A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.
What is a Complex Number?A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.
As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.
A.) x+y=y+x
[tex]x+y=y+x\\a+bi+c+di=c+di+a+bi[/tex]
As the two sides of the equation are equal, the equation is true.
B.) (x × y) × z = x × (y × z)
[tex](x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)[/tex]
[tex](ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\\\\\\acf+adfi+bcfi-bdf+acgi-adg-bcg-bdgi = acf+acgi+afdi-adg + bcfi-bcg-bfd-bdgi[/tex]
As the two sides of the equation are equal, the equation is true.
C.) x−y=y−x
[tex]x-y=y-x\\\\(a+bi)-(c+di)=(c+di)-(a+bi)\\\\a+bi-c-di=c+di-a-bi[/tex]
As the two sides of the equation are not equal, the equation is not true.
D.) (x+y)+z=x+(y+z)
[tex](x+y)+z=x+(y+z)\\\\(a+bi+c+di)+f+gi = a+bi+(c+di+f+gi)\\\\a+bi+c+di+f+gi = a+bi+c+di+f+gi[/tex]
As the two sides of the equation are equal, the equation is true.
E.) (x−y)−z=x−(y−z)
[tex](x-y)-z=x-(y-z)\\\\(a+bi-c-di)-f-gi = a+bi-(c+di-f-gi)\\\\a+bi-c-di-f-gi =a+bi-c-di+f+gi)[/tex]
As the two sides of the equation are not equal, the equation is not true.
Hence, all the statements are true except C and E.
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Joy and John MacAllister have agreed to purchase a house
for $379,900. First National Savings & Loan is willing to
lend the money at 6. 5% for 25 years, provided the
MacAllisters can make a $79,900 down payment. The total
closing cost is 3. 5% of the amount of the mortgage. What is
the total closing cost?
The total closing cost is 3. 5% of the amount of the mortgage. So, the total amount would be $10500.
What is down payment?An initial payment made when something is bought on credit to make the down payment.
First National Savings & Loan is willing to lend them money at 6. 5% for 25 years, provided the MacAllister's can make a $79,900 down payment.
$379,900 - $79,900 =$300,000
because down payments are never included with the total mortgage loan.
The total closing cost is 3. 5% of the amount of the mortgage.
3.5 percent for closing costs
= [tex]3.5/100 \times 300000\\\\3.5 \times 3000\\\\10500[/tex]
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Gerald would like to add a dental and vision option to the health insurance plan he purchased through his employer. in addition to the 65% of gerald’s $345 monthly health insurance premium, his employer has offered to pay 50% of a $38 monthly dental premium and 75% of a $23 monthly vision premium. if gerald adds both the dental and vision options to his insurance plan, how much will he pay each month towards health insurance? soopergood insurance option monthly premium employer contribution health insurance $345 65% dental $38 50% vision $23 75% a. $141.75 b. $145.50 c. $149.50 d. $260.50
From the calculations, Gerald will now have to pay the sum of $145.50 towards his monthly health insurance.
How is the above sum arrived at?
Note that the first sum being contributed by Gerald is (100%- 65%) of $345. This is 35% of $345 = $120.75
If his employer takes up 50% of $38, this leaves his contribution for dental as 50% of $38 = $19
Also if his employer takes up 75% of $23, his contribtuion for vision premium is 25% of 23 = $5.75
Hence his total contribution is now:
120.75 + 19.00 + 5.75 = $145.50
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PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
what is the exact value of tanC
Answer:
tan C = 5/√39
Step-by-step explanation:
tan C = opp/adj
For angle C, the opposite leg is AB, 5.
The adjacent leg is BC, √39.
tan C = 5/√39
consuela is displaying a cylindrical case on a pedestal. she wants it to be placed so that there is an even amount of space on either side of the case. if the volume of cylinder shown is 1,130.97 cubic inches, how much space will be on either side if its placed on a pedestal that is 18 inches across? round to the nearest inch
The space that will be on either side if its placed on the pedestal of the cylinder that is 18 inches across will be 4.47 inches.
How to compute the dimension?It should be noted that the volume of a cylinder is given as:
= πr²h
We'll then slot the values given into the formula. This will be:
Volume = πr²h
1130.97 = (3.14 × r² × 18)
1130.97 = 56.52r²
r² = 1130.97/56.52
r² = 20
r = ✓20
r = 4.47
In conclusion, the space will be 4.47 inches.
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If f(x) = 2x − 9 and g(x) = x2 + 3, what is (f + g)(4)? (1 point)
Group of answer choices
a. 18
b. 20
c. −19
d. −20
Answer:
a. 18Step-by-step explanation:
(f+g)(4) = f(4) + g(4)
= 2(4) - 9 + 4² + 3
= 8 - 9 + 16 + 3
= -1 + 16 + 3
= 15 + 3
= 18
The results of a survey of 200 adults are shown in the table?
Answer:
A. [tex]\frac{14}{200}[/tex]
Step-by-step explanation:
There are 200 people in total to choose from, and only 14 of them are 6' and male.
