Find the ratio(SOHCAHTOA)

\( \Large{\boxed{\sf \dfrac{1 + 2i}{3 - 4i} + \dfrac{2 - i}{5i } = - \dfrac{2}{5}}} \)

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Given sum:

\( \sf \: \dfrac{1+2i}{3-4i} + \dfrac{2-i}{5i}\)

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We can simplify the sum only if the denominators of the two fractions are the same. Since they are different, we have to multiply the numerator and the denominator of each fraction by the denominator of the other one.

\( \sf \: \dfrac{1+2i}{3-4i} + \dfrac{2-i}{5i} = \dfrac{5i(1 + 2i)}{5i(3 - 4i)} + \dfrac{(3 - 4i)(2 - i)}{(3 - 4i)5i} \\ \\ \\ \sf \: = \dfrac{5i + 10 {i}^{2} }{15i - 20 {i}^{2} } + \dfrac{6 - 3i - 8i + 4 {i}^{2} }{15i - 20 {i}^{2} } \)

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Replace i² with -1:

\( \sf \dfrac{5i + 10 {i}^{2} }{15i - 20 {i}^{2} } + \dfrac{6 - 3i - 8i + 4 {i}^{2} }{15i - 20 {i}^{2} } \: \\ \\ \\ \\ \sf \: = \dfrac{5i + 10( - 1)}{15i - 20( - 1)} + \dfrac{ 6 - 11i + 4( - 1)}{15i - 20( - 1)} \\ \\ \\ \\ \sf = \dfrac{5i - 10}{20 + 15i} + \dfrac{2 - 11i}{20 + 15i} \)

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Simplify the expression:

\( \sf = \dfrac{5i - 10}{20 + 15i} + \dfrac{2 - 11i}{20 + 15i} \\ \\ \\ \\ \sf \: = \dfrac{5i - 10 + 2 - 11i}{ 20 + 15i} = \sf \dfrac{ - 8 - 6i}{20 + 15i}\)

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To write our solution in the x + iy form, also known as the algebraic form, we have to understand what the conjugate of a complex number is.

\( \textsf{Let z be our complex number, and} \: \overline{\sf z} \: \textsf{its conjugate.} \)

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The conjugate of z, \( \overline{ \sf z}, \) is the complex number formed of the same real part as z but of the opposite imaginary part.

Since x is the real part of z, and y is its imaginary part, this can be expressed as:

\( \sf If \: z = x + iy \:, then \: \overline{ \sf z} = x - iy \)

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Now, we have to multiple both the denominator and the numerator of our fraction by the conjugate of its denominator:

\(\sf \dfrac{ - 8 - 6i}{20 + 15i} = \dfrac{( - 8 - 6i)( \overbrace{20 - 15i}^{ \overline{z}}) }{ (20 + 15i)( \underbrace{20 - 15i}_{ \overline{z}}) } \\ \\ \\ \sf = \dfrac{ - 160 + 120i - 120i + 90 {i}^{2} }{400 - 300i + 300i - 225 {i}^{2} } \\ \\ \\ \sf = \dfrac{ - 160 + 90 {i}^{2} }{400 - 225 {i}^{2} }\)

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One more time, substitute -1 for i²:

\( \sf \: \dfrac{ - 160+ 90 {i}^{2} }{400 - 225 {i}^{2} } \: = \dfrac{ - 160 + 90( - 1)}{400 - 225( - 1)} \\ \\ \\ \sf = \boxed{\sf - \dfrac{ 250}{625}} \)

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Finally, let's simplify our result:

\( \sf - \dfrac{250}{625} = - \dfrac{2 \times 125}{5 \times 125} = \boxed{ \boxed{ \sf - \dfrac{2}{5}}}\)

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Answer:

The exponential equation that passes through the points (0, 40) and (2, 360) is y = 40 x 2^x. This can be verified by substituting x = 0 and x = 2 into the equation to check that the respective points are on the line.

The situation can be represented by expression 3x + 5y = 900

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of cookies and y represent the number of cake slice.

The class wants to raise $900.Hence:

3x + 5y = 900

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The simplified Expression is (2x³ + 3x²)/ (8x-6).

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have to simplify the expression, quantity 6 x plus 9 over 15 x squared all over quantity 16 x minus 12 over 10 x to the fourth power.

