if i am right you would multiply x= -3 by -3 and you get 9 so you would do the same thing to the y as well so y= -7 and you multiply it by -3 and then y= 21
Let [tex]i[/tex] be the imaginary unit.
What complex number in standard form does the following simplify to:
[tex]i^{425}+i^{14}+i^{-14}+i^{44}[/tex]
Basically you are being asked to find A and B such that the following equality holds for real values A and B:
[tex]A+Bi=i^{425}+i^{14}+i^{-14}+i^{44}[/tex]
You must show all work.
Have fun.
[tex]Hey~freckledspots!\\----------------------[/tex]
[tex]We~will~solve~for~i^{425}![/tex]
[tex]Rule~of~exponent: a^{b + c} = a^ba^c\\Apply:~i^{425}~=~i^{424}i\\ \\Rule~of~exponent: a^{bc} = (a^{b})^c\\Apply: i^{424} = i(i^2)^{212} \\\\Rule~of~imaginary~number: i^2 = -1\\Apply: i(i^2)^{212} = -1^{212}i\\\\Rule~of~exponent~if~n~is~even: -a^n = a^n\\Apply: -1^{212}i = 1^{212}i\\\\Simplify: 1^{212}i = 1i\\Multiply: 1i * 1 = i\\----------------------\\[/tex]
[tex]Now~let's~solve~1^{14}!\\\\Rule~of~exponent: a^{b + c} = a^ba^c\\Apply: i^{14} = (i^2)^7\\\\Rule~of~imaginary~number: i^2 = -1\\Apply: (i^2)^7 = -1^7\\\\Rule~of~exponent~if~n~is~odd: (-a)^n = -a^n\\Apply: -1^7 = -1^7\\\\Simplify: -1^7 = -1\\----------------------\\Now,~we~have: i-1+i^{-14}+i^{44}\\----------------------[/tex]
[tex]Now~lets~solve~i^{-14}\\\\Rule~of~exponent: a^{-b} = \frac{1}{a^b} \\Apply: i^{-14} = \frac{1}{i^{14}} \\\\Rule~of~exponent: a^{bc} = (a^b)^c\\Apply: \frac{1}{i^{14}} = \frac{1}{(i^2)^7}\\ \\Rule~of~imagianry~number: i^2 = -1\\Apply: \frac{1}{(i^2)^7} = \frac{1}{-1^7} \\\\Simplify: \frac{1}{-1^7} = \frac{1}{-1} \\\\Rule~of~fractions: \frac{a}{-b} = -\frac{a}{b} \\Apply: \frac{1}{-1} = -\frac{1}{1} = -1\\----------------------\\Now,~we~have: i-1-1+i^44\\----------------------[/tex]
[tex]Now~let's~solve~i^{44}!\\\\Rule~of~exponent: a^{bc} = (a^b)^c\\Apply: i^{44} = (i^2)^{22}\\\\Rule~of~imaginary~numbers: i^2 = -1\\Apply: (i^2)^{22} = -1^{22}\\\\Rule~of~exponent~if~n~is~even: (-a)^n = a^n\\Apply: -1^{22} = 1^{22}\\\\Simplify: 1^{22} = 1\\----------------------\\Now,~we~have~i-1-1+1\\----------------------[/tex]
[tex]Now~let's~simplify~the~expression!\\\\= i-1-1+1 \\= 1 + i -2\\= -1+i\\----------------------[/tex]
[tex]Answer:\\\large\boxed{-1+i}\\----------------------[/tex]
[tex]Hope~This~Helped!~Good~Luck![/tex]
Answer:
[tex]i - 1[/tex]
Step-by-step explanation:
Complex Number System Rules
[tex]\sqrt{-1} = i \\ -1 = {i}^{2} \\ -i = {i}^{3} \\ 1 = {i}^{4} [Every \: multiple \: of \: four][/tex]
The Divisibilty Rule of 4 states that the last two digits of a number must be a multiple of four, so you will have this:
[tex]{i}^{425} + {i}^{14} + {i}^{-14} + {i}^{44} \\ \\ i - 1 - 1 + 1 = i - 1[/tex]
I am joyous to assist you anytime.
