Dividing Complex Numbers:
Simplify 5/-5i
By dividing the complex number 5 / -5[tex]i}[/tex] we get the answer as :
5 / -5[tex]i}[/tex] = [tex]i}[/tex]
Simplification:A complex number is a number system that extends the real numbers with a specific element denoted I known as the imaginary unit, and satisfying the equation [tex]i^{2}[/tex] = -1; each complex number can be expressed in the form a + bi, where a and b are real numbers.
Steps to simplify complex number:
On both the numerator and the denominator, multiply the given complex number by the conjugate of the denominator.Distribute the number in the numerator and denominator to remove the parentheses.Simplify i's powers.Given complex number , 5 / -5[tex]i}[/tex]
multiply the numerator and denominator with conjugate [tex]-i /-i[/tex]
= [tex]5(-i)/-5i(-i)[/tex]
by again simplifying we get ,
= [tex]-5i/-5[/tex]
-5 common from numerator and denominator is eliminated
so we get ,
5 / -5[tex]i}[/tex] = [tex]i[/tex]
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Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
The pencils and erasers that each student have is 14.
How to calculate the value?From the information, the person has 56 pencils and 42 erasers and wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers.
It should be noted that this has to do with looking for the highest common factor.
The highest common factor for 56 and 42 is 14.
The students will have 14 pencils each.
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The shortest side of a right angle triangle is 6cm shorter than the hypotenuse. The difference in length of the other two sides is 3cm. If the shortest side is n - 3, show that 2n squared equals 12n. Hence, n.
The value of n in the right triangle is 12 cm.
How to find the side of a right triangle?The shortest side of a right angle triangle is 6cm shorter than the hypotenuse.
The difference in length of the other two sides is 3cm.
The hypotenuse side is the longest side of a right triangle.
Hence,
hypotenuse side = n - 3 + 6
hypotenuse side = n + 3
Shortest side of the right triangle = n - 3
Other side = n
Therefore, using Pythagoras theorem,
(n + 3)² = (n - 3)² + n²
(n + 3)(n + 3) = (n - 3)(n - 3) + n²
n² + 3n + 3n + 9 = n² -3n -3n + 9 + n²
n² + 6n + 9 = 2n² - 6n + 9
Therefore,
2n² - n² + 9 - 9 = 6n + 6n
n² = 12n
n² - 12n = 0
n(n - 12) = 0
n = 0 and n = 12
Therefore,
n = 12
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Mr. Lou teaches 7 reading groups. Each reading group has 5 students. Find how many total
students Mr. Lou teaches today if 3 students are absent.
Which expression correctly represents the problem?
7x (5-3)
(7x5)-3
KC
7-(5 x 3)
D
(7-5) x 3
11
Based on the number of reading groups, and the number of absent students, the expression for the problem is (7 x 5) - 3.
How to find the expression?Every reading group taught by Mr. Lou has 5 students. There are also 7 reading groups. This means that the total number of students under Mr. Lou is:
= Number of reading groups x Number of students per group
= 7 x 5
Then out of this total number, 3 students are absent. The expression then becomes:
= Number of students - Number o absent students
= (7 x 5) - 3
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the
unit cost is given by the function C(x)=0.5x²-180x+25,885. What is the minimum unit cost?
Do not round your answer.
Answe(0.5x²-180x+25,885= 47,925.25
Step-by-step explanation:
x=1
ing Equations Practice
CONCEPT: Multi-Step Equations
C Level:
What is the value of x? Show your work and explain how you found the answer.
-4x-43 = -95
Answer:
X:15
Step-by-step explanation:
only a genius can explain i can ask my colic to help
please help asap. due monday
if I am correct that is the solution.
Why is the variable x called x?
Towns A and B are 240 km apart.
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at × km/h.
(a) Find the time, in hours,
taken by the bus and the car to travel between the two towns in terms of x
(b) Form an equation in × and
show that it reduces to ×2 + 15x - 2700 = 0
(c) Solve the equation and find the speed of the bus and
the time taken by the car to travel between the two towns.
The time (in hours) taken by the bus and the car to travel between the two towns in terms of x is 5 hours 20 minutes and 4 hours respectively and the equation in x formed is [tex]x^2 + 15x -2700=0[/tex]
Given that:-
Distance between towns A and B = 240 km
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at x km/h.