At the end of a basketball game the players were given the choice of having a bottle of water or a box of juice of all the players 12 chose a bottle of water which was three over four of the total number of players right and solve any equation to determine p the total number of players at the basketball game
The minimum wage in 1975 was $2.00. The minimum wage in 2010 was $7.25. Find the average rate of change of the minimum wage from 1975 to 2010. (Round to nearest hundredth) 0.08 $/yr 0.08 $/yr , 0.08 yr/$ 0.08 yr/$ , 0.15 yr/$ 0.15 yr/$ , 0.15 $/yr
Answer: $0.15/Yr
Step-by-step explanation:
Difference in year 2010- 1975= 35
Range = 7.25 - 2 = 5.25
Per year = 5.25/ 35
What is the completely factored form of f(x) = 6x3 – 13x2 – 4x 15? (x 1)(6x2 – 19x 15) (x 1)2(2x – 3) (x 1)(3x – 2)(5x – 3) (x 1)(2x – 3)(3x – 5)
The completely factored form of f(x) = 6x³ - 13x² - 4x + 15 is f(x) = (x + 1)(2x - 3)(3x - 5)
How to factor the expression?The expression is given as:
f(x) = 6x³ - 13x² - 4x + 15
Expand the expression
f(x) = 6x³ - 19x² + 6x² + 15x - 19x + 15
Rewrite as:
f(x) = 6x³ + 6x² + 15x- 19x² - 19x + 15
Factorize the equation
f(x) = (x + 1)(6x²- 19x + 15)
Expand (6x² - 19x + 15)
f(x) = (x + 1)(6x² - 10x - 9x + 15)
Factorize the expression
f(x) = (x + 1)(2x - 3)(3x - 5)
Hence, the completely factored form of f(x) = 6x³ - 13x² - 4x + 15 is f(x) = (x + 1)(2x - 3)(3x - 5)
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Answer: D
Step-by-step explanation:
BRAINLEST! PLUS POINTS for whoever gives all the answer
Answer:
start by thinking step by step
Step-by-step explanation:
20 points!!!
1. (07.01 MC)
Part A: Explain why x = 5 makes 4x - 1 s 19 true but not 4x -1 < 19. (5 points)
Part B: What value from the set {6, 7, 8, 9, 10) makes the equation 5x + 2 = 47 true? Show your work. (5 points)
Answer:
s part a i don't know what the question is asking, I think n n n the are the same equation
a part b is 9
p
Step-by-step explanation:
I know that 5*9 equals 45 so basically it turns into
5(9)=45
45+2=47
dsan168
4. there are nearly 10 thousand bacteria in the area of one square millimeter. how many bacteria will be there in the area of 12 square millimeter?
Answer:
Around 120,000 bacteria.
Multiply the amount of estimated bacteria by the amount of square millimeters.
[tex]10,000 * 12 = 120,000[/tex]
A baker has 40 pounds of sugar. He plans to store the sugar in 6 equal containers. He must store all of the sugar. How many pounds will be in each container.
40/6 = 6.666... in each container
hope it helps...!!!
Answer:
[tex]6\frac{2}{3}\text{ pounds}[/tex]
Step-by-step explanation:
The baker must have equal amounts in all countainers. Therefore we need to use division to solve this question.
In this scenario we divide the 40 pounds of sugar between the 6 equal containers.Therefore we get:
[tex]\frac{40}{6}[/tex]
Simplify the fraction:
[tex]\frac{20}{3}[/tex]
Write it as a mixed fraction:
20 divided by 3 is 6 with a remainder of 2This means the mixed fraction is:[tex]6\frac{2}{3}[/tex]
6 2/3 pounds will be in each container.
f(x) = (x + 1)(x - 3)(x - 4)
Step-by-step explanation:
[tex]f(x) = {x}^{3} + 6 {x}^{2} + 5x + 12[/tex]
x intercept = -1, 3 and 4
y intercept = 12
A cylindrical gas tank has a volume
of 1,808.64 m². Its height is 9 m. What is its radius?
Answer:
The radius is 32
Step-by-step explanation:
V= πr2h
So,
3.14(18)(x)=1808.64
56.52x=1808.64
= 32.
In 2011, Americans used 1.86 x 1011
kilowatt-hours to light their homes. They used
4.6 x 1010 kilowatt-hours to run their
computer and computer equipment.
Answer:
In 2011, Americans used 1.86x10" kilowatt-hours to light their home kilowatt-hours to run their computers and computer equipment. Circle the number that correctly completes the statement
Step-by-step explanation:
hope this helped
The triangles below are similar. Find x.
Answer:
x = 1
Step-by-step explanation:
Question is in photo below.
Answer:
ordered the numbers below from least to greatest
Ascending Order: -√100 , 9 4/11 , 9.46 , 9.5
hope that helped...
I need help can someone help me please
Answer:
I got 142
Step-by-step explanation:
A bag contains seven tiles labeled B, C, D, E, F, G, and H. One tile will be randomly picked. What is the probability of picking a vowel?
