5

b= 2

And the graph is:

Please see attached photo. The first word that is cut off is find. Thanks in advance!

What is the value of v? (help no links and thx)

What is the value of v? (help no links and thx)

Answers

Answer:

74.7

Step-by-step explanation:

The triangular prism below has a base area of 28.7 units² and a height of 11 units.
Find its volume.

The triangular prism below has a base area of 28.7 units and a height of 11 units.Find its volume.

Answers

The volume of the triangular prism is 315.70 units³.

What is the volume?

A triangular prism is a three-dimensional shape that has a triangular base.

Volume =base area x height

28.7 x 11 = 315.70 units³

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A whale swimming against an ocean current traveled 140 mi in 7 h. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 3.5 h. Find the speed of the whale in calm water and the rate of the ocean current.

Answers

The whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

How to estimate the speed of the whale in calm water and the rate of the ocean current?

Let x be the speed of a whale in calm water

and y be the speed of the current

In 7 hours the whale swims against the current and travels 140 miles:

7(x - y) = 140

x - y = 140/7

x - y = 20 ...........(1)

In 3.5 hours the whale swims the same distance with the current:

3.5(x + y) = 140

x + y = 140/3.5

x + y = 40 ...........(2)

Adding (1) and (2), we get the value of x:

x - y = 20  + ...........(1)

x + y = 40 ...........(2)

-----------------

2x = 60

x = 60/2

x = 30

Using this value for "x" in either (1) or (2) we can solve for "y":

x - y = 20 ...........(1)

substitute for "x"

30 - y = 20

10 = y

Therefore, the whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

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Assume that thermometer readings are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in celsius degrees)
Between -1.42 and 1.61
The probability of getting a reading between -1.42 degrees C and 1.61 degreesC is_______ ( round to four decimal places as needed)

Answers

Answer:

The probability of getting a reading between -1.42 degree C and 1.61 degree C is 0.8685.

Step-by-step explanation:

We are given that

\(Mean,\mu=0\) degree C

Standard deviation, \(\sigma=1\) degree C

We have to find the probability of the reading between -1.42 and 1.61.

\(P(-1.42<x<1.61)=P(\frac{-1.42-0}{1}<\frac{x-\mu}{\sigma}<\frac{1.61-0}{1})\)

\(P(-1.42<x<1.61)=P(-1.42<Z<1.61)\)

\(P(-1.42<x<1.61)=P(Z<1.61)-P(Z<-1.42)\)

Using the formula

\(P(a<z<b)=P(z<b)-P(z<a)\)

\(P(-1.42<x<1.61)=0.94630-0.07780\)

\(P(-1.42<x<1.61)=0.8685\)

Hence, the probability of getting a reading between -1.42 degree C and 1.61 degree C is 0.8685.

Assume that thermometer readings are normally distributed with a mean of 0 degrees C and a standard deviation

A gas station sells 1200 gallons of gasoline per hour if it charges $2.05 per gallon, but
only 900 gallons per hour if it charges $2.45 per gallon. Assuming a linear model...
(a) How many gallons would be sold per hour of the price is $2.20 per gallon?

Answers

The quantity of gallons that would be sold per hour when the price is $2.20 per gallon would be = 1288 gallons

How to calculate the quantity of gallons sold per hour?

When charges is $2.05 per gallon the number of gallons sold = 1200 gallons

When the charges is $2.45 per gallon the number of gallons sold = 900 gallons per hour.

That is;

$2.05 = 1200 gallons

$2.20 = X gallons

Make X gallons the subject of formula;

X gallons = 2.20×1200/2.05

= 2640/2.05

= 1287.8 gallons

= 1288 gallons ( approximately)

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!


1) A student has a Math placement of Math 111, Math 100 and Math 102+. What course should the student first start with according to their placement results to then continue to get to Math 103E?

Answers

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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A water tank holds 648 gallons but is leaking at a rate of 4 gallons per week. A second water tank holds 864 gallons but is leaking at a rate of 7 gallons per week. After how many weeks will the amount of water in the two tanks be the same?


The amount of water in the two tanks will be the same in ________ weeks.

Answers

Answer:

The first tank contains

486 gal - (4 gal/week) t

gal of water after t weeks.

Similarly, the second tank contains

648 gal - (7 gal/week) t

gal of water.

The tanks hold the same amount of water when these two amounts are equal:

486 gal - (4 gal/week) t = 648 gal - (7 gal/week) t

(7 gal/week) t - (4 gal/week) t = 648 gal - 486 gal

(3 gal/week) t = 162 gal

t = (162 gal) / (3 gal/week)

t = 54 weeks

Step-by-step explanation:

3x + 4y = -23
2y - x = -19

What is the solution (x, y) to the system of equations above?


(-5, -2)

(3, -8)

(4, -6)

(9, -6)

Answers

Step-by-step explanation:

I belive is choice 2 cause I only got -19 with that one

Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. The retail price of a particular smartphone and the number of units sold at that price

Answers

Answer:

no correlation

Step-by-step explanation:

The price of the smartphone is fixed beforehand, therefore price does not depend upon the number of units sold.

Hence, there is no correlation between the two given variables.

Hence, no correlation would be the answer.

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