The sale price of a swimming pool after 16.5% discount $1135.60. Find the original price of the pool
well, let's say the original price is "x", and thus is also the 100% price of the item, however the item is discounted by 16.5%, well 100% - 16.5% = 83.5%, so then the discounted price is really the 83.5% of the item, and we know that is $1135.60.
now, if 1135.60 is 83.5%, what is the 100% or namely "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 1135.60&83.5\\ x&100 \end{array}\implies \cfrac{1135.60}{x}=\cfrac{83.5}{100}\implies 113560 = 83.5x \\\\\\ \cfrac{113560}{83.5}=x\implies 1360 = x[/tex]
The original price of the swimming pool $1,360.
Original pool price=x
Percent discount=16.5% or 0.165
Sale price=$1135.60
Hence:
x-0.165(x)=$1135.60
x(1-0.165)=$1135.60
0.835x=$1135.60
Divide both side by 0.835x
x=$1135.60/0.835
x=$1,360
Inconclusion the original price of the swimming pool $1,360.
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If 120 million roses were sold on Valentine's Day, and 75% of the roses were red, how
many red roses were sold on Valentine's Day? Show your work.
Answer:
1,600,000
Step-by-step explanation:
120,000,000 divided by 75 is 1,600,000
Answer:
did the math its 90,000,000
thats how much 75% is
Step-by-step explanation:
A function is expressed by the equation y=0.3x−6. For what value of the independent variable will the value of the function be equal to −6; −3; 0?
Answer:
0; 10; 20
Step-by-step explanation:
x is the independent variable
y is the dependent variable
y is dependent on x
a) For what value of the independent variable will the value of the function be equal to −6
y=0.3x−6
-6 = 0.3x-6
0=0.3x
x = 0
Therefore, if the independent variable is 0, the value of the function will be -6.
b) For what value of the independent variable will the value of the function be equal to −3
y=0.3x−6
-3 = 0.3x-6
0.3x = -3+6
0.3x = 3
x = 3/0.3
x = 10
Therefore, if the independent variable is 10, the value of the function will be -3.
c) For what value of the independent variable will the value of the function be equal to 0.
y=0.3x−6
0=0.3x-6
6 = 0.3x
x = 6/0.3
x = 20
Therefore, if the independent variable is 20, the value of the function will be 0.
I’m doing the Order of operations and I’m asking what 6 x (8-3) - 5^2
Answer:
6 x 5 - 25 = 30 - 25 = 5
Answer : 5
Step-by-step explanation:
5² = 5 x 5 = 25
Jason Ayers works as a lifeguard earning $8.75 an hour for 20 hours per week. What is Jason’s straight-time pay for the week?
Hey!
-----------------------------------------------------
Straight-Time Pay - someone works the minimum and gets paid for working those hours. This person doesn't work any overtime hours.
-----------------------------------------------------
Solution:
8.75 * 20 = 175
-----------------------------------------------------
Answer:
Jason's straight-time pay for the week is $175!
-----------------------------------------------------
Hope This Helped! Good Luck!
Answer:
Jason’s straight-time pay for the week is $175.
Step-by-step explanation:
Given : Jason Ayers works as a lifeguard earning $8.75 an hour for 20 hours per week.
To find : What is Jason’s straight-time pay for the week?
Solution :
Jason Ayers works as a lifeguard earning in an hour = $8.75
In a week Jason Ayers works for 20 hours.
i.e. Jason Ayers works as a lifeguard earning in 20 hour =[tex]\$8.75\times 20[/tex]
Jason Ayers works as a lifeguard earning in 20 hour = $175
Therefore, Jason’s straight-time pay for the week is $175.
You buy 50 of your favorite songs from a web site that charges $.99 for each song. What is the cost of 50 songs?
