Find the quotient of 5+4i/6+8i , and express it in the simplest form

Answers

Answer 1

remember: i² = -1

[tex] \frac{5+4i}{6+8i}= \frac{(5+4i)(6-8i)}{(6+8i)(6-8i)}= \frac{30-40i+24i-32i^2}{36-64i^2}= \frac{30-16i-32(-1)}{36-64(-1)}= \\ \\ = \frac{30-16i+32}{36+64}= \frac{62-16i}{100}=0.62-0.16i[/tex]

Hope this helps

Related Questions

Twelve employees were sick. If the company has 360 employees, what percent of the employees were sick on Monday? Round to the nearest tenth.

Answers

Total number of employees = 360

Number that were sick = 12

Therefore,

Percentage of employees that were sick = [tex] \frac{12}{360} * 100 = \frac{1}{3} * 10 [/tex] = 3.3 %

2|x+1/4|=6
Can someone help me please, I'm so confused

Answers

First divide by 2
|x+1/4|=3
Then you pick the possible answers
|x+1/4|=3
|x+1/4|=-3
2 3/4 or -3 1/4

Use the student's t distribution to find tc for a 0.95 confidence level when the sample is 29. (round your answer to three decimal places.)

Answers

Using a t distribution table you can easily find the t critical value in a very easy way just look for the confidence level which is 95% or the 5% significance level and look for the degrees of freedom which is 28 (just to remind you degrees of freedom is always -1, so if you have 29 – 1 you will get 28 and it is the degrees of freedom), then the t distribution should give you 2.048 for your t critical value. When you use the significance level here you need to subtract the 100% by your confidence level of 95% you will get the 5% then you should divide it to 2, you will get the .025 if it only a two-tailed test you will use the significance level.

If 2+2=4 why is the answer fish

Answers

When you combjne 2 and 2 it makes the shape of the Jesus fish

Find the truth set of each of these predicates where the domain is the set of integers.
a.p(x): x3 ≥ 1
b.q(x): x2 =2
c.r(x): x < x2

Answers

a.p(x): x^3 ≥ 1

x^3 ≥ 1 => x ≥ 1 => all the integers equal or greater than 1 = { x ∈ Z | x ≥ 1} = {1, 2, 3, 4, 5, 6, ...}

That is the same that the natural numbers except 0 = N - {0}.

b.q(x): x2 = 2

x^2 = 2 => x = +/- √2, which is not an integer, so the truth set is the empty set = { } =∅

c.r(x): x < x2

x < x^2 => x^2 - x > 0

=> x (x - 1) > 0

=>

1) x > 0 and x - 1 > 0
   => x > 0 and x > 1
     => x > 1

2) x < 0 and x - 1 < 0
    => x < 0 and x < 1 => x < 0

=> the solution is the union of the two sets: x > 1 ∪ x < 0

That is all the integers except 0 and 1.

=> the truth set is { x ∈ Z | x < 0 or x > 1} = Z - { 0,1}

The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 120, 0. The vertex is at 60, 35.

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

Part B: What is an approximate average rate of change of the graph from x = 20 to x = 35, and what does this rate represent?

Answers

x - intercepts (0, 0) and (120, 0)

Vertex is at (60, 35).

Part A: What do the x-intercepts and maximum value of the graph represent?

The x-intercepts represent the points at the ground, so with that you have the width of the tunnel at ground level is 120 ft - 0 ft = 120 ft..

The vertex represents the maximum height, which is at the center of the tunnel. So, you know that the maximum height is at x = 60 ft and it is 35 ft

What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

The increasing interval is (0,60), and the decreasing interval is (60,120).

That represents that the height increase from the left border (x = 0) until the center of the tunnel (x = 60 ft), reaching a height of 35 ft, and starts to decrease toward the right border until the ground level (x = 120).

Part B: What is an approximate average rate of change of the graph from x = 20 to x = 35, and what does this rate represent?

Find the y -coordinate for x = 20 and for x = 35. Supposse they are (I do not have the figure, because you did not include it) y = 15 and y = 45.

Then the average rate of change is equal to [change in height] / [change in x] = [45 - 15] / [35 - 20] = 30 / 15 = 2.

Remember that you have to use the real approximate values for the height that you can read in the figure. If the number is positive means that the height is increasing in that interval.

