which of the following is equivalent to (i+3)+i(2i-4)

a. -5i + 1
b. -3i + 1
c. i-3
d. -i + 3

Answers

Answer 1

Answer:

answer is b

Step-by-step explanation:

i+3 -2 -4i = 1-3i

Answer 2

The expression that is equivalent to (i+3)+i(2i-4) is -3i  +  1

Option B is correct

The given expression is:

(i+3)+i(2i-4)

Open the parenthesis by expanding the expression using the distributive rule

i  +  3  +  2i²  -  4i

Note that i²  =  -1

The expression, therefore, becomes:

i  +  3  +  2(-1)  -  4i

i  +  3  -  2  -  4i

Collect like terms by bring the real parts together and the imaginary parts together

i  -  4i   +  3  -  2

Simplify to get the final expression

-3i  +  1

Therefore, the expression that is equivalent to (i+3)+i(2i-4) is -3i  +  1

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Related Questions

If the scale factor of a figure is 6, what is the new length of the enlarged figure matched to the length of the orginal?
Original: 1 cm
Enlarged: 6 cm
Original: 7 cm
Enlarged: 42 cm
Original: 2.5 cm
Enlarged: 15 cm
Original: 5 cm
Enlarged: 30 cm

Answers

Answers:

Original = 1 ----> Enlarged = 6Original = 7 ----> Enlarged = 42Original = 2.5 ----> Enlarged = 15Original = 6 ----> Enlarged = 30

It looks like you have the correct order. To get those answers above, we simply multiply the original length by the scale factor 6.

Example: 7*6 = 42

the value of ( 7 + 4root 3) ( 7 - 4 root 3) is​

Answers

Answer:

Step-by-step explanation:

(a + b)(a - b) = a² - b²

[tex](7 + 4\sqrt{3}) (7 - 4\sqrt{3}) = 7^{2}-(4\sqrt{3} )^{2}\\\\ = 49 - 4^{2}*(\sqrt{3})^{2}\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1[/tex]

[tex]\boxed{1}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex](7 + 4 \sqrt{3} ) \: (7 - 4 \sqrt{3} ) \\ \\ = 7 \: (7 - 4 \sqrt{3} ) + 4 \sqrt{3} (7 - 4 \sqrt{3} ) \\ \\ = 49 - 28 \sqrt{3} + 28 \sqrt{3} - 48 \: (since \: \sqrt{3} \times \sqrt{3} = 3)\\ \\ = 49 - 48 \\ \\ = 1[/tex]

You can also use the identity:

( a + b ) ( a - b ) = [tex] {a}^{2} - {b}^{2}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Mike drew a quadrilateral with 4 right angles and 2 pairs of opposite sides that are parallel. Name the quadrilateral she could have drawn

Answers

Answer:

Rectangle

Step-by-step explanation:

The polygon that contains 4 sides is known as the quadrilateral

Also there are 6 types of quadrilateral that are as follows;

a. The rectangle has 2 pairs of opposite sides & 4 sides of the interior angles

b. The square contains the 4 congruent sides & 4 right interior angles

c. The parallelogram has 2 pairs of opposite sides that are parallel & congruent and 2 pairs of angles that are opposite & congruent

d. The rhombus contains the 4 congruent sides and angles

e. The trapezium contains the one pair of parallel sides

f. The kite contains the two pairs of sides that are congruent adjacent

Earned income and capital gains (or "portfolio income") are acquired in different ways. Which statement describes how they are different?

Answers

Answer:

n

Step-by-step explanation:

Ben asked his 19 classmates whether they were right handed or left-handed. There were five more right handed classmates than left handed classmates. Write a system of equations that can be used to determine how many of Ben’s classmates were right and left handed.

Answers

Answer:

left handed = 7 ; right handed = 12

Step-by-step explanation:

r = right handed

l = left handed

r + l = 19

r = l + 5

If we use substitution method we have:

l +5 + l = 19

2 l = 14

l = 7

r = 7 + 5 = 12

Answers:

The system of equations is

[tex]\begin{cases}y = x-5\\x+y = 19\end{cases}[/tex]

where x and y is the number of right-handed and left-handed people respectively.

The system solves to (x,y) = (12,7)

Interpretation:

There are  12   right-handed people and  7   left-handed people in the class.