Answer: $49.5
Step-by-step explanation: If each song costs 0.99 cents then you multiply the number of songs you are buying by the cost. So that would be 0.99×50=49.5
Which is a possible benefit of having a good credit history?
having a checking account
low interest rate on a car loan
high interest rate on a credit card offer
bankruptcy
Answer:
low interest rate on a car loan
Answer:
B. low interest rate on a car loan
Solve number 20
traingle ABC with C=90 slove for the missing part
PLEASE HELP!!
Answer:
A ≈ 69.5°
Step-by-step explanation:
Given the triangle is right use the cosine ratio to find A
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{2.7}{7.7}[/tex], thus
A = [tex]cos^{-1}[/tex] ( [tex]\frac{2.7}{7.7}[/tex] ) ≈ 69.5° ( to 1 dec. place )
The expression 8x+2 factored using GCF
Answer:
2* (4x + 1)
Step-by-step explanation:
8x = 2 * 2 *2 * x
2 = 2* 1
GCF = 2
8x+2 = 2*2*2*x + 2*1 = 2* (4x + 1)
-4 1/3 + 5 2/3
step by step
Answer: 1 1/3
Step-by-step explanation:
-4 + 5 = 1
-1/3 + 2/3 = 1/3
OR
Turn them both into mixed numbers: -13/3 + 17/3
-13/3 + 17/3 = 4/3 = 1 1/3
What is 12 rounded to the nearest ten
Solve —2|5w – 7 |+9=-7
Helppppp! Angles PTQ and STR are vertical angles and congruent. Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn to connect the points on the circle and form secants P Q, Q R, R S, and S P. Angles P T Q and S T R are congruent. Which chords are congruent? QP and SR QR and PR and RS PR and PS
Answer:
[tex]\overline{QP} = \overline{SR}[/tex]
Step-by-step explanation:
Given: ∠PTQ ≅ ∠STR and TP, TQ, TR and TS are radii of the circle.
If two angle are equal, then they are equal in size and their measurements are equal.
IF ∠PTQ ≅ ∠STR then they are also equal in their measurements.
Now, In ΔPTQ and ΔSTR
∠PTQ ≅ ∠STR (vertically opposite angle)
[tex]\overline{TQ} \cong \overline{ST}[/tex] (Radius of the circle are equal and congruent in length)
[tex]\overline{PT} \cong \overline{TR}[/tex] (Radius of the circle)
∴ ΔPTQ ≅ ΔSTR (SAS postulate)
∴ [tex]\overline{QP}\cong \overline{SR}[/tex] (corresponding sides of congruent triangle are equal and congruent).
You can use the fact that a closed figure made by connecting the adjacent end points of two equal and intersecting line segment is a rectangle.
Option A: [tex]\overline{QP} \: \rm and \: \overline{SR}\\[/tex]correct choice since the line segment QP is and line segment SR are congruent.
Given that:
Angles PTQ and STR are vertical angle and congruent.Circle T(centered at T).Line segments TP, TQ, TR, and TS are radii.How to find which lines are intersecting?Since angle PTQ and angle STR are congruent, thus we have:
PR and SQ as straight intersecting lines.
Due to angle PTS and angle QTR are opposite angles made by intersecting lines, we have them as congruent or say of equal measurement.
[tex]\angle PTS \cong \angle QTR[/tex]
Since [tex]\overline{TP} = \overline{TQ} = \overline{TR} = \overline{TS}[/tex], thus we have got:
[tex]\overline{PR} = \overline{SQ}[/tex] in measurement ( as PR is sum of PT and TR and same for SQ)
How is a rectangle made?"A closed figure made by connecting the adjacent end points of two equal and intersecting line segment is a rectangle", we have PQRS as a rectangle.
As a rectangle have opposite sides parallel and equal, we have got:
[tex]\overline{PQ} \cong \overline{SR}[/tex]
Thus, Option A: [tex]\overline{QP} \: \rm and \: \overline{SR}\\[/tex] is the correct choice since the line segment QP is and line segment SR are congruent.