Answer:

i have the image of the tunnel and here is my work

Part B: x=20 y=20 x=35 y=60 so {60-20}/{35-20}=40/15=2.6

hope this helps

The price of a new pair of shoes is $52.00. If you order them directly from the company on the internet, you can save money and the price is only $42.64. What is the percent change?

Answers

Answer:

It will be 18% decrease, Because they said they lowered the price.

Step-by-step explanation:

The percentage decrease in buying shoes on the internet with respect to shop is 18%.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction of 100.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

Price in shop = $52.00

Prince in online = $42.64

The percentage decrease with respect to price in the shop ⇒

(Price in shop - Prince in online)/(Price in the shop) × 100

⇒ (52 - 42.64)/52 × 100

⇒ (9.36/52) × 100

⇒ 18%

Hence "The percentage decrease in buying shoes on the internet with respect to shop is 18%".

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How many different id cards can be made if there are 5 digits on a card and no digit can be repeated?

Answers

if no numbers can repeat then you have

1st digit = 10 numbers

2nd digit = 9 numbers

3rd digit = 8 numbers

4th digit = 7 numbers

5th digit = 6 numbers

10 * 9 * 8 * 7 *6 =30,240 different combinations

Final answer:

There are 30,240 different ID cards that can be made with 5 digits where no digit can be repeated, calculated as a permutation of 10 choices taken 5 at a time without replacement.

Explanation:

The question asks us to determine how many different ID cards can be made with 5 digits where no digit can be repeated. This is a problem of permutations where the order of the digits matters. We have 10 possible digits (0-9), and we need to choose 5 of them without repetition.

For the first digit, we have 10 choices (0-9). Once we choose the first digit, we have 9 choices left for the second digit (since one digit is already used and can't be repeated). Continuing this pattern, we have 8 choices for the third digit, 7 choices for the fourth digit, and 6 choices for the fifth digit.

The total number of different ID cards is calculated by multiplying these choices:

10 choices for the first digit9 choices for the second digit8 choices for the third digit7 choices for the fourth digit6 choices for the fifth digit

The calculation is 10 x 9 x 8 x 7 x 6, which equals 30,240 different ID cards.

A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?

Answers

Use proportion
106 % = x + 8,800 where x is the selling price
100 % = x

so 106 / 100 = 1.06 = (x + 8800) / x

1.06x = x + 8800
0.06x = 8800
x = 8800 / 0.06 = $146,666.67

How long does it take to drive 25 miles at 60 mph?

Answers

60 mph = 1 mile per minute ( 60 minutes per hour)

so it would take 25 minutes to drive 25 miles

Answer:

25 min

Step-by-step explanation:

25/60=5/12=25 min

Which positive integers less than 12 are relatively prime to 12?

Answers

Final answer:

To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1. The positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.

Explanation:

Two positive integers are relatively prime if their greatest common divisor (GCD) is 1. To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1.

The prime factors of 12 are 2 and 3. Therefore, any positive integer less than 12 that is not divisible by 2 or 3 will be relatively prime to 12.

Therefore, the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.

A man travels from town x to town y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he mage the round trip at an average of 55 mph. What is the distance from town x to town y

Answers

D/60 + D/50 = 2D/55 - 1/2

find common denominator ( 3300)

3300/60 = 55

3300/50 = 66

3300/55=60

so then you get 55D +66D= 60(2D)-1650

121D=120D-1650

D=1650 miles

check

1650/60 =27.5, 1650/50 = 33, 27.5 + 33 = 60.5 hours total

1650/55 = 30, 30 x 2 = 60

60.5-60 = 0.5 longer

so distance = 1650 miles

Find the indicated critical z value. Find zα/2 for α = 0.08

Answers

Refer to the diagram shown below.
The value of z that yields the expected central area takes into account the excluded areas at both tails.

Half the tail area is α/2 = 0.08/2 = 0.04.
The central area is 1 - 0.04 - 0.04 = 0.92.

From standard normal tables, obtain
z(α/2) = 1.75

Answer: 1.75

Final answer:

To find the critical z value for α = 0.08, we first divide α by 2 to get 0.04. This value corresponds to the tail regions in a two-tailed test. We then lookup or calculate the z value associated with a cumulative probability of 0.04, which gives us a z value of approximately 1.75.