=========================================================

Explanation:

x = number of right-handed people

y = number of left-handed people

x and y are positive whole numbers.

There are 5 more right-handed people compared to left-handed people, so we can say x = y+5 which is the same as y = x-5. So you could go for either equation. Let's go for the one where y is isolated.

The second equation to form is x+y = 19 because there are 19 people in the class, and you can only be one or the other (left-handed or right-handed but not both). I'm not considering the possibility anyone is ambidextrous though of course that may happen in a realistic setting.

The two equations then form the system

[tex]\begin{cases}y = x-5\\x+y = 19\end{cases}[/tex]

There are a number of ways we can solve this system. Substitution is possibly the quickest way.

x+y = 19

x+(x-5) = 19 ... replace y with x-5; due to the first equation

2x-5 = 19

2x = 19+5

2x = 24

x = 24/2

x = 12 .... this is the number of right-handed people

y = x-5

y = 12-5

y = 7 .... this is the number of left-handed people

Plz answer this question

Answers

Answer:

3,16,729

Step-by-step explanation:

What is the slope ? Simplify your answer and write it as a proper fraction

Answers

Answer: 1/2

(0,80) (90,20)

Use Slope Formula m= (y1-y2)/(x1-x2)

90-80/20 = 1/2

Your slope is 1/2

round 0.982 to 2 decimal places

Answers

Answer:

0.98

Step-by-step explanation:

0.982,0.98()2 (round up if 5+ down 4-) 0.98

The number 0.982 rounded of to two decimal places will be 0.98.

What is rounding a number to some specific place?

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

The digit 5 acts as a limit.

if the right-sided digit to the digit where we've to round off is < 5, we keep it the same and make all right-sided values 0, and if the right-sided digit is > 5, then we make it increase by 1, and the rest of the right-sided digits become 0. If the digit on right is 5, and after it, there are only zeros or no value, then we round up (increase by 1, as we did in 347500 -> 34800 ) (Well there are many detailed rules of rounding)

Since the given number is 0.982, and in this number the thousandth place is taken by 2, therefore, the number when rounded off will be equal to 0.98.

Hence, the number 0.982 rounded of to two decimal places will be 0.98.

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-3 + 4x = 25
help mee

Answers

Answer:

are u solving for  x  if so then

x=7

Step-by-step explanation:

hope this helps ...brainliest please!

-3+4x+=25
4x=25+3
4x=28
4x=4
x=7

if p = q and q = r then p = r

What statements is this?

A. Inverse statement

B.Contrapositive Statement

C.A syllogism

D.Converse statement.

Answers

Answer:

Syllogism, or C.

3
The school that Willie goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 12 senior citizen tickets and 5 child tickets for a total of $102. The
school took in $156 on the second day by selling 14 senior citizen tickets and 12 child tickets.
Find the price of a senior citizen ticket.
A $6
B $7
C$10
D $4

Answers

Answer: A $6

Step-by-step explanation:

Let x = price per child ticket, y= price per senior ticket.

As per given, we have

5x+12y=102  (i)

12x+14y=156  (ii)

From (i), we have

[tex]x=\dfrac{102-12y}{5}[/tex]   (iii)

Put value of x in (ii), we get

[tex]12(\dfrac{102-12y}{5})+14y=156\\\\\\ \dfrac{1224-74y}{5}=156\\\\\\1224-74y=5\times156\\\\\\ 1224-74y=780\\\\\\ 74y=1224-780\\\\\\ 74y=444\\\\ y=\dfrac{444}{74}\\\\\\ y=6[/tex]

Hence, the price of senior ticket = $6

Thus the correct option is A.

Giovanna has a score of

−5minus, 5 in Canasta. Vera's score is

Write an inequality that correctly compares the scores.

Answers

Answer:'

-9.7 minus, in 13

Step-by-step explanation:

Al trazar en el plano cartesiano el angulo a cuyo lado terminal es el punto de ( 3,4). Los valores de las funciones del coseno y cocecante son

Answers

Answer:

[tex]cos(\alpha)=\frac{3}{5}=0.6[/tex]

[tex]cosec(\alpha)=\frac{5}{4}=1.25[/tex]

Step-by-step explanation:

El cos(α) se define como el cociente entre el cateto adyacente y la hipotenusa.

El valor del cateto adyacente en nuestgro caso es CA = 3.

La hipotenusa se calcual de la siguiente manera:

[tex]h=\sqrt{3^2+4^2}=5[/tex]

Por lo tanto, el cos(α) sera:

[tex]cos(\alpha)=\frac{3}{5}=0.6[/tex]

El cosec(α)=h/CO.

El cateto opuesto CO = 4 y la hipotenusa h = 5

Por lo tanto, el cosec(α) sera:

[tex]cosec(\alpha)=\frac{5}{4}=1.25[/tex]

Espero te haya sido de ayuda!

What is the area of a rectangle with side lengths 25 2 5 feet and 46 4 6 feet? Use the grid to help you.

Answers

Answer:

1185 10/30 square feet

Step-by-step explanation:

Area of a rectangle = length * width

Given

Length = 25 2/5 feet

width = 46 4/6

Substitute into the formula;

Area = 25 2/5 * 46 4/6

Area = 127/5 * 280/6

Area = 35,560/30

Area = 1185 10/30

Hence the area of the rectangle is 1185 10/30 square feet

Write as many expressions as you can that have the same value as 10 to the 6 power. Focus on using
exponents and multiplication.

Answers

1,000,000

100 * 100 * 100

100^3

1,000^2

10,000 * 100

10^4 * 10^2

10^3* 10^3

10^5 * 10

1,000 * 1,000

100,000 * 10

400,000 * 2.5

500,000 * 2

250,000 * 4

200,000 * 5

10 * 10 * 10 * 10 * 10 * 10

10^3 * 10 * 10^2

10^4 * 10 * 10

10^7 / 10

10^10 / 10^4

I DON'T WANT TO WRITE MORE

The solution is: the expressions as we can that have the same value as 10 to the 6 power , using exponents and multiplication are given below.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

10 to the 6 power

i.e. 10^6

now, using exponents and multiplication the expressions as we can that have the same value as 10 to the 6 power are:

1,000,000100 * 100 * 100100^31,000^210,000 * 10010^4 * 10^210^3* 10^310^5 * 101,000 * 1,000100,000 * 10400,000 * 2.5500,000 * 2250,000 * 4200,000 * 510 * 10 * 10 * 10 * 10 * 1010^3 * 10 * 10^210^4 * 10 * 1010^7 / 1010^10 / 10^4

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Find a equation of a line that is parallel to y=5x-21 and passes through the point (3,7).

Answers

So to approach this problem, since we are given the slope of the first line we already know since the second line is going to parallel we will use same slope. Now use point slope form. Y-7=5(x-3). Distribute y-7=5x-15. Add 7 to both sides, -15+7=-8. Y=5x-8 that’s the equation that goes through 3,7.

Hope this helps!

What is the factored form of the following expression? 25x^2 + 70x+ 49​

Answers

Answer:

( 5x + 7 ) ²

Step-by-step explanation:

25 x ² + 70 x + 49

Identity Used

(a + b) ² = a ² + 2 ab + b ²

= 25 x ² + 35 x + 35 x + 49

= 5 x ( 5x + 7 ) + 7 ( 5 x + 7)

= ( 5x + 7 )

More to know about Algebraic Identities :-

➛ (a + b)² = a² + 2ab + b²➛ (a - b)² = a² - 2ab + b²➛ a² - b² = (a +b) (a-b)➛ (x + a) (x + b) = x² + (a + b) x + ab➛ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac➛ (a + b)³ = a³ + b³ + 3ab (a + b)➛ (a - b)³ = a³ - b³ - 3ab (a + b)➛ a³ + b³ + c³ = 3abc (If a + b + c = 0)➛ a² + b² + c² = (a + b + c)² - 2 (ab + bc + ca)

Answer:

(5x + 7)2.

The expression is in the form a2x2 + 2abx + b2, where a = 5 and b = 7.

Thus, it can be factored as a perfect square trinomial.

convert: 1 hour to seconds​

Answers

1 min = 60 seconds

1 hour = 60 mins = 60 x 60 = 3600 seconds .

Help us appreciated:)

Answers

answer:

reflect over y-axis and then translate 1 unit up



hope this helped

Which of the following are magnitudes for rotational symmetry of the regular octagon below about the marked point?

Answers

The answer to your question is a

The magnitude of rotational symmetry of the regular octagon below the marked point is 45°, so option A is correct.

What is octagon?

Eight sides, eight internal angles, and eight vertices are the characteristics of an octagon. An octagon is referred to as being regular if all of its sides and angles have the same measurements.

Given:

From the figure, the lengths of the side of the octagon are equal,

So the angle will also be equal,

And we know that octagon has 8 interior angles and their sum is 360 degrees.

Now for measure of one angle = 360° / 8 = 45°,

Therefore, the magnitude of rotational symmetry of the regular octagon below the marked point is 45°.

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f(x)=5x−3, find f(2)f(2)

Answers

Answer:

f(2)f(2) = 49

Step-by-step explanation:

Note that f(2)f(2) is the same as [f(2)]^2.

If f(x) = 5x - 3, then f(2) = 5(2) - 3, or f(2) = 7, and so:

f(2)f(2) = [f(2)]^2 = 7^2 = 49

Thus, f(2)f(2) = 49

Use 3.14 = 7 to find the volume of the composite shape below.
15 in
20 in
18 in
The total volume of this composite shape is

Answers

Awnser: 16022 in3

Step-by-step explanation:

find the volume of the 2 cones find the volume if the semicircle then add the 2 volumes together.

a lines y-intercept is -4, and it's slope is 2. what is its equation in slope-intercept form?

Answers

Answer:

2x-4

Step-by-step explanation:

2x-4

mx+b format

The isosceles triangle and the rectangle have equal perimeters. The triangle has x+5 on the left side. On its base it has x. The rectangle has x-1 on the left side. On the bottom, it has x+4.

Answers

Answer:

The value of x is 4.

Step-by-step explanation:

The perimeter of the triangle is the sum of the lengths of all its sides.

The perimeter of the rectangle is twice the sum of the length and the width.

base of triangle = x

two equal sides = x + 5

length of rectangle = x - 1

width of rectangle = x + 4

According to the question,

Perimeter of triangle = perimeter of rectangle

x + x + 5 + x + 5 = 2 ( x - 1 + x + 4)

3 x + 10 = 2 (2 x + 3 )

3 x + 10 = 4 x + 6

4 x - 3 x = 10 - 6

x = 4

What is 1/4 as a number?

Answers

Answer:

.25

Step-by-step explanation:

you divide 1 by 4 which equals .25

Answer:

1/4 as a number is 0.25

Step-by-step explanation:

Divide 1 by 4 = 0.25

why does safari take forever to load ...

Answers

Answer:

God knows. But I guess if you have iphone x and after it shouldn't take so long. I have iphone 12 pro max and it works flawlessly.

Answer:

I don't know but I've been thinking the same thing

Answer please best answer=brainliest

Answers

Answer:

Part A

median: 7, third quartile: 15, first quartile: 3, units: years

Part B

image doesn't show whole question

Step-by-step explanation:

2,2,4,7,7,14,16,18

2,2,4,(7\/7),14,16,18

2,2\/4,7\/7,14\/16,18

If f (n)= - 3n + 2, what is the value of f(12) ?

Answers

Answer:

Step-by-step explanation:

f(n)= -3n + 2

to find :f(12)

substitute 12 in place of n

f(12)= -3*12 + 2

f(12)=-36 + 2

f(12)= -34

The value of the  f(12) is equal to -46 where the expression is

f(n) = -3n + 2.

What is an expression?

Any mathematical statement which consist of numbers , variables and arithmetic operations is known as expression. An expression gives some numerical value when we put the value of variables in it.

Here, f(n)= -3n + 2 is the given expression.

So, we can find the value of f(12) by putting n=12 in f(n).

Put n=12 in f(n), we get

          f(12)= (-3)×12 + 2

                 = -48 + 2

                 = -46

Hence, the value of f(12) is -46.

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(15 points)Please help out if you can!

Answers

Answer:

The maximum is -3

Step-by-step explanation:

A parabola that opens down (- in front), the vertex represents the highest point on the graph, or the maximum value.

The vertex of the equation is (-7,-3)

So, the maximum y value is -3

pls help me on this i don't know what to do ​

Answers

Answer:

[tex]\text{A. The zeroes are 8 and -4, because }y=(x-8)(x+4)[/tex]

Step-by-step explanation:

[tex]x^2-4x-32=0,\\(x-8)(x+4)=0,\\\begin{cases}x-8=0, x=\boxed{8},\\x+4=0, x=\boxed{-4}\end{cases}[/tex]

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