Answer:
3
Step-by-step explanation:
Find the product of each expression using properties of complex numbers.
1. (x + 3i)(x − 3i)
2. (x − 4i)(x + 4i)
3. (x + 8i)(x − 8i)
Answer:
[tex](x+3\mathbf{i})(x-3\mathbf{i})=x^2+9[/tex]
[tex](x-4\mathbf{i})(x+4\mathbf{i})=x^2+16[/tex]
[tex](x+8\mathbf{i})(x-8\mathbf{i})=x^2+64[/tex]
Step-by-step explanation:
Complex Numbers
The complex numbers are known by having an 'imaginary' part along with the real part. They can be expressed like a + bi, where
[tex]\mathbf{i}=\sqrt{-1}[/tex]
Or, equivalently:
[tex]\mathbf{i}^2=-1[/tex]
Let's find the result of the following products. On each one of them, there is a sum of a binomial multiplied by the subtraction of a binomial with the very same terms. It leads to a well-known polynomial identity:
[tex](a+b)(a-b)=a^2-b^2[/tex]
1. [tex](x+3\mathbf{i})(x-3\mathbf{i})[/tex]
Applying the above-mentioned identity:
[tex](x+3\mathbf{i})(x-3\mathbf{i})=(x^2-(3\mathbf{i})^2)[/tex]
[tex]=x^2-9\mathbf{i}^2[/tex]
Since [tex]\mathbf{i}^2=-1[/tex]
[tex](x+3\mathbf{i})(x-3\mathbf{i})=x^2-9(-1)[/tex]
[tex]=x^2+9[/tex]
2. [tex](x-4\mathbf{i})(x+4\mathbf{i})[/tex]
Proceed in the same way as before:
[tex](x-4\mathbf{i})(x+4\mathbf{i})=(x^2-16\mathbf{i}^2)[/tex]
[tex]=(x^2-16(-1))[/tex]
[tex]=x^2+16[/tex]
3. [tex](x+8\mathbf{i})(x-8\mathbf{i})[/tex]
[tex](x+8\mathbf{i})(x-8\mathbf{i})=(x^2-64\mathbf{i}^2)[/tex]
[tex]=(x^2-64(-1))[/tex]
[tex]=x^2+64[/tex]
Solve using elimination.
2x + y = 5
x - 3y = 6
Answer:
then substitute y in eq 1 to get x
hope this helped you
Please mark as the brainliest (ㆁωㆁ)
simplify start root 80 end root
Answer:
If your question is [tex]\sqrt{80}[/tex], your answer is 8.94 or [tex]4\sqrt{5}[/tex]
Hope this helps!
Find the slope of the line y = 8/9x - 1/3
Answer:
8/9
Step-by-step explanation:
The general form of linear functions are y = mx+b. Here, m is the slope and b is the y intercept. Therefore we can already see that m = 8/9 as the question is already in the general form y = mx+b.
I HAVE 5 MINS ANSWER THIS FOR (15 POINTS)
Answer:
d
Step-by-step explanation:
Answer:
Domain: 0,2,3
Range: -1,-3,-2
Step-by-step explanation:
The area of a square garden is approximately 125 square feet. To the nearest foot, what is the length of the garden? Explain how you know in the work space provided.
Answer:
Length = 11.2 ft
Step-by-step explanation:
Area of a square garden = 125 square feet
Formula to find
Area of a square = length^2
Substitute the value of the Area of the square garden
Area of a square = length^2
125 = length^2
Find the square root of both sides
√125 = √length^2
11.18 = length
Approximately
Length = 11.2 ft
Ben bought 1 2/3 pounds of jelly beans and 2 3/8 pounds of jolly ranchers. What are the total pounds of candy that Ben bought?
Answer:
4 1/24
Step-by-step explanation:
1 2/3 +2 3/8 = 5/3 +2 3/8 = 5/3 + 19/8 = 97/ 24 =4 1/24
The product of 12 and a number is greater than 24.
You decide to borrow a loan of $2,500 to go on vacation. The banks loans you the money at 9%for 7 months. How much interest will you pay?
Answer:
umm 1500? hmqmmmmmm
ye
You are a screenwriter who is writing a script for an hour-long police drama. You have written 20 1/2 pages for act 1 and 5 1/2 pages for act 2.
How many pages have you written in total?
Answer:
You have written 26 pages in total.
Step-by-step explanation:
I always enjoyed adding fractions. Something about it is so... simple.
The problem is basically asking us to add 20 1/2 and 5 1/2 together.
I would first suggest adding both halves together, to make 1.
That way, we're left with 20 + 5 + 1. That seem easier, doesn't it?
Then we would add 20, 5 and 1 together, to get 26 whole pages.
And that, to an extent, is how I did it.
Hope this helps! :D
Answer:
Given:
Written pages for Act 1 = 20 1/2
Written pages for Act 2 = 5 1/2
For making mixed numbers like this easier to add, let's convert them first into an irrational number with this formula,
((Whole Number × Denominator) + Numerator)/Denominator
Thus,
for 20 1/2
((20 × 2) + 1)/2 = 41/2
for 5 1/2
((5 × 2) + 1)/2 = 11/2
Then we add,
41/2 + 11/2
Since, they have the same denominator, no more conversions need, proceed adding the numerators,
(41 + 11)/2 = 52/2 = 26
You've written 26 pages in total.
#1 What is the difference between
an expression and an equation?
I WILL MARK AS BRAINLLIEST TO WHOEVER ANSWER THIS RIGHT AWAY:)!
and 50 points
The distributive property can be used to rewrite the expression 3(4 + 2) as 3(4) + 3(2).
True or False
Answer:
18
Step-by-step explanation:
Henri owns a cupcake shop that also takes special orders. Henri starts the day baking and frosting 120 dozen cupcakes before the store opens. On Wednesday, he received a special order for 20 dozen assorted cupcakes to be delivered the same afternoon. He also sold 98 dozen cupcakes that day. How many dozen cupcakes does Henri have left at the end of the day? Explain your answer.
Answer: He has 2 dozen cupcakes
Step-by-step explanation:
120*12=1440
20*12=240
1440-240=1200
98*12=1176
1200-1176=24
24= 2 dozens
how many solutions does the equation 8x+16=8x-16 have?
Answer:
8*x+16-(8*x-16)=0
Step-by-step explanation:
Solve : 32 = 0
This equation has no solution.
A. a non-zero constant never equals zero.
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Choose the property that justifies each step.
5(x - 1) = 4x+ 13
1) 5x- 5 = 4x + 13 ________
2)X- 5 = 13 ________
3) x= 18________
Options for each answer:
•Addition Property of Equality
•Distributive Property
•Multiplication Property of Equality
•Subtraction Property of Equality
•Transitive Property of Equality
Answer:
1. Distributive Property
2. Subtraction Property of Equality
3. Addition Property of Equality
The property that justifies each step of 5(x-1) = 4x + 13 is 5x - 5 = 4x + 13.
What is distributive property ?Distributive property is when we distribute and multiply in between addition and subtraction
Given 5(x-1) = 4x + 3.
We know a(b+c) = ab + ac which is distributive property.
So, 5(x-1) = 4x + 3.
5x - 5 = 4x + 3.
Solving these problem and finding the value of x
5x - 5 = 4x + 13.
5x - 4x = 13 + 5.
x = 18.
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If I deposit $1500 in my bank account and it increased by 15% at the end
of the year, how much money is now in my bank account
Answer:
$1725
Step-by-step explanation:
15 percent of 1500 = 225 and then you add 225 to 1500, 225 + 1500 = 1725
f(x) = x^2- 51 when f (-7)
Answer:
f(x)= -2
Step-by-step explanation:
f(x) = x^2- 51
-7^2-51
49-51
-2
f(x)= -2
Find the mean of:
1.8,1.7,1.3,1.1,1.2,1.6,1.8
Answer:
A.1.6
Step-by-step explanation:
put them in order
1.1, 1.2, 1.3, 1.6, 1.7, 1.8, 1.8
theirs seven numbers cross out the lowest numbers n the highest numbers and you should get 1.6
NEED HELP IM BEGGING YOU PLEASE !!!!!
Answer:
1.5t+2=4 and 2/3
1.5t=2 and 2/3
t= 1 and 7/9
Three families bought food at the baseball game. The Smith family spent $16.50 on 3 hot dogs, 2 sodas, and 1 candy bar. The Patterson family spent $26 on 4 hot dogs, 4 sodas, and 2 candy bars. The Nguyen family spent $13.75 on 2 hot dogs, 1 soda, and 3 candy bars. Which of the following systems of equations could be used to determine the price of each item?
Answer:
Step-by-step explanation:
Let
Price of
Hotdogs = x
Sodas = y
Candy bar = z
Smith family
Hotdogs = 3
Sodas = 2
Candy bar = 1
Total cost = $16.50
3x + 2y + z = 16.50
Patterson family
Hotdogs = 4
Sodas = 4
Candy bar = 2
Total = $26
4x + 4y + 2z = 26
Nguyen family
Hotdogs = 2
Sodas = 1
Candy bar = 3
Total cost = $13.75
2x + y + 3z = 13.75
The equations
3x + 2y + z = 16.50 (1)
4x + 4y + 2z = 26 (2)
2x + y + 3z = 13.75 (3)
Multiply (1) by -2
-2(3x + 2y + z = 16.50)
-6x - 4y - 2z = -33
-6x - 4y - 2z = -33 (1a)
4x + 4y + 2z = 26 (2)
Add (1a) and (2)
-6x + 4x = -33 + 26
- 2x = -7
x = -7/-2
= 3.5
x = $3.5
Multiply (3) by -4
-4(2x + y + 3z = 13.75) (3)
-8x - 4y - 12z = -55 (3a)
Add (3a) and (2)
-8x - 4y - 12z = -55 (3a)
4x + 4y + 2z = 26 (2)
-8x + 4x -12z + 2z = -55 + 36
-4x - 10z = -29
Substitute the value of x into
-4x - 10z = -29
-4(3.5) - 10z = -29
-14 - 10z = -29
-10z = -29 + 14
-10z = - 15
z = -15 / - 10
= 1.5
z = $1.5
Substitute values of x and z into (1)
3x + 2y + z = 16.50
3(3.5) + 2y + 1.5 = 16.50
10.5 + 2y + 1.5 = 16.50
12 + 2y = 16.50
2y = 16.50 - 12
2y = 4.50
y = 4.50 / 2
y = $2.25
is 2/2 a improper fraction ?
Answer:
no
Step-by-step explanation:
Multiply. Enter the product in simplest form.
17/8 x 14/51
Answer:
7/12 or in decimal form it is .583
Step-by-step explanation:
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hope this helps!
If x=-1, then which of the following equations makes a true statement?
A.) 4x+9=20
B.) -4x–5=-15
C.) -3x+15=18
D.) -5x–15=-22
Answer:
Option C
Step-by-step explanation:
Option A:[tex]4(-1)+9=20\\\\-4+9=20\\\\\boxed{5\neq 20}[/tex]Option B:[tex]-4(-1)-5=-15\\\\4-5=-15\\\\\boxed{-1\neq -15}[/tex]Option C:[tex]-3(-1)+15=18\\\\3 + 15 = 18\\\\\boxed{18=18}[/tex]
Option C is the correct answer.
Option D:[tex]-5(-1)-15=-22\\\\5-15=-22\\\\\boxed{-10\neq -22}[/tex]
Hope this helps.
For the value of x = - 1, the correct equation is,
⇒ - 3x + 15 = 18
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.
Given that;
The value of x is,
⇒ x = - 1
Now, Substitute the value of x in all equations and check the correct equation.
For equation 3;
⇒ - 3x + 15 = 18
Substitute x = - 1 ;
⇒ -3×-1 + 15 = 18
⇒ 3 + 15 = 18
⇒ 18 = 18
Thus, The correct equation is,
⇒ - 3x + 15 = 18
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How much is the number 727731000 in percent form
I need yall to answer this question quickly you will recieve a ton of points if you do.
Answer:
72773100000%
Step-by-step explanation:
"Percent" means "per 100" or "over 100". So, to convert 727731000 to percent we rewrite 727731000 in terms of "per 100" or over 100.
Multiply 727731000 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.
7277310001×100100=72773100000100
72773100000/100 is 72773100000 over 100 and means 72773100000 per 100. 72773100000 "per 100" means 72773100000 "percent" or 72773100000%
Therefore, we have shown that
727731000 = 72773100000%
Simplified Conversion:
Multiply by 100 and add the percent sign %
727731000 × 100 becomes 72773100000%
Shortcut Conversion:
Move the decimal point 2 places to the right and add the percent sign %
727731000 becomes 72773100000%
I have been stuck on this for 1 hours someone plz help me
Answer:
answers in PDF
Step-by-step explanation:
Hint: Use the number line to find the missing value.
-2=_______+6
Answer:
4
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
I will give you branilest!
Here is a circle with center H and some line segments and curves joining points on the circle. Identify ONE example of each of the following.
a. Diameter
__________
b. Radius
_________
(Be sure that your book includes your written reasoning.)
Answer:
a) line [EA]
b) line [HA]
Step-by-step explanation:
Answer:
a) line(EA)
b) line(HA)
Step-by-step explanation:
20 POINTS AND 5 STARS
The food truck also offers catering services. The food truck makes different kinds of salads for parties and other events. Tammy looks at the paper menu to
decide what to buy
Macaroni Salad
$5 per pound
Potato Salad
$8 por pound
Tammy will order both macaroni and potato salad. She estimates that she will spend a total of 538 on 7 pounds of salad. She uses this system of equations to
show how many pounds of macaroni salad, m, and potato salad, p, she plans to buy.
5m +6p = 38
m+p=7
How many pounds of each salad does Tammy plan to buy?
Answer:
4 pounds of mac 3 pounds of potato
Step-by-step explanation:
5+6=11+5+6=22+5+6=33+5=38
How are the slope formula and finding slope using "rise over run" related?
Answer:
they are the same thing
Step-by-step explanation:
Answer:
They are practically the same thing but if you want to get technical then they are related because A slope a measure of steepness. A line with a large slope, such as 25, is very steep. A line with a small slope, such as 1 /10 is very flat. So this means it will rise over run if that makes sense.
Hope this helps!