Simplify the expression (10 + 3i)(10 - 3i)

91
109
100-30i
100+30i

Answers

Answer 1

Answer:

(10 + 3i)(10 - 3i)=109

Step-by-step explanation:

[tex](10+3i)(10-3i)=(10^{2} -10*3i)+(3*10i-3*3i^2)\\ =100-30i+30i-9i^2\\=100-9*(-1)\\=100+9=109[/tex]

Answer 2

Answer:

B) 109

Step-by-step explanation:

I took the test and got a 100%


Related Questions

Solve 5(g-2)+g=6(g-4

Answers

0 =/ 14 is the answer to the problem

Answer:

g = -13

Step-by-step explanation:

5(g-2)+g=6(g-4)

5g - 10 + g = 6g - 24

5g + g - 6g = -24 + 10

6g - 6g = -13

g = -13

The radius of the earth is 3959 miles. A meteor with a diameter of 750 miles strikes the earth in an unpopulated area. What percent of the earths surface is affected by the meteor strike? Is it a 36% be 0.9% C9% or D3.6%

Answers

Answer:

B. 0.9%

Step-by-step explanation:

If the diameter of the meteor is 750 miles, then its radius is 750/2 = 375 miles

The radius of the earth is 3959 miles

Assuming that both bodies are spherical, their surface are:

meteor's surface: π*r² = π*375² = 441786.467 miles²

Earth's surface: π*3959² = 49240321.1 miles²

If 49240321.1 miles² represents 100% then 441786.467 miles² represents:

49240321.1 miles² / 100% = 441786.467 miles² / x%

x = 441786.467/49240321.1*100

x = 0.9%

Answer:

B) 0.9%

Step-by-step explanation:

How to solve a system of equation using a graph?

Answers

Answer:

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation:

Which equation best represents the data given in the table ?

Answers

Answer:

B

Step-by-step explanation:

The equation that satisfies the above table is y = 8[tex](\frac{1}{2})^{x}[/tex]

Given,

Table between x and y .

Here,
To get the equation between x and y first justify the data given in the table.

So,

When,

x = -3 , y = 64

x = -2 , y = 32 .

In the equation  y = 8[tex](\frac{1}{2})^{x}[/tex] substitute the values of x and check for y .

Put x = -3 ,

y = 8[tex](1/2)^{-3}[/tex]

y = 8 * 8

y = 64

Thus it satisfies the value given in the table .

So the correct equation will be Option B .

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It’s on probability please help

Answers

Answer:

The number of meal combinations, She has to choose:

N = 3 x 4 x 3 =36

Hope this helps!

:)

How does knowing the absolute value of an integer help in determining the distance of two ordered pairs?

Answers

Hey there!

The absolute value helps because when you the absolute value is the the distance of a number away from 0. Meaning that if your finding distance it will never be negative.

Finding the distance between the two is subtracting one of the numbers from each ordered pair from each other. Whether the number is negative or positive, you always turn it, or leave it into a positive number because distance is always positive.


Hope this helps !

please help me out! i have a few more of these questions, about 4

Answers

Step-by-step explanation:

You can make a table of values to find the points that belong to the line and then draw the line through those points. Here are some: (-6, -2), (0, -1), and (6, 5). You can use any value for x in your table. Hope this helps!

Answer:

Step-by-step explanation:

put a point in at negative 1 first; that is the y value.

Then, go up 1 then to the right six points. that should result in the next point being at (0,6).

Keep going and draw a line

Find the area. Will mark brainliest.

Answers

Step-by-step explanation:

Area of the parallelogram=bh

b=20cm

h=12cm

Area=12*20=240cm²

Solve this for me please

Answers

is there a picture to this??

we need a picture to answer this question

Drag the tiles to the correct boxes to complete the pairs.
Match each situation to the simulation that represents it.

Althea has to select 1 student
as the class representative
from 13 students.

Fiona is deciding which of three
forests to research for a
geography project: evergreen,
deciduous, or coniferous.