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tins eats 8 crackers for a snack each day at school.on Friday,she drops 3 and only eats 5. multy
Answer:
[tex]37[/tex] [tex]crackers[/tex]
Step-by-step explanation:
Tins (or Tina) ate 8 crackers for a snack each day on school , then on Friday, she drops three and only eats 5.
Meaning that for 4 days, she ate 8 crackers not including Friday.
So meaning we have to multiply how many crackers she ate for those 4 days in total:
[tex]8 * 4[/tex]
[tex]==> 32[/tex]
Then on Friday, she only ate 5, so we add 5 for how many crackers she ate into how many we have right now:
[tex]32 + 5[/tex]
[tex]==> 37[/tex]
To find out how many crackers Tins ate on Friday, you can subtract the number of dropped crackers from the total number she normally eats.
Explanation:In this question, the subject is mathematics and the grade level is middle school. The question asks about a student named Tins who eats 8 crackers for a snack each day at school. On Friday, she drops 3 crackers and only eats 5. To find out how many crackers she ate on Friday, we can subtract the number of dropped crackers from the total number she normally eats.
Number of crackers normally eaten: 8
Number of crackers dropped on Friday: 3
Number of crackers eaten on Friday: 8 - 3 = 5 crackers
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The elementary school students are putting on a play as a fundraiser. The student tickets cost $2.00 each and
the adult tickets cost $4 each. They sold 5 times as many student tickets as adult tickets. They made $140. How
many student and adult tickets were sold?
Answer:
850 for student and 850 for students
Step-by-step explanation:
Let student tickets sold be=x
and adult tickets sold=y
They sold 5 times as many student tickets as adult tickets.
i.e. x=5y
The student tickets cost $2.00 each and
the adult tickets cost $4 each.
They made $140.
i.e. 2x + 4y = 140
Dividing both sides by 6, we get
x + 2y = 70
or 5y + 2y= 70
i.e. 7y=70
i.e. y=10
x= 5y
⇒ x = 50
Hence, Student tickets sold= 50
and Adult tickets sold= 10
11x+19y=
I don't understand this I hate math
are they asking to graph or just answer it?
Answer:
you can't get an answer from that question unless they are asking you to graph it or something else
Write a subtraction problem involving two positive integers with a negative difference. Explain the relationship between the two integers that must exist for the difference to be negative.
Answer:
When both integers have the same value, the difference is zero. The difference between a positive and a negative integer can be positive or negative. When you subtract a negative integer from a positive integer, the difference is always positive this might help
Step-by-step explanation:
Write a subtraction problem involving two positive integers with a negative difference.
1) When you subtract a positive integer from a negative integer, the difference is always negative.
For example : [tex]-7 - 3 = -10[/tex]
2) When you subtract a larger positive integer from a smaller integer, the difference is always negative.
For example : [tex]5-7=-2[/tex]
3) When you subtract two negative integers and the first integer (or minuend) is smaller than the second integer (or subtrahend), the difference is negative.
For example : [tex]-8 - (-2) = -6[/tex]
What’s Equivalent to 2 to the fifth power
Answer:
32
Step-by-step explanation:
1 = 2
2 = 4
3 = 8
4 = 16
5 = 32
Answer:
4 to the fifth power
Step-by-step explanation:
I think u just to find what is the same as 2 and or equivalent to 2 to the fifth power
A 2-column table with 8 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20. Which could be the entire interval over which the function, f(x), is positive? (–∞, 1) (–2, 1) (–∞, 0) (1, 4)
The entire interval over which the function, f(x), is positive is from (-2, 1), according to the provided table of function values.
Explanation:You are asking for the interval over which the function f(x) is positive based on the provided table of values.
A function is positive when its value, represented as f(x), is greater than 0. Looking at the table, f(x) is positive when x is in between -2 and 1. Therefore, the interval over which the function, f(x), is positive is from (-2, 1).