Explanation:

The question is about finding the indicated critical z value. In statistics, critical values are used to make decisions about the null hypothesis in hypothesis testing. When α = 0.08, α/2 = 0.04 which refers to the tail regions in a two-tailed test.

First, we find the z value associated with α/2=0.04. This is found by looking at a standard z-table, or using a statistical calculator or a software tool that can calculate the inverse of the standard normal cumulative distribution function. For α/2=0.04, the z value is approximately 1.75.

Therefore, the critical z value (zα/2) is approximately 1.75.

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STVU is an isosceles trapezoid. If SV = 3x - 11 and TU = x + 13, find the value of x
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The given trapezoid will have the sides ST, TV, VU, and US. Each of these can be assigned as base or legs. By this, it can be deduced that the given sides, SV and TU are the diagonals. Because the trapezoid is isosceles, the values of SV and TU should also be equal.

SV = TU
3x - 11 = x + 13

Transpose the terms with x and the constants in each sides of the equation.

3x - x = 13 + 11
2x = 24
x = 12

Thus, the value of x from the equation is 12.

The probability that a train leaves on time is 0.4. The probability that the train arrives on time and leaves on time is 0.28. What is the probability that the train arrives on time, given that it leaves on time?

0.4
0.12
0.28
0.7

Answers

You need to use the conditional probability formula:
P(A|B) = P(A∩B) / P(B)
Key:
P(A|B): Probability of A given B
P(A∩B): Probability of A and B

If we say A is the event that the train arrives on time and B is the event that the train leaves on time, then according to the information:
P(B) = 0.4
P(A∩B) = 0.28
Just insert into the formula:
P(A|B) = 0.28 / 0.4 = 0.7
(or 70% as a percentage).

Final answer:

The probability that the train arrives on time, given that it leaves on time is 0.7

Explanation:

The question asks for the probability that the train arrives on time, given that it leaves on time. This is a conditional probability problem, and we can use the formula for conditional probability, which is P(A|B) = P(A and B)/P(B).

In this case, event A is the train arrives on time, event B is the train leaves on time. We know that P(A and B) = 0.28 (the probability that the train arrives on time and leaves on time) and P(B) = 0.4 (the probability that the train leaves on time).

By substituting these values into the formula, we get P(A|B) = 0.28/0.4 = 0.7. So, the probability that the train arrives on time, given that it leaves on time is 0.7.

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Which of the following is equivalent to 5√13^3?

A) 13^2

B) 13^15

C) 13^5/3

D) 13^3/5

Answers

LOL...it took me a few seconds to realize what you were attempting to express...which is the fifth root of 13 cubed...

(13^3)^(1/5) rule: (a^b)^c=a^(b*c)

13^(3*1/5)

13^(3/5)

Solve the equation for x and round your answer to the nearest hundreth. 5 = ln(x + 1)

Answers

5=ln(x+1) raise e to each side of the equation

e^5=e^(ln(x+1))

e^5=x+1

x=e^5-1

x≈147.41 (to nearest hundredth)

HELP PLEASE!!!! :((((((((

Answers

The correct answer is B. u+2b=30. This is because unicycles (represented by u) only have one wheel while bicycles (represented by b) have 2 wheels. You set it equal to 30 because that is the total number of wheels.

The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 3 ft long with a diameter of 2.4 ft . Suppose gas is poured into the tank at a rate of 2.5 ft 3 per minute. How many minutes does it take to fill the empty tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.

Answers

Find out the volume of the cylinder using the formula for the volume of a cylinder. When you do that, you get that the volume of the tank, when it's full, is 4.5216 ft^3. If the tank is being filled at a rate of 2.5 ft^3 per minute, just divide the total volume by 2.5 to get that, after rounding, it takes 2 minutes to fill the tank. 1.80864 before rounding.

the diameter of the gas tank is 2.4, that means the radius is half that, or 1.2, check the picture below.

now, the tank is filling up at 2.5 ft³/min

how many times is 2.5 into V?

[tex]\bf V=\pi ft \cdot 1.2^2 ft\cdot 3 ft\implies 4.32\pi\ ft^3 \\\\\\ \textit{the rate is filling up is }2.5\frac{ft^3}{min} \\\\\\ \cfrac{4.32\pi \ ft^3}{\frac{2.5\ ft^3}{min}}\implies \cfrac{\frac{4.32\pi \ ft^3}{1}}{\frac{2.5\ ft^3}{min}}\implies \cfrac{4.32\pi \ ft^3}{1}\cdot \cfrac{min}{2.5\ ft^3}\implies \cfrac{4.32\pi }{2.5}min[/tex]

that many minutes, round it away.

find the arc length of a central angle of 90° in a circle whose radius is 4 inches

Answers

this is 1/4 * circumference
Circumference = 2 * pi * 4 = 8pi

arc length = 1/4 * 8pi = 2pi or 6.28 ins to nearest hundredth.

Answer:

2 pie in

source: Trust me bro

Matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35. what is the greatest age that andy could be?

Answers

Since there are two unknowns, Matt's age and Andy's age, we need to formulate two algebraic equations in order to solve the system. The first independent equation that we could form, is the relation ship of their ages. Suppose we let Matt's age be equal to x. Andy's age will be denoted as y. Then,

x = 5 + 2y

The second independent equation would be the sum of their ages:
x + y ≤ 35
As you can observe, I used an inequality with the symbol ≤ which means less than or equal to. It means that their sum could be less than or equal to 35. So, the equation is

x + y ≤ 35

Solving the equation,
5 + 2y + y ≤ 35
3y ≤ 35-5
3y ≤ 30
y ≤ 10

Thus, Andy's greatest age could be 10 years old.

A seamstress is paid $9.55 for every pair of pants made. how many pants would have to be made to receive $525.00 a week?

Answers

Let the number of pants have to be made be x.

So,

9.55 * x = 525.00

x = [tex] \frac{525}{9.55} [/tex] ≈ 54.97

Thus, the number of pants have to be made are 54.

To receive $525.00 a week, a seamstress being paid $9.55 per pair of pants made would need to make approximately 55 pairs of pants.

Let’s denote the number of pairs of pants that need to be made as x.

The seamstress is paid $9.55 for every pair of pants.

We want to find the number of pairs of pants needed to earn $525.00, so we set up the equation:

[tex]9.55 \times x = 525.00[/tex]

Solve for x:

[tex]x = \frac{525.00}{9.55} \approx 54.97[/tex]

Since we can’t make a fraction of a pair, we round up to the nearest whole number:

The seamstress would need to make 55 pairs of pants (which means a total of 110 pants) to receive $525.00 a week.

Solve for number 9 please:)

Answers

i think the answer is 6

You traveled for 3 hours, it's just solving for t

Kite WXYZ is graphed on a coordinate plane. What is the area of the kite? 7 square units 8 square units 14 square units 16 square units

Answers

The area of the kite can be found as follows;
Area=[area of XWY]+[areaYWZ]
area XWY=1/2*b*h
=1/2*4*3=6 sq units

area YWZ=1/2*b*h
=1/2*4*4=8 sq units

Hence the area of the kite will be:
Area=6+8=14 sq. units

The area of the kite will be equal to 14 sq. units

What is an area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the Kite in a two-dimensional plane is called the area of the kite.

The area of the kite can be found as follows;

Area = [area of XWY] + [areaYWZ]

Area XWY = 1/2 x b x h

Area XWY = 1/2 x 4 x 3 = 6 sq units

Area YWZ = 1/2 x b x h

Area YWZ = 1/2 x 4 x 4 = 8 sq units

Hence the area of the kite will be:

Area = 6 + 8 = 14 sq. units

Therefore the area of the kite will be equal to 14 sq. units

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Which statement is correct when a scatterplot is constructed? A.The independent variable is the input variable and should be represented by the x-axis. B.The independent variable is the input variable and should be represented by the y-axis. C.The dependent variable is the input variable and should be represented by the x-axis. D.The dependent variable is the input variable and should be represented by the y-axis.

Answers

Answer:- A.The independent variable is the input variable and should be represented by the x-axis.

Explanation:-

A. Correct.

B. Not correct.

Reason:- The independent variable is the input variable and should be represented by the x-axis.

C. Not correct.

Reason:- The dependent variable is the output variable and should be represented by y-axis.

D. Not correct.

Reason:-The dependent variable is the output variable and should be represented by y-axis.

Answer:

A.The independent variable is the input variable and should be represented by the x-axis.

Step-by-step explanation:

It was right on the test.

Oq is a diagonal of quadrilateral nopq. if noq=pqo, no = 5x + 12, and pq = 7x – 8, find the length of no for which nopq is a parallelogram.
a. 10
b. 24
c. 47
d. 62

Answers

If quadrilateral NOPQ is a parallelogram then:
NO = PQ
5 x + 12 = 7 x - 8
12 + 8 = 7 x - 5 x
20 = 2 x
x = 20 : 2
x = 10
NO = 5 * 10 + 12 = 50 + 12 = 62
Answer: d. 62

Since it is a parallelogram, NO = PQ

5 x + 12 = 7 x - 8

12 + 8 = 7 x - 5 x

20 = 2 x

x = 20 : 2

x = 10

NO = 5 * 10 + 12 = 50 + 12 = 62

Answer: 62

Hope this helps, have a BLESSED and wonderful day, as well as a safe one! Also, have a merry Christmas! :-)

-Cutiepatutie

Tom has deposited $500 in an account which earns 2% interest each year. Which expression correctly shows the total value of his account after 3 years?

A) 500 + 0.02 + 0.02 + 0.02
B) 500 + 0.02[500 + 0.02(500 + 0.02*500)]
C) 500 + 0.02*0.02*0.02(500)
D) 500 + 3(0.02)500

Answers

It's D
500+3×0.02×500=530

the product of 18 and q

Answers

The product what you get when two numbers are multiplied together, therefore the product of 18 and q or 18 x q would equal 18q.

Final answer:

The product of 18 and q is expressed as 18q in an algebraic expression, representing the multiplication of 18 by a variable, q. The value of the expression depends on what value q has.

Explanation:

The phrase 'the product of 18 and q' is a mathematical term used in algebra. It represents the multiplication of 18 and a variable 'q'. In algebraic expression, it can be written as 18q, where 18 is the constant multiplicand, and 'q' is the variable multiplier. The value of this product depends on the value of 'q'. For example, if q is 2, the product of 18 and q would be 36.

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A mail distribution center processes as many as 150,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier takes 1800 pieces per load and each air carrier 1500 pieces per load. The loading equipment is able to handle as many as 150 loads per day. Let x be the number of loads by land carriers and y the number of loads by air carriers. Which system of inequalities represents this situation? Click on the correct answer. 1500x + 1800y ≥ 150,000 x + y ≤ 150 1800x + 1500y ≤ 150,000 x + y ≤ 150 1800x + 1500y ≥ 150,000 x + y ≥ 150 1500x + 1800y ≤ 150,000 x + y ≤ 150

Answers

x = land carriers = 1800x

y = air carries = 1500y

as many as means up to that amount so <=150000 and <= 150

so equation is:

1800x + 1500y ≤ 150,000 x + y ≤ 150

Final answer:

The correct system of inequalities for this problem is: 1500x + 1800y ≤ 150,000 and x + y ≤ 150 - representing mail distribution limitations of a center.

Explanation:

In order for the mail distribution center to process the maximum amount of mail (150,000 pieces) with the available resources, the inequalities should be framed as follows:

The total pieces of mail loaded should be equal to or less than 150,000: 1500x + 1800y ≤ 150,000The total loads done by air and land carriers should not exceed the limit of 150: x + y ≤ 150

This mathematical model sets the limitations of the mail distribution process and can be used to predict the optimal allocation of mail to air and land carriers.

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State how many imaginary and real zeros the function has. f(x) = x^5+7x^4+2x^3+14x^2+x+7

Answers

Since the degree of the equation is 5, then the number of zeros is also equal to 5. We can find for the 1st value of the root by trial and error. To do this, we find for the value of x which makes the equation equal to zero, that is:

x^5 + 7x^4 + 2x^3 + 14x^2 + x + 7 = 0 (find x)

By trial and error I made (which I will not show anymore), the possible root is -7. This is equivalent to x + 7.

To find more roots, we divide x^5 + 7x^4 + 2x^3 + 14x^2 + x + 7 by x + 7. The answer of the division results in x^4 + 2x^2 + 1 which is a perfect square trinomial in the form of:

(x^2 + 1)^2

Therefore the other 4 roots are:

x^2 + 1 = 0 ---> i, -i

and

x^2 + 1 = 0 ---> i, -i

Therefore the answer is:

1 real and 4 imaginary zeros

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