Let the speed of the bus be s km/hr and,
The time taken by the car to travel from A to B be t hours.
Hence,
(15+x)*t = (t + 80/60)*x
15t + xt = xt + 4x/3
15t = 4x/3
t = 4x/45 hours.
Hence,
(15 + x)*(4x/45) = 240
x(x + 15)/45 = 60
[tex](x^2 + 15x) = 60*45[/tex]
[tex](x^2 + 15x) = 2700\\x^2 + 15x -2700=0\\x^2-45x+60x-2700 = 0[/tex]
x(x-45) +60(x - 45) = 0
(x - 45)(x + 60) = 0
x = 45,-60
As the time cannot be negative,
x = 45 km/hr
t = (4*45)/45
t = 4 hours (time taken by car)
Time taken by bus = 4 hours + 80 minutes = 5 hours 20 minutes
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Answer the questions about the following function.
f(x) =
X+11
X-9
(a) Is the point (3,-9) on the graph of f?
Answer:
No
Step-by-step explanation:
I just graphed f(x)=x+11, f(x)=x-9, and (3,-9) in Desmos, and you can visibly see that it isn't.
80p as a fraction of £3
simplest form
Answer:
Step-by-step explanation:
4/15
Based on the concept of fraction, 80p is equivalent to 4p/15p as a fraction of £3.
What is a fraction?Fraction is a term that is used to describe the portion or part of the whole thing.
Generally, the term fraction represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator.
In this case, to find the fraction of 80p as a fraction of £3, we divide 80p by £3.
Since there are 100 pence in 1 pound the fraction can be expressed as 80p/£3.
To simplify the fraction divide both the numerator and the denominator by 10:
80p/£3 = 8p/30p
Simplifying further both the numerator and the denominator can be divided by 2:
8p/30p = 4p/15p
Therefore, in this case, it is concluded that 80p is equivalent to 4p/15p as a fraction of £3.
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Jenna is making knit hats for Christmas presents.
Each hat requires her to use 1 1/3 yards of yarn. If she has 30 yards of yarn, how many hats can she make?
This problem is asking me to determine?
Write the equation you will be using to solve.
Answer:
22 hats
Step-by-step explanation:
30÷1 1/3=22.5
The question is implying how many completed hats she can make, and since half a hat is not completed, she can only make 22 completed hats.
The formula for the volume of a cylinder with a base radius equal to 3 inches (in) is shown below. v ≈28.3h where v=volume and h=height What is the closest estimate of the height of the cylinder if the volume is 200 in ³?
Answer:
7 inches
Step-by-step explanation:
π * 3^2 *7 = 197.920337
Find system of equations algebraically. d = f; 2d + 4e - 3f = 1; - 3d + 2e + 4f = 5
The solution of the system of equation is [tex]e=1 , d= 3[/tex] [tex],f=3[/tex]
How do you solve algebra?The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.
The solution is written as below:
Given: d= f
2d + 4e - 3f = 1 --------------1
and - 3d + 2e + 4f = 5----------------------2
Put the value of f as d because it is given,
thus equation becomes; 2d+ 4e - 3d= 1 ⇒ 4e- d= 1 ----3
-3d+2e +4d= 5 ⇒ 2e+ d=5 ----4
Thus on solving 3 and 4 we get;
[tex]4e-d=1\\+2e+d=5\\[/tex]
We get 6e= 6 which implies e= 1
And putting this value of e in equation 3 we get,
4X1 -d=1
-d= 1-4 ⇒ -d= -3
thus d = 3
Thus [tex]e=1 , d= 3[/tex]
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Which of the following functions is graphed below?
The functions that are shown on the graph are:
Square function.Linear function.What is square function and linear function?General equation of square function is :
f(x) = x2
It's called a parabola.It is symmetric around the y-axis (like a mirror image).Domain : R (Real numbers).It has a range of Non-Negative Real Numbers: [0, +∞)General equation of linear function is :f(x) = mx + b
where 'm' and 'b' are real numbers.
