9.5 or 9 1/2 inches per second in miles per hour is 0.5 .
What is conversion of units?
The process of translating measurements of a given quantity between different units, frequently using multiplicative conversion factors that change the value of the measured quantity without changing its effects, is known as unit conversion. The specific circumstances and the desired result dictate the conversion process. This may be governed by a regulation, contract, set of technical requirements, or other publicly available standards.
What is the conversion factor for inch to mile?
A value in inch when divided by 63360 gives a value in mile.
What is the conversion factor for second to hour?
A value in second when divided by 3600 gives a value in hour.
Given, the speed of Caroline in inches per second = 9 1/2 = 9.5/1 - (i)
Therefore following above literature and dividing numerator by 63360 and denominator by 3600, we get the speed in miles per second.
Thus, required speed = [9.5/63360]/[1/3600) = 0.539 = 0.5
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he profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?
y=48x−2
y=48x+2
y=2x−48
y=2x+48
The linear function that represents the profit earned is: C. y = 2x − 48.
How to Write a Linear Function?The linear Function can be written as y = mx + b, which is in slope-intercept form, where we have:
x and y as the variables.m as the slope/unit rate.b as the starting value or y-intercept of the linear function.From the information given, we have:
x = number of hot dogs sold
y = Profit earned
m = unit rate = 2
b = starting value = -48 (this is negative because the profit on each hot dog sold must be deducted from the cost for each morning.)
Therefore, substitute m = 2 and b = -48 into y = mx + b to write the linear function:
y = 2x - 48
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Answer:
C
Step-by-step explanation:
i said so
2 regular pizzas and 3 small pizzas cost £43 8 regular pizzas and 9 small pizzas cost £151 find the cost of one of each
Taking into account the definition of a system of linear equations, a small pizza and a regular pizza cost £7 and £11 respectively.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This mieans thar systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"r" is the cost of a regular pizza."s" is the cost of a small pizza.You know:
2 regular pizzas and 3 small pizzas cost £43.8 regular pizzas and 9 small pizzas cost £151.The system of equations to be solved is
2r + 3s= 43
8r + 9s= 151
Of the several methods to solve a system of equations. it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "r" from the first equation:
2r= 43 - 3s
r= (43 -3s)÷2
r= 43/2 - 3/2s
Replacing this expression in the second equation:
8×(43/2 - 3/2s) + 9s= 151
Solving:
8×43/2 - 8×3/2s + 9s= 151
172 -12s + 9s= 151
-12s + 9s= 151 - 172
-3s= -21
s= (-21)÷ (-3)
s= 7
Remembering that r=43/2 - 3/2s you get:
r=43/2 - 3/2×7
r= 11
Finally, a small pizza cost £7 and a regular pizza cost £11.
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Determine the bonus based upon the formula 2 weeks' salary plus 1 percent commission:
annual salary: $48,000.00
yearly sales: $76,000.00
The bonus based upon the given formula is $2606.15 approximately
Given,
Annual salary = $48,000
Yearly sales = $76,000
Bonus is given according to the formula:
2 weeks salary + 1 percentage commission
Here,
Annual salary is given as $48,000
We have to find the weekly salary:
There is 52 weeks in a year.
So, salary for one week = Annual salary / number of weeks = 48000/52 = $923.077
Now, salary for two weeks = 923.077 × 2 = $1846.154
Rate of annual commission is 1%
The commission amount:
1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760
So,
The bonus amount = 2 weeks salary + 1 percentage commission
The bonus amount = 1846.154 + 760
The bonus amount = 2606.154
Therefore, the bonus given based upon the given formula is $2606.154
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AB is parallel to DE
.
.
CO
Alicia noticed that:
ZwLx
Ly La
.
B
.
A
w
I
F
E
D
Note: Alicia used the following theorems:
When a transversal crosses parallel lines, alternate interior angles are congruent.
Vertical angles are congruent
Choose 1 answer
A.Angles that form a linear pair are complementary
B. when a transversal crosses parallel lines same side interior angles are congruent
C. when a transversal crosses parallel lines alternate exterior angles are supplementary
D. when a transversal crosses parallel lines corresponding angles are congruent to.
When a transversal crosses parallel lines corresponding angles are congruent.
What are corresponding angles?
Two lines are parallel if and only if the two angles of any pair of transversal corresponding angles are congruent (equal in measure). Proposition 1.28 of Euclid's Elements, an absolute geometry theorem (therefore true in both hyperbolic and Euclidean Geometry), demonstrates that if the angles of two transversals are corresponding, the two lines are parallel (non-intersecting). According to Euclid's parallel postulate, if two lines are parallel, the angles of a pair of corresponding angles are congruent (Proposition 1.29 of Euclid's Elements). If the angles of one pair of related angles are congruent, the angles of the remaining pairs are likewise congruent.
The correct option is (D) When a transversal crosses parallel lines corresponding angles are congruent.