Jenny is picking a marble from
a jar with two green marbles, six
yellow marbles, and two red
marbles.

rolling a six-sided die



selecting a playing card from
the hearts suit



spinning a spinner divided into
five equal sections


Answers

Answer: rolling a six sided die☞︎Fiona forest research

Hearts suit☞︎Althea class representative

Spinner☞︎ Jenny marbles

Step-by-step explanation:

Answer:

Fiona= die

Althea=cards

Jenny=Spinner

Step-by-step explanation:

starting off Fiona has three which can evenly go into six.

Althea has 13 options which matches with the number of suits in the hearts

the Jenny would be spinner because 5 times 2 is 10

Mark placed a pool in his backyard, which is enclosed by a triangular fence. The radius of the pool is 20.5 feet.

Answers

Answer:

A. 3,864 ft²

B. 1,319.585 ft²

C. 2,544.415 ft²

Step-by-step explanation:

Area of triangle:

½ × 92 × 84

3864 ft²

Area of circle:

pi × r²

3.14 × 20.5²

1319.585 ft²

Difference:

3864 - 1319.585

2544.415 ft²

Event A: stops on red

Event B: stops on yellow

Find P(A or B)

A.) 1/4
B.) 1/8
C.) 1/2
D.) 1/16

Answers

Answer:it is 1/2

Hopefully this helps

Answer:

Event A: stops on red

Event B: stops on yellow

Find P(A or B)

1/2

What is the maximum of f(x) = sin(x)?
- 2π
-1
01
2π​

Answers

Answer:

1

Step-by-step explanation:

The maximum value of sin(x) is 1.

When x = 90 degrees sinx = 1.

Hey guys I need help with this exercise can someone plz help me for 20 points?? Also write the explamation to your answer plzz!

Math problem: 13 of the same cookbooks weigh 442 grams. What is the weight of 10 of these books?

Answers

Answer:

340

Step-by-step explanation:

442 / 13 = 34

34 × 10 = 340

Answer:

340

Step-by-step explanation:

442 / 13 = 34

34 × 10 = 340

COME ON ITS 1 QUESTION FOR 50 POINTS!

If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!

Answers

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

Step-by-step explanation:

Step 1:  Solve using the first point

(2, 28)

[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]

[tex]28 = 8a + 4b + 2c + d[/tex]

Step 2:  Solve using the second point

(-1, -5)

[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]

[tex]-5 = -a + b - c + d[/tex]

Step 3:  Solve using the third point

(4, 220)

[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]

[tex]220 = 64a + 16b + 4c + d[/tex]

Step 4:  Solve using the fourth point

(-2, -20)

[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]

[tex]-20 = -8a + 4b - 2c + d[/tex]

Step 5:  Combine the first and fourth equations

[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]

[tex]8 = 8b + 2d[/tex]

[tex]8 - 8b = 8b - 8b + 2d[/tex]

[tex](8 -8b)/2 = 2d/2[/tex]

[tex]4 - 4b = d[/tex]

Step 6:  Solve for c in the second equation

[tex]-5 + 5 = -a + b - c + d + 5[/tex]

[tex]0 + c = -a + b - c + c + d + 5[/tex]

[tex]c = -a + b + d + 5[/tex]

Step 7:  Substitute d with the stuff we got in step 5

[tex]c = -a + b + (4 - 4b) + 5[/tex]

[tex]c = -a + b + 4 - 4b + 5[/tex]

[tex]c = -a - 3b + 9[/tex]

Step 8:  Substitute d and c into the first equation

[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]

[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]

[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]

[tex]6 / 6 = (6a - 6b) / 6[/tex]

[tex]1 + b = a - b + b[/tex]

[tex]1 + b = a[/tex]

Step 9:  Substitute a, b, and c into the third equation

[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]

[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]

[tex]220 - 100 = 60b + 100 - 100[/tex]

[tex]120 / 60 = 60b / 60[/tex]

[tex]2 = b[/tex]

Step 10:  Find a using b = 2

[tex]a = b + 1[/tex]

[tex]a = (2) + 1[/tex]

[tex]a = 3[/tex]

