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Plz i really need help and plz show everything step by step I have to give in!!

The expressions which are equivalent to the complex number 45 + 2i is E. (9 + 4i) + (36 - 2i)

D. (2 + 8i) + (30 - 6i)

To determine which expressions are equivalent to the complex number 45 + 2i, we can simplify each expression and check if it matches the given number.

Let's evaluate each option:

A. (2 + 8i) + 2(9 + 6i)(1 - i) = 2 + 8i + 2(9 + 6i - 9i - 6i^2) = 2 + 8i + 2(9 + 6i - 9i + 6) = 2 + 8i + 2(15 - 3i) = 2 + 8i + 30 - 6i = 32 + 2i

B. (9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 2(4 + 7i - 8i - 14i^2) = 9 + 4i + 2(4 + 7i - 8i + 14) = 9 + 4i + 2(23 - i) = 9 + 4i + 46 - 2i = 55 + 2i

C. (13 + 4i) + 2(7 + 2i)(2 - i) = 13 + 4i + 2(7 + 2i - 14i - 4i^2) = 13 + 4i + 2(7 + 2i - 14i + 4) = 13 + 4i + 2(24 - 12i) = 13 + 4i + 48 - 24i = 61 - 20i

D. (2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i = 32 + 2i

E. (9 + 4i) + (36 - 2i) = 9 + 4i + 36 - 2i = 45 + 2i

F. (13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i = 45 - 2i

From the evaluations above, we can see that options E and D are equivalent to the given complex number 45 + 2i.

The correct options are:

E. (9 + 4i) + (36 - 2i)

D. (2 + 8i) + (30 - 6i)

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The  expressions that are equivalent to the given complex number 45 + 2i are: (9 + 4i) + (36 - 2i) and (2 + 8i) + (30 - 6i).

Thus, option (D) and (E) are correct.

Given complex number 45 + 2i.

A. (2 + 8i) + 2(9 + 6i)(1 - i)

Simplifying: (2 + 8i) + 2(9 + 6i - 9i - 6)

= (2 + 8i) + 2(3 + 3i)

= 2 + 8i + 6 + 6i

= 8 + 14i

B. (9 + 4i) + 2(4 + 7i)(1 - 2i)

Simplifying: (9 + 4i) + 2(4 + 7i - 8i - 14)

= (9 + 4i) + 2(-10 - i)

= 9 + 4i - 20 - 2i

= -11 + 2i

C. (13 + 4i) + 2(7 + 2i)(2 - i)

Simplifying: (13 + 4i) + 2(14 + 4i - 7i - 2)

= (13 + 4i) + 2(12 - 3i)

= 13 + 4i + 24 - 6i

= 37 - 2i

D. (2 + 8i) + (30 - 6i)

Simplifying: 2 + 8i + 30 - 6i

= 32 + 2i

E. (9 + 4i) + (36 - 2i)

Simplifying: 9 + 4i + 36 - 2i

= 45 + 2i

F. (13 + 4i) + (32 - 6i)

Simplifying: 13 + 4i + 32 - 6i

= 45 - 2i

Thus, option (D) and (E) are correct.

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Answer:

mark me brailist if it helped

Answer:

A.-5

Step-by-step explanation:

I have used an online calculator to check my answer against so this answer is 100% correct. I used "Slope Calculator" by Omni.

PLEASAE MARK BRAINLIEST

Answer:

2 and 6, 1 and 5

Step-by-step explanation:

Answer:

1&5

Step-by-step explanation:

Answer:

This is a linear graph.

Step-by-step explanation:

Since the x values increase at a constant of 1. The y-values have a 1st difference of -4 which means the graph is linear.

Answer:

B. There are no discounts or charges per month.

Step-by-step explanation:

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Answer:

k = 3/2

Step-by-step explanation:

assuming k is your slope

rise/run = y/x

k = 1/3 therefore, (3,1) is your (x,y) points

k=3/2 therefore, (2,3) is your (x,y) points

as you can see, you move 2 more units up on the y-axis with k =3/2. Therefore, it is steeper.

Answer:

x=4

Step-by-step explanation:

Answer:

b. (-5, 4)

Step-by-step explanation:

edge2020

Answer:

The answer to the expression in simplest form is:

[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}[/tex]

Step-by-step explanation:

Given the function

[tex]\frac{\frac{1}{3}}{\frac{1}{4}}[/tex]

solving to get the simplest form

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{1\cdot \:4}{3\cdot \:1}[/tex]

[tex]\mathrm{Apply\:rule}\:a\cdot 1=a[/tex]

[tex]=\frac{4}{3}[/tex]

Thus, the answer to the expression in simplest form is:

[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}[/tex]

Answer:

x = (y - 3)/4.

Step-by-step explanation:

y = 4x + 3

y - 3 = 4x

x = (y - 3)/4.

Step-by-step explanation:

y=4x+3

all divide by 3

4x=y/3

cross multiple

12x=y

divide both sides by 12

therefore, x is equal to y/12

Answer:

(0, 0), (20, 1), (40, 2), (60, 3), (80, 4)

Step-by-step explanation:

An inequality that represents the number of bags of chips, x, the teacher can purchase is [tex]2.95x \leq 36[/tex].

Given the following data:

To write an inequality that represents the number of bags of chips, x, the teacher can purchase:

In this exercise, you're required to write a mathematical expression to represent the total number of bags of chips (x) that a teacher can purchase without exceeding his or her budget of $36.

Translating the word problem into an algebraic expression, we have;

[tex]2.95x \leq 36[/tex]

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Answer:

1. m<1 + <2 = m<4; given

2.  m<3 + m<4 = 180; linear pair postulate

3. m<1 +m<2 + m<3 = 180; substitution property

1. <1 is congruent to <4; given

2. <1 is congruent to <2, <3 is congruent to <4; vertical angle congruency theorem

3. <2 has to be congruent to <3; transitive property

Step-by-step explanation:

Answer:

0.3+0.27=0.57

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

0.3-0.27=0.57

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Is there anything needed for this question? I'm not willing to take "free points"

Answer:

51

Step-by-step explanation:

find the percent for each (34 and 33) subtract from their whole (220 and 170) then subtract from each other

Answer:

Y=-3/5x

Step-by-step explanation:

Answer:

y = 3/2x -14

Step-by-step explanation:

y = -2/3 x

has a slope of -2/3

We want a line perpendicular

Take the negative reciprocal to find the slope

- (1 / -2/3)

3/2

The slope of a line perpendicular is 3/2

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = 3/2x +b

Substitute a point into the equation

-8 = 3/2(4) +b

-8= 6+b

Subtract 6 from each side

-8-6 = b

y = 3/2x -14

Let n = the number we need to find.

0.50(0.25)n = 96

0.125n = 96

Can you finish?

The number if 50% of 25% of the number is 96 is 768

Let the unknown number be x

50% of 25% of the number is expressed as 0.5(0.25)x

0.5(0.25)x = 0.125x

Equating the result to 96 will give;

0.125x = 96

Divide both sides by 0.125

0.125x/0.125 = 96/0.125

x = 96/0.125

x = 768

Hence the number if 50% of 25% of the number is 96 is 768

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Answer:

4 hours

Step-by-step explanation:

120 ÷ 30 = 4

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Answer:

B ) 2 g + 12

Step-by-step explanation:

Answer:

The distance from vertex B to the midpoint of AC is 3 units

Step-by-step explanation:

we are given a triangle with vertices  A (1,-3), B (3,0) and C (5,-3).

Mid point of of AC  (x,y) =  ( 1+5/2 , -3 -3/2)

                                     = ( 6/2 , -6/2)

                                     = (3 , -3)

Distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

                              = [tex]\sqrt{(3-3)^2 + (0 + 3) ^2}[/tex]

                               = [tex]\sqrt{(3)^2}[/tex]

                                = 3 units

Answer:

B and D

Step-by-step explanation:

Because only those two equations on the graphs are straight. and are increasing or decreasing in a constant pace.

Answer:

162.1%

Step-by-step explanation:

Given that:

Size of previous living space = 1450 sq ft

Size of new living space = 3800 sq ft

% increase in living space ;

Increase in living space = 3800 - 1450 = 2350 sq feet

(Increase / previous size) * 100%

(2350 / 1450) * 100%

1.6206 * 100%

= 162.06%

= 162.1%

Answer:

hope

Step-by-step explanation:

Answer:

4 + 3p ≥ 40

Step-by-step explanation:

4 points in the first round plus 3p (identical scores) has to be at least 40 points or higher to move on.

Answer:

Total trip cost = $2,158

Step-by-step explanation:

Given:

Cost of each ticket = $26

Number of student = 83

Find:

Total trip cost

Computation:

Total trip cost = Cost of each ticket x Number of student

Total trip cost = $26 x 83

Total trip cost = $2,158

Answer:

Amount earned = $151,113

Step-by-step explanation:

Here, we are interested in calculating the banker’s earnings rounded to the nearest dollar;

We proceed as follows; we have the following;

1. Annual salary of $75,000

2. 2.35% on approved loans.

Approved loans = 2.8 million

Commission = 2.35/100 * 2.8 million = $65,800

3. $3.75 for each processed loan application

Total = 2750

Amount = 3.75 * 2750 = $10,312.50

Total amount earned is thus;

$75,000 + $65,800 + $10,312.50 = 151,112.5 = 151,113 to the nearest dollar

Answer:

c

Step-by-step explanation:

16-4=12

7+6=11

The false statement is;

C. 16 - 4 = 7 + 6

Given that;

The mathematical expression is;

A. 16 + 3 = 11 + 8

B. 16 = 16

C. 16 - 4 = 7 + 6

D. 16 = 19 - 3

We have to state the false statement.

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The mathematical expression is;

A. 16 + 3 = 11 + 8

Left hand side,

16 + 3 = 19

Right hand side,

11 + 8 = 9

Left hand side = Right hand side

Hence, This is true.

B. 16 = 16

Left hand side = Right hand side

Hence, This is true.

C. 16 - 4 = 7 + 6

Left hand side;

16 - 4 = 12

Right hand side,

7 + 6 = 13

Hence, This is false.

D. 16 = 19 - 3

Left hand side;

16

Right hand side,

19 - 3 = 16

Left hand side = Right hand side

Hence, This is true.

Therefore, The false statement is;

C. 16 - 4 = 7 + 6

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