This can be confirmed visually if you were to plot the x-values with their corresponding f(x) values and look for the section of the graph where the curve is above the x-axis (y>0).
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what is 3/5 + 4/5 can you help me
Answer:
[tex]\frac{3}{5}[/tex] + [tex]\frac{4}{5}[/tex] = [tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Since 3/5 & 4/5 are both over 5 we can add the numbers on the top (numerators) normally while keeping the bottom number (denominator) the same.
[tex]\frac{3}{5}[/tex] + [tex]\frac{4}{5}[/tex] = [tex]\frac{7}{5}[/tex]
-4p + 19 = 11
please help me due tomorrow
Answer:
p=2
Step-by-step explanation:
−4p=11−19
−4p=−8
then you divide both sides by -4 and two negatives make a positive.
Round 751.623 to the nearest hundredth
Answer: 751.62
Step-by-step explanation: 3 is lower than 5 so you have to round it to zero
751.623 rounded to the nearest hundredth is 751.62
To round the number 751.623 to the nearest hundredth, follow these steps:
Look at the digit in the thousandth place (the third digit after the decimal point). In this case, it’s 3.Since 3 is less than 5, we round down the hundredth place.Drop all digits after the hundredth place.The rounded value is 751.62.Therefore, 751.623 rounded to the nearest hundredth is 751.62
5z ^ 3 - 2z ^ 4 - 9z ^ 2 + z What is the degree of the polynomial ?
Answer:
Step-by-step explanation:
For any polynomial, we can determine the degree by finding the variable with the largest exponent. For the given polynomial:
[tex]5z^{3} - 2z^{4} -9z^{2} + z[/tex]
we can see that [tex]-2z^{4}[/tex] contains the variable with the highest exponent, 4, so the degree of this polynomial is 4.
Answer:
4
Step-by-step explanation:
khan academy help
missing length??
3 cm
8 cm
i need big help
Answer: 8.5 (rounded)
Step-by-step explanation:
a squared + b squared = c squared
3 squared= 9
8 squared= 64
64+9=73
the square root of 73 is 8.5 (rounded)
write an inequality for each set of numbers on the number line
x<-4
x≥-7
-4≤5
i dont think the last one is right
I need answers for b and 4 (: <3
4: Geraldine wanted custom keychains. The store she went to has a service fee of 5 dollars, then 8 dollars per key chain. Geraldine payed 37 dollars. How many key chains did she buy?
(She bought 4 keychains)
As for b, I need to see question 3 in order to answer
Pls help and break down :) I’ll give u a thnx and brainlest when another person answers
Answer:
b=3in
Step-by-step explanation:
SO first of all, the formula for area is lxw (length x width)
And our question tells us that
l x w=24in^2
4 x w = 24 (question tells us that length is 4 inches as listed on side)
4 x (b+3) = 24 (b+3 is the total width of the postcard)
4b + 12 =24 (multiply by 4 inside the bracket)
4b=12 (subtract 12 from both sides)
b=3 (solve for b by dividing by 4)
HELP PLZ WITH HOMEWORK !!!!!!!!!!!!!!!!!!!!!!
Answer:
The sum of 3 + (-2) = 1 because it's just like 3 - 2
The sum of -6 + 3 = - 3 because the negative number is greater than positive number it's a negative.
For B you fill in Six negative, -6; three positive, 3. And you are left with three negative counters.
For A you are left with one positve counters.
What is the least number of transformations performed to create similar rectangle K' from rectangle K?
A. 1; rotation about the origin
B. 2; rotation about the origin, dilation
C. 3; rotation about the origin, translation, dilation
D. 4; reflection across y-axis, dilation, translation, rotation about origin
(not B.)
Answer:
C. 3; rotation about the origin, translation, dilation
Step-by-step explanation:
The first obvious step is to rotate it 270° counterclockwise [90° clockwise], next you translate it, then you dilate [long and wide].
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
C
Step-by-step explanation: