Calculate 6+9i/-1+4i

Answers

Answer 1

Multiply the numerator and denominator by the conjugate of the denominator:

[tex]\dfrac{6+9i}{-1+4i} \times \dfrac{-1-4i}{-1-4i} = \dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2}[/tex]

Simplify:

[tex]\dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2} = \dfrac{-6-9i-24i-36i^2}{1-16i^2} = \dfrac{-6-33i-36i^2}{1-16i^2} = \dfrac{-6-33i+36}{1+16} = \boxed{\dfrac{30-33i}{17}}[/tex]


Related Questions

What are the steps involved in multiplying/ dividing rational expressions??

Answers

Answer:

Multiplication:

Step 1: Factor both the numerator and the denominator.

Step 2: Write as one fraction.  Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.

Step 3: Simplify the rational expression.

Step 4: Multiply any remaining factors in the numerator and/or denominator.

Division:

Step 1: Completely factor both the numerators and denominators of all fractions.

Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal.

Step 3: Cancel or reduce the fractions. Remember that to reduce fractions; you can cancel something in the numerator with something in the denominator, but in order to cancel something in the numerator and denominator the two factors must be EXACTLY the same.

Step 4: Rewrite the remaining factor. Notice that you do NOT need to actually multiply anything in the numerator or denominator.

Step 1: Factor both the numerator and the denominator. ...
Step 2: Write as one fraction. ...
Step 3: Simplify the rational expression. ...
Step 4: Multiply any remaining factors in the numerator and/or denominator. ...
Step 1: Factor both the numerator and the denominator.
Step 2: Write as one fraction.

Hope this helps :))

√3 is a polynomial of degree ________.

Answers

Step-by-step explanation:

Therefore, the degree of polynomial √3 is zero.

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

[tex]\tt{\sqrt{3}}[/tex] is a polynomial of degree 0

[tex]\sf\huge\underline\color{pinl}{༄Note:}[/tex]

The expression is constant, which means it can be rewritten with a factor of x^0. The degree is the largest exponent on the variable.

[tex]\color{pink}{==========================}[/tex]

-#CarryOnLearning

-Park Hana Moon

Can someone explain this I don't understand

Answers

Answer:

16°

Step-by-step explanation:

For this problem, it's helpful to know SOH-CAH-TOA. When you see which sides are given, you can use that acronym to figure out which trigonometric function you need to use. In this case, the side adjacent to the angle in question (53) and the hypothenuse (55) are given. So we would look at CAH, and know we need to use cosine. However, since we are finding an angle, we need to use [tex]cos^{-1}[/tex] (inverse cosine). Now we just solve:

? = [tex]cos^{-1} (adjacent / hypotenuse)[/tex]

? = [tex]cos^{-1} (53/55)[/tex]

? = 15.5° -> 16°

The value of w???????

Answers

Answer:

Step-by-step explanation:

The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:

[tex]\frac{15}{18}=\frac{w}{30}[/tex] and cross multiply.

18w = 450 so

w = 25

Could someone please answer this question for me

Answers

Answer:

Yes

Step-by-step explanation:

It's a right angled triangle as 14^2+48^2=50^2.

If f(x)=16x-30 and g(x)=14x-6 for which value of x does (f-g)(x)=0

Answers

Answer:

12

Step-by-step explanation:

f(x)=16x-30

g(x)=14x-6

f(x) - g(x) = 16x-30 - (14x-6)

               = 16x - 30 - 14x +6

                = 2x -24

Set this equal to zero

2x-24 = 0

Add 24 to each side

2x-24 +24 = 0+24

2x = 24

Divide by 2

2x/2 =24/2

x = 12

x=12

Answer:

Solution given:

f(x)=16x-30 and g(x)=14x-6

(f-g)(x)=0

or

f(x)-g(x)=0

16x-30-14x+6=0

2x-24=0

2x=24

x=24/2

x=12

help please for functions​

Answers

Answer:

A

Step-by-step explanation:

The domain of a graph is the set of number you can input for x that will give you a y value. From the looks of it, this graph has all x-values larger than zero.

We know it is not b since we see x-values of the graph go past x=10.

We know it is not c because there are no negative x-values.

We know it is not D because there are no negative x-values. Real number include negative numbers.

2 cm = 7.5 m in the drawing the mall is 8.6 cm tall how tall is the actual mall

Answers

Step-by-step explanation:

here's the answer to your question

Which represents a unit rate?

Answers

Answer:

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Someone please help

Answers

Answer:

Why wont anyone help me please

Latoya's annual salary is $26,000. A total of $7352.24 will be deducted for taxes and health insurance. She will receive her paycheck monthly in 12 equal installments. How much will she get paid with each paycheck?

Answers

Step-by-step explanation:

Lets translate this word problem into math.

"Latoya's annual salary is $26,000" = We start with the number 26,000

"A total of $7352.24 will be deducted for taxes and health insurance" = It's the number we started with "deducted" (minus) 7352.24

"She will receive her paycheck monthly in 12 equal installments" = Our number will be divided by 12

"How much will she get paid with each paycheck?" = "Find answer pls thx"

To put it all together...

