Type the correct answer in the box.
Simplify the given expression into the form , where a and b are rational numbers.
2(-36-3i)+5(+2i)12-2i)
Answers
Answer:
[tex]\huge\boxed{-8+8i}[/tex]
Step-by-step explanation:
[tex]2(-36-3i)+(5+2i)(12-2i)\\\\\text{use the distributive property and FOIL}\\\\=(2)(-36)+(2)(-3i)+(5)(12)+(5)(-2i)+(2i)(12)+(2i)(-2i)\\\\=-72-6i+60-10i+24i-4i^2\\\\i=\sqrt{-1}\to i^2=-1\\\\=-72-6i+60-10i+24i-4(-1)=-72-6i+60-10i+24i+4\\\\=(-72+60+4)+(-6-10+24)=-8+8i[/tex]
The expression in the form of a + ib is
-88 + 8i
where a = -88 and b = 8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2(-36 - 3i) + (5 + 2i)(12 - 2i)
Remove the parenthesis.
-72 - 6i + 60 - 10i + 24i + 4
Add like terms.
-88 + 8i
This is in the form of (a + ib).
Where a = -88 and b = 8
Thus,
-88 + 8i is our final expression.
Learn more about expressions here:
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Related Questions
A pizza shop sells pizzas that are 10 inches in diameter or larger.A 10 inch pizza costs 8$ each additional inch costs $1.50 and each addition topping costs 0.75
Answers
A pizza shop sells pizzas that are 10 inches orr larger. A 10-inch cheese pizza costs $8 and each additional costs $1.50 and each additional topping costs $0.75.
The equation that represents the cost of a pizza is:
P = $10 + $1.50a + $0.75b
Where 'a' represents the number additional inches and 'b' represents the number of additional toppings.
HELP ASAP
1.A term that is a known number without variables. is called?
Answers
Answer:
constants
Step-by-step explanation:
Constants are the terms in the algebraic expression that contain only numbers. That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value.
You work for a poster company that sells prints of album covers. You sell posters at the prices given in the table.
Number of Posters Price
2 $40
3 $50
5 $70
10 $120
What is the best deal for posters?
A.
2 posters for $40
B.
3 posters for $50
C.
5 posters for $70
D.
10 posters for $120
Answers
Answer:
Option A is the best deal for posters
Is 5/4 a solution to the problem: 3(+9)=4−7+7.
Answers
Answer:
No the soultion is not equal to 1 1/4
The solution to the given question is either 6 3/4 or 4 /27
Step-by-step explanation:
Let
3(+9)=(4−7+7)x
27 = 4x
x= 27/4
x= 6 3/4 is the answer
or
Let
3(+9) x=(4−7+7)
27x = 4
x= 4/27
The plus sign inside the bracket indicates that 3 is multiplied with positive nine and -7 and +7 are cancelled and 4 is left behind.
If x is on the left side the answer will be 6 3/4 and if it is on the right side the answer is 4/27 .
In both cases the answer is not equal to 5/4 .
5/4 means 1 1/4 which is not equal to either 6 3/4 or 4/27
There are 550 people at the school carnival. If 385 of the people are
students, what percentage of the people at the school carnival are
students?
Answers
Answer:
70 percent
Step-by-step explanation:
Write this as a fraction: 385/550, then simplify to get 77/110-->7/10.
The fraction 7/10 is equivalent to 70%.
Answer:
70% i belive, Sorry if im wrong :c
Step-by-step explanation:
i need help with this ?
Answers
Answer:
-2 ≤x ≤10
Step-by-step explanation:
the domain refers to the x
the x is in between -2 and 10
a 300$ mountain bike is discounted by 30% and then discounted an additional 10% for shoppers who arrive before 5am. explain why taking off 30% and then 10% off is NOT the same as a 40% discount
Answers
24. Marissa needs 2 2/3yards of ribbon for a wall-hanging she wants to make. She has 2 3/4 yards. Does she have enough ribbon? Explain.
Answers
Answer:
no
Step-by-step explanation:
because she just has one less so all she need to do is get one more and then she'd have enough
Answer:
yes, she has enough ribbon.
Step-by-step explanation:
find common denominator for 2 2/3 and 2 3/4 which is 12
2 2/3 becomes 2 8/12 [what she needs]
2 3/4 becomes 2 9/12 [what she has]
she has 1/12 more than she needs.
Gracie is sharing 75 marshminnows among 4 of her friends. If each of her friends gets
the same number of marshminnows, and she gives them as many marshminnows as
possible, how many are left for Gracie?
none
3
18
19
Answers
Given:
Gracie is sharing 75 marshminnows among 4 of her friends.
Each of her friends gets the same number of marshminnows, and she gives them as many marshminnows as possible.
To find:
The remaining number of marshminnows she has.
Solution:
We have,
Total number of marshminnows = 75
Number of friends = 4
Divide 75 by 4.
[tex]4|\overline{75}|{18}\\ -4\\\text{\quad }\overline {35} \\ -32\\\text{\quad }\overline {\ 3\qaud }[/tex]
Here, quotient is 18 and remainder is 3. It means, each friend can be get maximum 18 marshminnows and the number of remaining marshminnows is 3.
Therefore, the correct option is B.
A contractor building an airport needs to know how far a water tower is away from
end of the runway. Using her diagram below can you determine how far away the
water tower is?
Answers
Answer:
B.
Step-by-step explanation:
tan(82)= X/100
100•[tan(82)]= [X/100] •100 Multiply each side by 100 to get the X by itself on the right side
X= to 711.537
x = 0 O 5x + 7 = 37 Plz answer I need da answer
Answers
Answer:
5x + 7 = 37
x= 1.97435
Step-by-step explanation: Hope this help
Fencing How much fencing is required to enclose a circular garden whose radius is 28 m? Use 3.14 for . About nothing m of fencing is required to enclose the circular garden. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answers
Answer:
175.84 m
Step-by-step explanation:
Given that:
A circular garden which has a radius of 28 m.
[tex]\pi[/tex] = 3.14
To find:
The fencing required to enclose the circular garden ?
Solution:
Here, we are given a circle and its radius.
We are required to find the perimeter of the circle in order to find the fencing required to enclose the circular garden..
Formula for finding the perimeter of a circle is:
Perimeter = [tex]2\pi r[/tex]
where [tex]r[/tex] is the radius of the circle.
Using the given values in the formula:
Perimeter = [tex]2\times 3.14 \times 28[/tex] = 175.84 m
Therefore, 175.84 m of fencing is required.
Find the product -3,-4.-2.5
Answers
Answer:
[tex]-30[/tex]
Step-by-step explanation:
[tex]-3(-4)(-2.5)[/tex]
Apply rule [tex]-(-a) = a[/tex]
[tex]=-3*4*2.5[/tex]
Multiply the numbers: [tex]3*4*2.5=30[/tex]
[tex]=-30[/tex]
Any number that can be written as a fraction is called a
A percent
B proportion
C rational number
D percent proportion
Answers
I need some help please
Answers
A roller coaster at a theme park takes fans on an exciting ride. In the first 20 seconds, it carries passengers up a 30-meter hill, plunges them down 30-meters, and takes them back up a 15-meter rise. How much higher or lower from the start of the ride are they after these 20 seconds?
step-by-step answer extremely needed please:)!
Answers
Answer:15 meters higher
Step-by-step explanation: 30-30+15
15 meters higher from the start of the ride are they after these 20 seconds.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Let's say they were initially at level x from ground
After the first 20 seconds.
Level = x + 30
Then plunges down
So,
Level = x + 30 - 30 = x level.
Now 15-meter rise
So,
Level = x + 15
Now level from initial = (x + 15) - x = 15 meter.
Hence "15 meters higher from the start of the ride are they after these 20 seconds".
To learn more about the arithmetic operators,
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Pls help!!!! MATH IS CERTAINLY NOT MY BEST SUBJECT LOL
Answers
Answer:
Well it isnt the negative answers because it's going up because the sales are going up, and your not going up $333.33/ day, so it should be D
Step-by-step explanation:
I hope this helps
A movie club is having a new-member sale, so Mindy signs up. The equation
-0.4x + 0.05y - 1.25 = 0 relates y, the total cost, and x, the number of
months. What is the y-intercept of the line represented by the equation?
A -1.25
B 0.05
c 8
D 25
Greg chose c as the correct answer.how might he have gotten the answer
Answers
Answer:
D is the correct choice
Step-by-step explanation:
To get the y-intercept, we write the equation in the standard form
The standard form is ;
y = mx + b
So we have to rewrite the equation this very form
Thus, we have that;
0.05y = 0.4x + 1.25
we simply isolate the y value
To do this, we divide through by 0.05 and the y-intercept value will be ;
1.25/0.05 = 25
Help please
How are the properties of exponents used to rewrite expressions?
Answers
Answer: The five exponent properties are
Product of Powers: When you are multiplying like terms with exponents, use the product of powers rule as a shortcut to finding the answer. It states that when you are multiplying two terms that have the same base, just add their exponents to find your answer.
Power to a Power: When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. ... Then multiply the two expressions together. You get to see multiplying exponents (raising a power to a power) and adding exponents (multiplying same bases).
Quotient of Powers: When you are dividing like terms with exponents, use the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer. The key is to only subtract those exponents whose bases are the same.
Power of a Product: The Power of a Product rule is another way to simplify exponents. When you have a number or variable raised to a power, it is called the base, while the superscript number, or the number after the '^' mark, is called the exponent or power.
Power of a Quotient: The Power of a Quotient rule is another way you can simplify an algebraic expression with exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent or power
You can use these any way you want to rewrite an equation.
Hope this helped
Step-by-step explanation:
If the exponential function is decreasing, the b value has to be
Answers
If I had $2million to pay for 20 million meals, how much does each meal cost?
Answers
Answer:
$0.10
Step-by-step explanation:
Divide 2 million by 20 million:
2,000,000/20,000,000
= 0.1
So, each meal costs $0.10
Choose all of the equations for which x = 2 is a solution.
A. x + 3 = 5
B. +2 = 8
C. X+1=1
D. x - 2 = 4
EX - 7= -5
Answers
EXPLANATION
x + 3 = 5
2+3=5
x - 2 = 4
2-2=4
hopes this helps :)
Please answer correctly !!!!!!!!!!!!!!! Will mark Brianliest answer !!!!!!!!!!!!!!!!!
Answers
Answer:
x = 8√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Trigonometry
[Right Triangles Only]: Pythagorean Theorem: a² + b² = c²Step-by-step explanation:
Step 1: Define
We are given a right triangle. We can use PT to solve for the missing length.
Step 2: Identify Variables
Leg a = 8
Leg b = 8
Hypotenuse c = x
Step 3: Solve for x
Substitute [PT]: 8² + 8² = x²Exponents: 64 + 64 = x²Add: 128 = x²Isolate x: 8√2 = xRewrite: x = 8√2Simplify: 20 - (-2) to the second power ÷ ( 7 - 9) × 13
A. 46
B. -104
C. 286
D. 262/13
Answers
Answer:
The answer to the statement provided is 46.
16 . Each child going to a science museum had to pay $9. One-third of this was for bus fare.
What was the admission fee for adults, if children get in for half price?
17. Brian's tyre is leaking at a rate of 10ml per minute. If it went unchecked for one and a
quarter of an hour, how much air would be lost?
18. Glasses were on sale at the rate of 4 for the price of 3. If they were $1 each, how much
would a dozen cost?
19. Everybody in a class plays soccer or Rugby. Half of the class plays soccer. Of those
that play soccer, half also play rugby. If 24 students play rugby, how many students are
in the class
20. Kylie's petrol tank was half full but she used one third of this petrol in travelling to Ryde
and back. What fraction of a tank remained after the trip?
Answers
Answer:
16. Adults = $12
17. 750 ml
18. $9
19. 96 students
20. 5/6x
Step-by-step explanation:
16.
A child pays = $9
Bus fee = 1/3 of $9
= 1/3× 9
= $3
Admission fee for a child= amount paid - bus fee
= $9 - $3
= $6
What was the admission fee for adults, if children get in for haprice
Children = 1/2 of adults
$6 = 1/2 × adults
Adults = 6÷ 1/2
= $12
Adults = $12
17.
Leaking rate = 10 ml per minutes
One and quarter of an hour
1 hour = 60 minutes
Quarter of an hour = 15 minutes
Total time = 75 minutes
Air lost in 75 minutes = 10 ml × 75
= 750 ml
18. 4 glasses for $3
1 dozen of glasses = 12
12 glasses = $x
4 = 3
12 = x
Cross product
4*x = 3*12
4x = 36
x = 36 / 4
= 9
x = $9
19.
Total students = x
1/2x = soccer
Rugby = 1/2 of 1/2x
= 1/2 * 1/2x
= 1/4x
24 = 1/4x
x = 24÷1/4
= 24 × 4/1
x = 96 students
20.
Total petrol = x
Petrol in the tank = 1/2x
Petrol used = 1/3 of 1/2x
= 1/3 × 1/2x
= 1/6x
Petrol remaining after the trip = x - 1/6x
= 6x-x/6
= 5/6x
Apple stock fell 3% and is currently at $134 . What was the original amount this morning?
Answers
Answer:
138.02
Step-by-step explanation:
Linda is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $30. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Linda has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks. Equation: ? X Total amount of money after 11 weeks: $ ]
Answers
Answer:
680
Step-by-step explanation:
30 times11 then you get 330 then add to 350
Solve the equation.
16% of 40 =
Answers
Answer:
16% of 40= 6.4
Answer:
6.4 would be your answer...Step-by-step explanation:
have this same question -_-
A bag contains 3 blue, 4 red and 3 yellow marbles. How many blue marbles must be added to the bag for it to contain 75% blue marbles?
Answers
Answer:
18
Step-by-step explanation:
Note that 75% = 75/100 = 3/4, so 3/4 of the marbles must be blue. Let x be amount of blue marbles added. We can write an equation using this.
75% = 3/4 = (3 + x blue marbles)/(3 + 4 + 3 + x total marbles) = (3+x)/(10+x)
Multiplying by 4(10 + x) on both sides:
3(10 + x) = 4(3+x)
30 + 3x = 12 + 4x
18 = x
Therefore, we must add 18 blue marbles for 75% of the marbles to be blue.
I hope this helps! :)
Which statement is true about the slope of the graphed line?
Answers
Answer:
I cannot say without a picture, send one and I'll be glad to help.