Simplified Expression = (6x+ 9) / (15 x²) ÷ (16x - 12)/ 10 \(x^4\)

Now, dividing the Expression

=  (6x+ 9) / (15 x²) . 10 \(x^4\) / (16x - 12)

= 3(2x+3) / (15 x²) × 10 \(x^4\) / 4 (4x - 3)

= (2x+3) / 5x² × 5 × x² × x² / 2(4x-3)

= (2x³ + 3x²)/ (8x-6)

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The perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.

The perimeter of an object or a shape is the distance around the edge of the shape.

Length of AB = √[(6 - 3)² + (5 - 5)²] = 3 units

Length of AC = √[(4 - 3)² + (-1 - 5)²]  = 6.1 units

Length BD = √[(6 - 1)² + (5 - -1)²] = 7.81 units

Length CD = √[(1 - 4)² + (-1 - -1)²]  = 3 units

Perimeter of the shape ABCD = 3 units + 6.1 units + 7.81 units + 3 units = 19.91 units.

The formula for area of a trapezoid will be used to determine the area of the shape as shown below;

A  = ¹/₂(6.1 + 7.81) x 3

A = 20.87 sq. units

Thus, the perimeter of the shape is determined as 19.91 units and the area is 20.87 sq. units.

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Answer:

1.1 Pull out like factors

6x+3= 3•(2x+1)

2.1 This equation has no solution

A non-zero constant never equals zero

2.2 Solve: 2x+1=0

Subtract 1 from both sides of the equation: 2x= -1

Divide both side of the equation by 2

x= -1/2= -0.500

Answer:

a

Step-by-step explanation:

The image of the point after the transformation is (2,-3)

Here, we want to get the image of the point after translation, followed by rotation

When we translate, we move some units up and below the axes

With the given relation, we are going to move 1 units vertically, and 2 units horizontally

This means that we are to add 1 to the vertical axis and 2 to the horizontal axis

We have this as;

what is left is the rotation by 90 degrees

Given the pre-image (x,y); after 90 degrees clockwise rotation, we are going to have the coordinates as (y,-x)

Thus, what we have after rotation is (2,-3)

Answer: 40 IN THE LOWEST FORM

Step-by-step explanation:

The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Question

If you draw scaled copies of this triangle using the scale factors in the

table, what will the areas of these scaled copies be?

Answer: Hi, There! Mika-Chan

The Answer for the Scale Factor is....

→1 Scale and 36 Units ←

Hope this Helps!

Answer: the answer is 1020

Step-by-step explanation: Because lets say 1032-133=899

so if we do 899+121=1020

Answer:

It must contain carbon.

Step-by-step explanation:

get it right on test.

Answer: it must contain Carbon.

Step-by-step explanation: If a compound doesn’t contain carbon, it isn’t an organic compound

Answer:

y diles que yo me se tu pose favorita, que te hablo mal y que eso te U-U

Step-by-step explanation:

Answer:

4a^2+4ab+b^2

Step-by-step explanation:

To find the square we multiply the expression with itself

(2a+b)×(2a+b) = 4a^2+4ab+b^2

Answer: 14

Step-by-step explanation:

To Solve for M

Multiply 6 by 7/3 (reciprocal of 3/7)

6x7/3=42/3

Divide 42 by 3 to get 14.

Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

Answer:

1.125

Step-by-step explanation:

Answer:

Step-by-step explanation:

To help put this into simpler terms, we can convert 2.5 to 2 4/8,

Now we just subtract

3 5/8-2 4/8=1 1/8

Let me know if you have any questions

The True statements are:

Each element of X is given exactly one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

For D (x) = 2 x:

- x is the independent variable,

- D ( 6 ) = 2 · 6 = 12.

10 = 2 · 5,     12 = 2 · 9,     - 4 = 2 · ( - 2 ).

True statements are:

A ) D ( x ) is a function.

D ) D ( x ) is a direct variation.

E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).

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Answer:

Step-by-step explanation:

Jim drank 2 and 4/5 orange juice

2and 4/5=14/5 orange juice

jack drank  1and 1/10 less than Jim= 11/10 less than Jim

I introduce the whole numbers into the fractions

we will convert the number 14/5 into a fraction that has the denominator 10, by multiplying by 2 both numerator and denominator

(14/5 )*2=28/10

Now we can find out how much juine Jack drank

28/10- 11/10= 17/10

so Jack drank 17/10 orange juice , the fraction can be written also as

1 and 7/10

Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Let's solve for x.

5x+4y=20

Step 1: Add -4y to both sides.

5x+4y+−4y=20+−4y

5x=−4y+20

Step 2: Divide both sides by 5.

5x/5 = -4y+20/5

x= -4/5y + 4

Answer is -4y+20/5

The X-intercepts are (4,0).

The Y-intercept is (0,5).

I uploaded a picture of the graph below.

Answer:

C

Step-by-step explanation:

7 - 2 = 5

11 - 3(2)

11 - 6 = 5

4(2) - 3

8 - 3 = 5

C is the only one that doesn't equal 5

The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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Answer: D

Step-by-step explanation:

2x-36=0                                                

+36     +36

___________

2x=36

x=18

Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.

Hello there!

$500 invested at 4% compounded annually for 10 years

time: 10 years

compound: annually

interest: 4%

y = 500(1.04)^10

1.04^10 = 1.48

500 x 1.48 = 740

Value after 10 years: $740

Answer:

  $740.12

Step-by-step explanation:

The amount is multiplied by 1.04 each year, so after 10 years, the balance will be ...

  $500(1.04^10) = $740.12

Answer:

a > -9

Step-by-step explanation:

-9 + 2a < 3a

1. Add 9 to both sides

-9 + 2a + 9 < 3a + 9

2. Simplify

2a < 3a + 9

3. Subtract 3a from both sides

2a - 3a < 3a + 9 - 3a

4. Simplify

-a < 9

5. Multiply both sides by -1 (reverse the inequality)

(-a)(-1) > 9(-1)

6. Simplify

a > -9

Assuming all points in the triangle \(T\) are uniformly distributed, we have the joint density

\(f_{X,Y}(x,y)=\begin{cases}\frac1A&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}\)

where \(A=\frac{8^2}2=32\) is the area of the triangle \(T\).

(a)

\(P(X<5)=\displaystyle\iint_{T^*}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx\)

(where \(T^*\) is the portion of \(T\) for which \(x\) is between 0 and 5)

\(P(X<5)=\displaystyle\frac1{32}\int_0^5\int_0^{8-x}\mathrm dy\,\mathrm dx\)

\(P(X<5)=\displaystyle\frac1{32}\int_0^5(8-x)\,\mathrm dx\)

\(P(X<5)=\dfrac1{32}\cdot\dfrac{55}2=\boxed{\dfrac{55}{64}}\)

(b) Generalizing the previous result, we have

\(P(X\le x^*)=\displaystyle\iint_{T^*}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx\)

(this time with \(T^*\) being the portion of \(T\) where \(0\le x\le x^*\) for some \(x^*\) between 0 and 8)

\(P(X\le x^*)=\displaystyle\frac1{32}\int_0^{x^*}\int_0^{8-x}\mathrm dy\,\mathrm dx\)

\(P(X\le x^*)=\displaystyle\frac1{32}\int_0^{x^*}(8-x)\,\mathrm dx\)

\(P(X\le x^*)=\displaystyle\frac1{32}\left(8x^*-\frac{(x^*)^2}2\right)\)

That is, the CDF of \(X\) is

\(P(X\le x)=\begin{cases}\frac{8x-\frac{x^2}2}{32}&\text{for }0\le x\le8\\0&\text{otherwise}\end{cases}\)

or

\(\boxed{P(X\le x)=\begin{cases}\frac{16x-x^2}{64}&\text{for }0\le x\le8\\0&\text{otherwise}\end{cases}}\)

(c) Obtain the PDF by differentiating the CDF:

\(f_X(x)=\dfrac{\mathrm d}{\mathrm dx}P(X\le x)\)

\(\boxed{f_X(x)=\begin{cases}\frac{8-x}{32}&\text{for }0<x<8\\0&\text{otherwise}\end{cases}}\)

(d) Compute the expectation of \(X\):

\(E[X]=\displaystyle\int_0^8xf_X(x)\,\mathrm dx\)

\(E[X]=\displaystyle\frac1{32}\int_0^8x(8-x)\,\mathrm dx=\boxed{\frac83}\)

Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).

Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.

90 students are in a club and play a sport.

140 total students play a sport.

Therefore, 140 - 90 = 50 students play a sport but are not in a club.

The total number of students who play a sport is 140 + 50 = 190.

200 total students are in a club.

Therefore, 200 - 90 = 110 students are in a club but do not play a sport.

The total number of students who do not play a sport is 325 - 190 = 135.

The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.

This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.

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Answer:

5

Step-by-step explanation:

Divide 5/6 by 1/6 to get 5 as your answer.