It is an algebraic functionThe domain is entirely made up of real numbers. A function's range is the set of all possible output values.To learn more about type of functions refer to :
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Solve the inequality 1/4 (x-20)<-6 or -6x+5≤-1. Write your solution in algebraic form, interval notation, and graphed on a number line.
The solution of the given inequality is:
x ≥ 1.
And the graph on the number line can be seen in the image at the end.
How to solve and graph the inequality?
The inequality we want to solve and graph is:
-6x + 5 ≤-1
To solve this, we need to start by isolating the variable x in one of the sides, we will get:
-6x + 5 ≤-1
-6x ≤-1 - 5
-6x ≤ -6
Now we can divide both sides by -6 to get:
x ≥ 1.
Then the graph will be like the one below. You need to have a closed dot on x = 1 (because that is a solution to the inequality) and then shade all the region to the right of x = 1, because x also can be larger than 1.
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Solve the answer
100*0.5=a
a*2=
Answer:
a = 50
50*2=100
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-2
Step-by-step explanation:
-2y^2=-2y^2
Lucy used 3 3/4 cups of sugar for her lemonade stand. She divided the
sugar, in equal amounts, into 6 pitchers. How much sugar went into each
pitcher?
The amount of sugar that went into each pitcher was 0.375, which was taken from the 3(3/4) cups of sugar utilized for the lemonade stand.
What is the point of dividing?Division allows us to divide a large number of objects into equal-sized groups. Division is represented by the symbol ÷.
Which property is employed in division?We can use the distributive property to divide larger numbers by breaking them down into smaller factors.
It is implied that Lucy made her lemonade stand using 3 3/4 cups of sugar.
Further, she distributed the sugar into 6 pitchers in equal portions.
Therefore, we need to divide the total cups of sugar by 6 to get the value of sugar that went into each pitcher.
sugar went into each pitcher = 3(3/4) ÷ 6
= (9/4) ÷ 6
= 2.25 ÷ 6
= 0.375
Therefore, each pitcher of sugar contained 0.375 of the 3(3/4) cups of sugar utilized for the lemonade stand.
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Look at this angle:
What is the vertex?
Answer:
T. The vertex is where the angle is measured. It is often associated as the vertex angle.
Step-by-step explanation:
Hope it helps! =D
Answer:
T is the vertex
Step-by-step explanation:
the point where the angle lies , is the vertex, in this case T
using the letters forming the angle , with the vertex T placed in the middle
∠ STU or ∠ UTS
if y=3x write 5y in terms of x
explanation?
The value of 5y in terms of x in the equation is 5y = 15x
How to solve equation?The equation is given as y = 3x
Therefore, we are ask to find 5y in terms of x.
This simply means we have to make 5y the subject of the formula in the equation.
In other words, we have to isolate 5y in terms of x in the equation.
Therefore,
y = 3x
multiply both sides by 5
5 × y = 3x × 5
5y = 15x
Therefore,
5y = 15x
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A(c-b)=d
Solve for c
Please and thank
[tex]a(c - b) = d \\ \frac{a(c - b}{a} = \frac{d}{a} \\ c - b = \frac{d}{a} \\ c = \frac{d}{a} + b \\ c = \frac{d}{a} + \frac{b}{1} \times \frac{a}{a} \\ c = \frac{d}{a} + \frac{ab}{a} \\ c = \frac{d + ab}{a} [/tex]
THIRD OPTION IS THE ANSWER.
HOPETHIS HELPS
Divide. Express your answer in scientific notation.
7.2x 10-4
3x10-3
7.2x10-4
3x10^-3
(Use scientific notation. Use the multiplication symbol in the math palette as needed.
The value of 7.2 × 10^-4 divided by 3 × 10^-3 when expressed in scientific notation is 2.4 × 10^-7.
What is scientific notation?It should be noted that scientific notation is simply used to illustrate the numbers that are either too large or too small. It is denoted as a × 10ⁿ.
It should be noted that the exponents will be added. Therefore, 7.2 × 10^-4 divided by 3 × 10^-3 will be:
= 7.2 × 10^-4 / 3 × 10^-3
= 2.4 × 10^-7.
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The length of Rectangle A is 5 inches more than its width. The perimeter of Rectangle B is 17. The difference between the perimeters of the rectangles is less than 9. What are the possible integer values for the width of Rectangle A? 1in. 2in. 3in. 4in.5in. 6in. 7in. 8in.
Answer:
Step-by-step explanation:
Let L and W be the length and width of a triangle.
Rectangle perimeter (Px) = 2L + 2W, where x is triangle a or b.
Rectangle A: La = 5Wa [The length of Rectangle A is 5 inches more than its width.]
Perimeter Rectangle A: Pa = 2La + 2Wa
Substitute L = 5Wa:
Pa = 2La + 2Wa
Pa = 5Wa + 2Wa
Pa = 7Wa
Perimeter Rectangle B: Pb = 17 [The perimeter of Rectangle B is 17]
Pb = 17
Difference between Pa and Pb: Is it < 9?
See the attached table. The perimeters of rectangle A are computed for each of the answer options that define the width. Length (rectangle A) is 5 inches more than the width. The perimeter is 2*Length + 2*Width, and shown as Pa.
The perimeter of rectangle b is 17, shown as Pb on the table. The last column of the table is the absolute value of the difference of Pa and Pb. If it is less than 9, the cell is green (it is a possible integer value for the width of rectangle A), Red mean it does not meet the "less than 9" requirement, One cell has the difference as 9. The problem states "less than 9," so it does not meet the requirement.
two packages of strawberries are sold for $10. how much could you buy with $25?
F.) 3
G.) 4
H.) 5
J.) 6
K.) 7
Answer:
G.) 4
Step-by-step explanation:
If you get two packs of strawberries for $10, with another $10 you could get another two packs. 2+2=4, and 10+10=20. So you could get 4 packs with with $20.
six tickets to a movie cost 76.50 what constant of proportional relates the number of tickets and total cost
Based on the number of movies, $12.75 is the constant of proportionality per movie
How to determine the constant of proportionality?The given parameters are
Number of the movie tickets = 6
Cost of the movie tickets = 76.50
The constant of proportionality of the movie tickets is calculated as
Constant of proportionality = Cost of the movie tickets/Number of the movie tickets
Substitute the known values in the above equation
So, we have
Constant of proportionality = 76.50/6
Evaluate the quotient
So, we have
Constant of proportionality = 12.75
Hence, the constant of proportionality per movie is $12.75
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Answer:
Step-by-step explanation:
$12.75
Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
The value of her investment at compound interest after 4 years will be £8934.34.
What is compound interest?
Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of making an investment interest, or adding it to the lent assets, rather than repaying it out or requesting return from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm. Compound interest differs from simple interest in that previously accrued interest is not added to the main amount of the current month, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods per year.
Given,
Principal (P) = £8000
Rate of interest (r) = 2.8% compound interest p.a.
Time (n) = 4 years
Then, according to compound interest compounded annually,
Amount = P(1+r/100)ⁿ
= 8000(1+2.8/100)⁴
= 8000(102.8/100)⁴
= 8934.34
Hence, the value of her investment at compound interest after 4 years will be £8934.34.
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1. Bobbi is on a diet to lose weight. After losing 26 pounds, Bob weighs 231 pounds. What was Bobbi's weight
before his diet? Let x represent Bobbi's original weight.
Answer:
231+26=x
x=257 pounds
What is rate of change for 3=2x-21
Answer:
Step-by-step explanation:
I believe I need 2 variables to properly work this out but x=12
3=2x-21
24=2x
12=x
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
An inequality which best models the situation described above is: D. 52 + 3w ≥ 90.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Less than or equal to (≤).Less than (<).Greater than or equal to (≥).Greater than (>).In order to solve this word problem, we would assign a variable to the number of weeks and then translate the word problem into algebraic equation as follows:
Let w represent the number of weeks.
Translating the word problem into an algebraic equation, we have;
Volunteering hours = 52 hours.Remainder of her volunteer hours = 3w hours.Total time to graduate (at least) = 90 volunteer hours.Next, we would combine the above parameters to form an algebraic equation as follows:
52 + 3w ≥ 90
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Complete Question:
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
answer choices
A. 52w + 30w ≥ 90
B. 52w + 30w ≤ 90
C. 52 + 3w ≤ 90
D. 52 + 3w ≥ 90