Write your answer as a fraction in simplest form
Answer:
[tex]\sf \dfrac{1}{7}[/tex]
Step-by-step explanation:
Given labeled tiles: B, C, D, E, F, G, H
Total number of tiles = 7
Vowels = A, E, I, O and U
⇒ Total number of vowel tiles in bag = 1
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf Probability\:of\:picking\:a\:vowel= \dfrac{Number\:of\:vowel\:tiles}{Total\:number\:of\:tiles}=\dfrac{1}{7}[/tex]
What is the line of the equation PERPENDICULAR to the slope of -6/5 and through the y-intercept of 3?
Answer:
y = 5/6x+ 3
Step-by-step explanation:
Given
slope = -6/5y-intercept = 3Solving
The slope of the perpendicular line is the negative reciprocal of the original lineSo, the new slope is : -(1/-6/5)) = 5/6It mentions the line passes through the y-intercept of 3y = mx + c⇒ y = 5/6x+ 3SOMEONE HELP THIS IS THE LAST QUSETION I NEED IT FAST QUICK PLS
Answer:
18
Step-by-step explanation:
to solve this we need to find how frequent pink is landed on. to find the frequency we add all the total
12+6+9+13=40
then we divide 6 (frequency of pink) by 40 to fing how frequent 6 is in percentage
6÷40=.15=15%
then we multiply 15% by 120
120×.15= 18
Please help. Thank you!
Answer:
B
Step-by-step explanation:
When you think about it, turn all the answers upside down and see if any of them look just like the figure you are given
If we know the area of this base, we'll know how many cubes can fill the bottom layer. We can find the area of the rectangle by multiplying the length times the width. Help me out.
The base of the prism is a rectangle with a length of 6 inches and a width of 4 inches.
Find the area of the base.
rectangular prism
Answer: i think you need a math tutor
Answer:
24
Step-by-step explanation:
Plato
When y is 4, p is 0. 5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
x p m y = 8
StartFraction x y Over p m EndFraction = 8
StartFraction x p m Over y EndFraction = 0. 5
StartFraction x Over p m y EndFraction = 0. 5
Answer:
[tex]\dfrac{xy}{pm}=8[/tex]
Step-by-step explanation:
If x varies directly as the product of p and m, and inversely with y, the relation can be written ...
x = k(pm)/y . . . . where k is the constant of proportionality
__
This can be solved for k:
k = xy/pm
For the given values, the value of k is ...
k = (2)(4)/((0.5)(2)) = 8
Then the relation between the variables can be written ...
(xy)/(pm) = 8
Answer:
B
Step-by-step explanation:
Select the correct description for the polar function, r = 6 sin
The correct description for the polar function, r = 6sin(θ) is: D. Circle symmetric on the line theta = 0, with a radius of 6.
The conversion of polar coordinates.In Mathematics, the relationship between the polar coordinates (r, θ) and rectangular coordinates (x, y) is given by these polar functions:
On the horizontal plane:
x = rcosθ
On the vertical plane:
y = rsinθ
Where:
θ is the angle.r is the diameter of a circle.In conclusion, the correct description for the polar function, r = 6sin(θ) is circle symmetric on the line with an angle (θ) equal to zero (0) and a radius of 6.
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3. Select all the sectors which have an area of 3pi square units.
a)a sector with a radius of 6 units and a central angle of 30 degrees
b)a sector with a radius of 6 units and a central angle of 45 degrees
c)a sector with a radius of 3 units and a central angle of 60 degrees
d)a sector with a radius of 3 units and a central angle of 120 degrees
e)a sector with a radius of 3 units and a central angle of 180 degrees
Answer:
Sector A sector C sector D correct answers
Answer: A, C, D
Step-by-step explanation:
The reason for this is because you plug it in as a fraction to simplify.
Example: 9π/3 simplify to 3π/1 because both divide by 3
need help with question 16
Answer:
C)
Step-by-step explanation:
u = x + 1
u - 1 = x
[tex]\int\limits {\dfrac{x}{\sqrt{x+1}}} \, dx = \int\limits {\dfrac{u-1}{\sqrt{u}}} \, du \\\\[/tex]
[tex]=\int {\left(\dfrac{u}{u^{\frac{1}{2}}}-\dfrac{1}{u^{\frac{1}{2}}} \right )\, du \\\\ = \int {u^{1-\frac{1}{2}}-1*u^{\frac{-1}{2}}} \, du\\\\ =\int {(u^{\frac{1}{2}}-u^{\frac{-1}{2}})} \, du[/tex]
If Sn=n2+2n then find the first five term
Answer
first term put n=1 that is equal to 3
Which piecewise function represents the graph?
Answer:
D
Step-by-step explanation:
If you look at the right side of each piecewise function, you will see the x-values. That is what we will be focusing on in this explanation. All four equations have x > 4, and we know that to be true. If you look at the equation on the graph going South West, you will see that the endpoint is at x=1. Only 1 equation, D, has this in the piecewise function. To confirm it is D, you can see that 1<x<4 is also in the piecewise function, and all the values line up with their corresponding y-values.
Hope this helps! :)