[tex]\frac{26,000-7,352.24}{12}[/tex]

Now all we have to do is solve!

[tex]\frac{26,000-7,352.24}{12}[/tex]

Subtract.

[tex]\frac{18,647.76}{12}[/tex]

Divide.

[tex]1,553.98[/tex]

Answer:

Latoya will get paid $1,553.98 with each paycheck.

The perimeter of a rectangle is 74 inches. If the length is five more than the width, what are the rectangle's measurements?

Answers

Answer:

P=2(74)+2(5)

148+10=158

Is the answer option c?

Answers

Answer:

No it isnt corret answer.

Answer:  Choice D

Explanation:

Recall that the quadrants are labeled such that Q1 (shorthand for quadrant 1) is in the upper right corner. Then we have Q2 in the upper left corner. We work counterclockwise around as shown in the diagram below.

Therefore, the curve is found in Q1 and Q3

Jackie is 8 years younger than her neighbor, Paula. The sum of their ages is 30. How old are Jackie and Paula?

Answers

Answer:

Jackie: 11

Paula: 19

Step-by-step explanation:

11+19 = 30

BRAINLEST IF CORRECT!!!!

Answers

x + 133 = 180

x = 180 - 133 (Linear Pair)

x = 47

Therefore x° = 47°

Answered by Gauthmath must click thanks and mark brainliest

Answer:

47

Step-by-step explanation:

reason: Being sum of supplement angle

SEE QUESTION IN IMAGE

Answers

Answer:

Step-by-step explanation:

15) should be b) 6.7, 6 as the median is the average of the 25th and 26th result, these both occur in the 6 group and is the only option with a whole number for median

To check the mean

(2(4) + 7(5) + 17(6) + 10(7) + 8(8) + 6(9)) / 50 = 6.66 ≈ 6.7

16) mode is 1 child as the single largest grouping is 11 families

there were 46 families polled so the median occurs between 23 and 24

7 + 11 + 6 is 24 therefore median falls under 2 children.

a) 1, 2

A giant and a dragon live next door to each other. The giant's house is 23 meters tall. His house is 35 meters shorter than the dragon's house.

Answers

The answer is
The dragon’s house is 58 meters tall

Sue wants to put rectangular garden on her property using 90 meters of fencing. There is a ns through her property, so she decides to increase the size of the garden by ne side of the rectangle. (Fencing is then needed only on the other three river that runs through her property, so she using the river as one side of the rectangle. (ren sides). Let x represent the length of the side of the rectangle parallel
a. Express the garden's area as a function of x.
b. Using your graphing calculator, determine the maximum area that Sue will be able to enclose for her garden and the dimensions of that area. (Hint: A good viewing window might be (-40, 100; 0, 1100])

Answers

Answer:

a) A(x)  = 90*x/2  -  x²/2

b) A(max) = 1012.5 m²

Step-by-step explanation:

L = 90 meters of fencing

Rectangular area is

A(r) = x*y .            where  x  and  y  are the sides of the rectangle

the perimeter is  ( we are going to fence only 3 sides, then)

x + 2*y = 90    or .    y  = ( 90  - x ) /2

Area as a function of x is:

A(x)  = x * ( 90 - x)/2

A(x)  = 90*x/2  -  x²/2

Tacking derivatives on both sides of the equation:

A´(x) =45  -  2*x/2         A´(x) =45  - x

A´(x) = 0 .      45  - x = 0 .      x  = 45 . meters

and . y   =  ( 90  - x ) 2

y = ( 90- 45 )/2  

y = 22.5 meters

A(max) =  45*22.5  m²

A(max) = 1012.5 m²

If we get the second derivative of A(x) .  A"(x) = - 1       A"(x) < 0

Then A(x) has a maximum for x = 45

the area of a square table is 225/81 square meters. find the length of a side of the table​

Answers

9514 1404 393

Answer:

  5/3 meters

Step-by-step explanation:

The area is the square of the side length, so the side length is the square root of the area.

  s = √(225/81) = 15/9 = 5/3 . . . meters

The length of a side of the table is 5/3 meters.

B
C
5
C
A
12
Find the length of “c” using
the Pythagorean Theorem.
Enter

Answers

Answer:

13

Step-by-step explanation:

We know that a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144 = c^2

169 = c^2

Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 =c

Which equation below has a slope greater than the slope of the line shown above?
A. y = 2 x + 2
B.y = 3x - 1
C. y = - 3
D. y = 4 + 1.75 x​

Answers

Answer:

B.y = 3x - 1

Step-by-step explanation:

Pick two points on the line

(0,1) and (2,5)

The slope using the slope formula

m = (y2-y1)/(x2-x1)

   = ( 5-1)/(2-0)

  = 4/2

  = 2

We want a slope that is greater than 2

The slope intercept form of the equation is

y = mx+b where m is the slope

y = 3x - 1  has a slope of 3 which is greater than 2

help asap------------

Answers

Answer:

the real is -19

the imaginary is -24 (or -24i depending on what the computer is looking for as an answer)

Step-by-step explanation:

The Chesapeake Bay holds about 18 trillion gallons of water. The bay covers 4,480 square miles or 2,867,200 acres. Each acre can hold 750,000 oysters. Each oyster can filter 50 gallons of water each day. Can there be enough oysters to filter the whole Chesapeake Bay in one day

Answers

Answer:

There are enough oysters

Step-by-step explanation:

Given

[tex]Volume = 18\ trillion\ gallon[/tex]

[tex]Area = 2867200\ acre[/tex]

[tex]1\ acre = 750000\ oysters[/tex]

[tex]1\ oyster = 50\ gallons[/tex]

Required

Determine if there is enough water for a day

We have:

[tex]1\ oyster = 50\ gallons[/tex]

Convert to oysters: multiply both sides by 750000

[tex]750000 * 1\ oyster = 50\ gallon *750000[/tex]

[tex]750000\ oysters = 37500000\ gallons[/tex]

Given that:

[tex]1\ acre = 750000\ oysters[/tex]

So, we have:

[tex]1\ acre= 37500000\ gallons[/tex]

Convert to acre: Multiply by 2867200

[tex]2867200 * 1\ acre= 37500000\ gallons * 2867200[/tex]

[tex]2867200\ acres= 107520000000000\ gallons[/tex]

By comparison:

[tex]18000000000000\ gallons < 107520000000000\ gallons[/tex]

i.e. the volume of water in the bay is less than the capacity of the oysters. Hence, there are enough oysters.

10) It takes 1 'A cups of sugar and 3 cups of flour to make Sarah's cookies. What is the ratio of sugar to cookies?​

Answers

Answer:

Step-by-step explanation:

Hello!

1-3

Match the two numbers with their least common multiple (LCM).

Answers

Answer:

Step-by-step explanation:

6 and 4 : LCM is 12

6 and 8: LCM is 24

6 and 10 LCM is 30.

6&4: option C
6&8: optionA
6&10: option B

Example 2 Determine the sum of the first 100 terms for the series 2+5+ 8 + ...​

Answers

Answer:

15050

Step-by-step explanation:

Hello!

So basically, this arithmetic sequence follows the rule (3n-1). What you are looking for is the summation of (3n-1) with a lower limit of 1 and an upper limit of 100. This, plugging it into a calculator (etc. symbolab) or even calculating it manually, we get ∑↑100↓n=1⇒3n-1=15050.

Answer:

S₁₀₀ = 15050

Step-by-step explanation:

There is a common difference between consecutive terms

5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 3 , then

S₁₀₀ = [tex]\frac{100}{2}[/tex] [ (2 × 2) + (99 × 3) ]

       = 50 (4 + 297)

       = 50 × 301

       = 15050

Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.
A26
B27
C23
D32

Answers

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{n}{2}\left(a + x_n\right)[/tex]

Where n is the number of terms, a is the first term, and x_n is the last term.

We know that the initial term a is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find n.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n=a+d(n-1)[/tex]

Since the initial term is 13 and the common difference is 7:

[tex]x_n=13+7(n-1)[/tex]

Substitute:

[tex]\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)[/tex]

We are given that the initial term is 13 and the sum is 2613. Substitute:

[tex]\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))[/tex]

Solve for n. Multiply both sides by two and combine like terms:

[tex]5226 = n(26+7(n-1))[/tex]

Distribute:

[tex]5226 = n (26+7n-7)[/tex]

Simplify:

[tex]5226 = 7n^2+19n[/tex]

Isolate the equation:

[tex]7n^2+19n-5226=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 7, b = 19, and c = -5226. Substitute:

[tex]\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}[/tex]

Evaluate:

[tex]\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}[/tex]

Evaluate for each case:

[tex]\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}[/tex]

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

Uma maneira de realizar a operação 9972 - 9 de forma rápida e correta é calculando 1 000 * 994, que é igual a 994 000. A igualdade que justifica esse fato está expressa em:

a) (a + b)² = a² + b² + 2ab
//
b) a² - b² = (a + b)(a - b)
//
c) a² - b² = (a - b)²
//
d) (a - b)² = a² - 2ab + b²
//
e) a² - b² = 1 000(a + b)

Answers

Answer:

a)

Step-by-step explanation:

Need help asap... thanks!

Answers

Answer:

90

Step-by-step explanation:

We know that area of ∆BCD = half of the area of rectangle BEFD, since any triangle drawn from taking a side and base and a point on the opposite side as the 3rd vertex has the half area of the rectangle

so, area of ∆BCD = 15×12/2 = 90 (since two legs of the right triangle are 15 and 12)

since area ∆BCD is half the area rectangle BEFD and sum of the area of ∆BEC and ∆CFD will be the rest of the area of rectangle BEFD, which is 90

Convert the credit card rate to the APR. Ohio, 0.02192% daily rate. Please round your answer to the nearest percent. (zero decimal place.) Enter only the number without $ sign.

Answers

Answer:

8%

Step-by-step explanation:

APR means annual percentage rate.

To convert the daily rate to an APR, multiply the daily rate by the number of days in a year

365 days = 1 year

0.02192% x 365 = 8.0008%

To round off to the nearest percent, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

The tenth digit is 0, so the number would be rounded off to 8%

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