Step 11:  Find c using a = 3 and b = 2

[tex]c = -a - 3b + 9[/tex]

[tex]c = -(3) - 3(2) + 9[/tex]

[tex]c = -3 - 6 + 9[/tex]

[tex]c = 0[/tex]

Step 12:  Find d using b = 2

[tex]d = 4 - 4b[/tex]

[tex]d = 4 - 4(2)[/tex]

[tex]d = 4 - 8[/tex]

[tex]d = -4[/tex]

Answer:  [tex]a = 3, b = 2, c = 0,d = -4[/tex]

Suzanne bought a sweater at the sale price of $29.99. the original cost of the seater was $49.99. what percent represents the discount they suzanne received when buying the sweater?
a: 40% discount
b: 60% discount
c: 50% discount
d: none of the above

NEED HELP ASAP MASTERY GRADE

Answers

Answer:

= 40%

Step-by-step explanation:

Original price = 100%

Discount = Op - Np = $49.99 - $29.99 = $20

If $49.99 = 100%

What about $20 = ?

= (20 x 100) ÷ 49.99

= 2000 ÷ 49.99

= 40.008

= 40%

The reduction in price is:
37.5
%

Original price

$40
Reduced to


$25

Writing this as a fraction of the original price we have
25/40

But this represents the final price.
What we need is the amount of reduction


The price has been reduced by

$40−$25=$15

So as a fraction of the original price the reduction is:
15/40

Converting this to a percentage

Let the unknown value be
x

15/40=x/100


Multiply both sides by 100
15/40×100 = x × 100/100


But 100/100= 1

x = 15/40 × 100 = 37 1/2→37.5 giving: 37.5/100 = 37.5 × 1/100 = 37.5%

Below are two truths and one lie, choose the lie.

Answers

Answer:

The horizontal asymptote is x-axis

Step-by-step explanation:

The horizontal asymptote is the y axis not x axis

Well so basically the answer is that your life is a lie and all this poop is meaningless

5(x-10)=30-15x
Ox=1
Ox=4
Ox=5
Ox=8

Answers

Answer:

x = 4

Step-by-step explanation:

5x-50=30-15x

5x +15x =30+50

20x= 80

Divide both sides of the equation by 20

x = 4

I hope it helps

Will give brainliest answer

Answers

Answer

Step-by-step explanation:

To find the area of a shape multiply its height by its width. For a square  you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

please mark me as brainliest.

Answer:

[tex]7 units^2[/tex]

Step-by-step explanation:

You can split this irregular shape into a square and a trapezoid.

The formula for a square is:

[tex]A=lw[/tex]

The formula for a right trapezoid:

[tex]A=\frac{1}{2} (h)(a+b)[/tex]

Area of square:

[tex]A=(2)(2)\\A=4[/tex]

Area of right trapezoid:

[tex]A=\frac{1}{2} (2)(1+2)\\A=3[/tex]

Add up the individual areas to find the overall:

4 + 3 = 7

Simplify: (1 + 3i) + (7 - 2i)

Answers

Answer:

8+i

Step-by-step explanation:

Answer:

8 + 1 i

if im wrong soooooorrrrrrryyyyyy

Step-by-step explanation:

5. The length of a rectangle is 5 inches greater than the width.
Question
Answer
a. Write an expression for the width of the rectangle.
b. Write an expression for the length of the rectangle.
multiply

Answers

Answer:

see below

Step-by-step explanation:

Let w = width

L = length = w+5

The area is l*w

A = (w+5)*w

A = w^2 +5w

Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 4x + 12
O A. (3.2 + 4)(x+4)
O B. (3x2+3)(x + 4)
O c. (3x2 + 4)(x+3)
O D. (3x + 3)(x+3)​

Answers

Answer:

C. (3x^2+4)(x+3)

Step-by-step explanation:

3x^3+9x^2+4x+12

=(3x^3+9x^2)+(4x+12)

=3x^2(x+3)+4(x+3)

=(3x^2+4)(x+3)

Therefore, C. (3x^2+4)(x+3)

The correct factor of the polynomial is,

⇒ (x + 3) (3x² + 4)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3x³ + 9x² + 4x + 12

Now, We can factor the polynomial as;

⇒ 3x³ + 9x² + 4x + 12

⇒ 3x² (x + 3) + 4 (x + 3)

⇒ (x + 3) (3x² + 4)

Thus, The correct factor of the polynomial is,

⇒ (x + 3) (3x² + 4)

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Please help
find the area of a trapezoid base 1 measures 20 ft base 2 messages 10 ft height measures 3 ft ​

Answers

Answer:

Step-by-step explanation:

(20+10)*3/2 = 45

Answer:

45 ft squared

Step-by-step explanation:

Area of a trapazoid = a plus b divuded by 2 times h

20 plus 10 divided by 2 equals 15

then 15 times 3 equals 45

Help I will mark BRAINLIEST if correct please help

Answers

Answer:

[tex](-\frac{1}{4}, \frac{5}{8} )[/tex]

Step-by-step explanation:

If you label the points on the axes, it will show that point K is actually on [tex]\frac{5}{8}[/tex] not [tex]\frac{3}{4}[/tex]

this box holds cereal. how many cubic inches of cereal can it hold the size of the box is 6 in,2 in,12 in

Answers

If you multiply all three of those numbers you should get 144 cubic inches.

PLS HELP John’s patio needs to be re-painted.
He needs orange paint for one portion of his patio and gray paint for the other portion. Determine the total area of the patio that needs orange paint and the total area that needs gray paint. Show all calculations.

Answers

Answer:

368 square feet of orange paint.

292 square feet of grey paint.

Step-by-step explanation:

Here is a picture of my work that you can follow to show how i did it. hope this helps!

       

Both perpendicular lines and parallel lines must
A
never meet.
В
meet at right angles.
C
exist on the same plane.
D
be curved in the same place.

Answers

Answer:

A.) Never meet.

Step-by-step explanation:

It’s A they never meet

10 points need help asap​

Answers

Answer:

D

Step-by-step explanation:

please help asap, 20 points

Answers

Solving for each equation:

A: True.

[tex]\frac{n}{2} +3 *4 = \frac{n}{2}+12\\\\\frac{n}{2} + 12 = \frac{n}{2} + 12[/tex]

B: False.

[tex]\frac{1}{3}z+\frac{2}{3}z * 9 = 9z\\\\\frac{1}{3} z+6z = 9z[/tex]

C: True, given that y = 1

[tex]-8y +4.3y + 3.7 = 0\\\\-3.7y = -3.7[/tex]

D: True, given that b = 6.66667

[tex]12-1.8b+1.8b=1.8b\\12 = 1.8b[/tex]

E: True.

[tex]\frac{m}{8} + 7(\frac{m}{8} ) =m\\\\\frac{m}{8} + (\frac{7m}{8} )= m\\\\\\\frac{8m}{8} = m\\[/tex]

Twenty-four 4-inch wide square posts are evenly spaced with 5 feet between adjacent posts to enclose a square field, as shown. What is the outer perimeter, in feet, of the fence? Express your answer as a mixed number.

Answers

Answer:

129 1/3

Step-by-step explanation:

According to Alcumus, "There are 20 square posts which are not on a corner, so there are $20/4=5$ square posts on each side, not including the corner posts. Including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts. Altogether the length of a side is $7\left(\frac{1}{3}\right)+6(5)=32\frac{1}{3}$ feet. The perimeter of the square is four times the side length, so the perimeter is $4\cdot 32\frac{1}{3}=\boxed{129\frac{1}{3}}$ feet."

The outer perimeter is 129 1/3 feet.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Twenty-four 4-inch wide square posts are evenly spaced with 5 feet.

So, there are $20/4

                   =5$ square posts on each side, not including the corner posts.

and, including the corner posts, there are 7 posts on a side, which means that there are 6 five-foot gaps between posts.

Then, the length of a side is

= 7 1/3 + 6(5)

= 32 1/3 feet

and, The perimeter of the square

= 4 x 32 1/3

= 129 1/3 feet

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