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You are one of five people who have been hired to mow the lawn at the local college . Each week, the dimensions of the plot you are responsible to mow changes. The college conducts a lottery, and whichever number is drawn, represents the value. Your plot has a length which is five more than two times and the width is three less than three times x.
A.) What are the dimensions of your mowing plot ? Length : Width :
B.) What is the area of your plot (area=length x width)? Show all steps.
Area:
C.) if x=13 meters , how many square meters is your plot? Area:
An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products.
What is meant by factored form?An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products. A factored form can represent any logic function, and every factored form represents some logic function.
1a)The length given as words is "3 more than 7 times x"
The width given as words is "4 times x minus 2"
The expression for length would be 7x + 3
The expression for width would be 4x - 2
1b)Area = length × width
To estimate the algebraic expressions for length and width
Area = (7x + 3)(4x - 2) = 28x² - 14x + 12x - 6 = 28x² - 2x - 6
Area = 28x² - 2x - 6
Given x = 10,
Let the equation be 28 x² - 2x - 6
substitute the value of x, in the above equation, we get
= 28(10)² - 2(10) - 6
= 2774
Area = 2774 sq . m
2. We can group the first two terms and next two terms:
xy - 4y + 7x - 28 = (xy - 4y) + (7x - 28)
simplifying the above equation, we get
y(x - 4) + 7(x - 4) = (x - 4)(y + 7)
Therefore, the equation is in factored form.
The complete question is:
1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow change. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length that is three more than seven times x and the width is four times x minus 2.a.) What are the dimensions of your mowing plot? (2 points)
Length: ______________________________________
Width: ______________________________________
b.) What is the area of your plot (remember area = length x width)? (2 points)
Area: _________________________________________
c.) If x = 10 meters, how many square meters is your plot? (show steps)(2 points)
Area: _________________________________________
2.) Factor by grouping: (4 points)
xy − 4y + 7x − 28
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Can someone help me solve this please ? I’m having a really hard time solving it
The features of the triangle are summarized below:
AC = √7 + √6 AB² = AC² = 13 + 2√42, BC² = 13 + 2√42.There is 45-45-90 right triangle as BC = √2 · AB = √2 · AC. The triangle has an area of approximately 12.980 square units.How to analyze a given triangle based on its sides
In this problem we find the case of a triangle whose three sides (AB, AC, BC) are known. First, we rationalize the expression for AC, that is, eliminate the irrational denominator by algebraic means:
AC = 1 / (√7 - √6)
AC = [1 / (√7 - √6)] · [(√7 + √6) / (√7 + √6)]
AC = (√7 + √6) / [(√7 - √6) · (√7 + √6)]
AC = (√7 + √6) / (7 - 6)
AC = √7 + √6
Second, we determine the square of each side:
AB² = (√7 + √6)²
AB² = 7 + 2√42 + 6
AB² = 13 + 2√42
AC² = (√7 + √6)
AC² = 13 + 2√42
BC² = (√14 + 2√3)²
BC² = 14 + 4√42 + 12
BC² = 26 + 4√42
BC² = 2 · (13 + 2√42)
BC² = 2 · AB² = 2 · AC²
Third, deduce the nature of the triangle:
Since BC = √2 · AB = √2 · AC, then the triangle ABC is a right triangle with internal angles 45° - 45° - 90°.
Fourth, calculate the area of the triangle by Heron's formula:
s = 0.5 · (AB + AC + BC)
s = 0.5 · (√7 + √6 + √7 + √6 + √14 + 2√3)
s = 0.5 · (2√7 + 2√6 + √14 + 2√3)
s = √7 + √6 + 0.5√14 + √3
A = √[s · (s - AB) · (s - AC) · (s - BC)]
A = √[(√7 + √6 + 0.5√14 + √3) · (√7 + √6 + 0.5√14 + √3 - √7 - √6) · (√7 + √6 + 0.5√14 + √3 - √7 - √6) · (√7 + √6 + 0.5√14 + √3 - √14 - 2√3)]
A = √[(√7 + √6 + 0.5√14 + √3) · (0.5√14 + √3) · (0.5√14 + √3) · (√7 + √6 - 0.5√14 - √3)]
A = √[8.698 · (8.698 - 5.095) · (8.698 - 5.095) · (8.698 - 7.206)]
A = √(8.698 · 3.603² · 1.492)
A ≈ 12.980
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solve for missing length, round to nearest if necessary. (check if all of these are correct) if it’s not correct say the number and the answer
Answer:
2. 14.42
3. 17.69
6. 12.8
9. 10.29 (I cant see your answer)
Rest is correct ;D
Step-by-step explanation:
x² - 6 = 54
I don’t understand
Answer:x squared = 60
Step-by-step explanation:
x2-6=54, first you have to cancel out the 6 on the left side by adding 6 to -6 after doing that you are left with
x2-(-6+6)=54
but since you did +6 on the right side you have to do +6 on the left so after that you are left with
x2=54+6
now you just do 54+6=60 so after all of that you get
x2=60
(you can use a calculator to find the square root of 60)
Classify the following numbers as rational
or irrational.
3.1415926535... 0 V1 7.4 15 V3
pls helpp
Answer: 2.5.02
Step-by-step explanation:
What is the name of the line of reflection for the pair of figures?
Enter your answer in the box.
line
Answer: r
Step-by-step explanation:
The figures are symmetrical about line r.
A pancakes recipe needs 6 eggs to make 16 servings. If Ms. Moon wants to make a pancakes that serves 24 people, how many eggs will she need?
The table of paired values represents a proportional relationship.
x 1 3 6 7
y 4 y 24 28
What is the missing y-value in the table?
Responses
8
8
12
12
16
16
I don't know.
I don't know.
Answer:
12
Step-by-step explanation:
because you can see that in the first column, the y value is 4 times the x value
and in the third column, the y value is still 4 times greater than the x value
meaning that you need to find a number that is 4 times the value of 3 (because that is the x value)
3 times 4 is 12
What is the equivalent fraction?
I think the answers are 2/3 and 1/3
Answer the 2 question in the photo ( easy points + brainliest )
Answer:
I think the first number is 45 and the second number is 81.
Step-by-step explanation:
45 > 42 but 45 < 55 81 > 80 but 81 < 89
The school mary goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 7 senior citizen tickets and 6 students tickets of $69. The school took in $53 on the second day by selling 7 senior citizen tickets and 4 student tickets. find the price of one senior citizen ticket an the price of one child ticket
The price of one senior citizen ticket is $8 and that of a child ticket is $3.
Let the price of one senior citizen ticket be x
and the price of one student ticket be y
Thus, for the first day, we can make the following equation-
7x + 6y = 69
and similarly, we can make an equation for the second day as-
7x + 4y = 53
Now, we can solve these two linear equations to find the value of x and y.
Subtracting equation 2 from 1 we get-
(7x + 6y) - (7x + 4y) = 69 - 53
7x - 7x + 6y - 4y = 16
6y - 4y = 16
2y = 16
y = 16/2
y = 8
Substituting the value of y in any of the two equations we can find the value of x-
7x + 6(8) = 69
7x = 69 - 48
x = 21/7
x = 3
Thus, the price of one senior citizen ticket is $8 and that of a child ticket is $3.
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Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5.
A. 24 = 10.5 + 4.5m; m = 60.75
B. 24 = 10.5 + 4.5m; m = 3
C. 24 equals 10.5 plus m over 4.5; m = 3
D. 24 equals 10.5 plus m over 4.5; m = 60.75
What is the least common multiple of 15, 45, and 37?
Answer: 1665
Step-by-step explanation:
Prime factorization of the numbers:
15 = 3 × 5
45 = 3 × 3 × 5
37 = 37
LCM(15, 45, 37)
= 3 × 3 × 5 × 37
= 1665
Hope this helps!
Jeffrey invests $500 every month and earns interest at a rate of 12% p.a, compounded monthly.
a. Jeffrey wants to buy a car worth $41000 after five years. Can he afford it? If not, how much does he need? (2.d.p)
b. How much is the fund worth after 20 years? (2.d.p)
c. How much interest did he earn over 20 years? (2.d.p)
a) Jeffrey needs an extra amount of $40,357.5 for buying a car.
b) After 20 years fund is worth $1364.
c) After 20 years $1200 interest had been earned.
a) P = $500
r = 12% = 12 ÷ 100 = 0.12
n = 12 because it was compounded 12 times in a year.
t = 5 years
Therefore,
A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]
A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]
A = 500 × 1.285
A = $ 642.5
Jeffrey needs an extra $40,357.5 for buying a car.
b) P = $500
r = 12% = 12 ÷ 100 = 0.12
n = 12 because it was compounded 12 times in a year.
t = 20 years
Therefore,
A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]
A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]
A = 500 × 2.728
A = $1364
After 20 years fund is worth $1364.
c) Simple interest = P × R × T ÷ 100
Simple interest = 500 × 12 × 20 ÷ 100
Simple interest = $1200
After 20 years $1200 interest had been earned.
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ded Assignment
A truck can carry a load of 6000 lb. Assuming that it could be cut to fit, how many feet of steel beam weighing 32.9 lb/ft (pounds per foot) can the truck carry?
The truck can carry feet of steel bearn weighing 32.9 lb/ft
(Round to the nearest hundredth as needed.)
The number of steel beam the truck can carry given the truck's capacity is 182.37.
How many steel beams can the truck carry?In order to determine the number of steel beam the truck can carry divide the capacity of the truck by the weight of each steel beam.
Division is the mathematical operation that is used to group a number into equal parts using another number. The sign used to denote division is ÷. Other operations used in mathematics are addition, subtraction and multiplication.
Number of steel beams the truck can carry = capacity of the truck / number of steel beams
6,000 / 32.9 = 182.37
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A rectangle has length 8*10^4 mm and width 4*10^4 mm. The rectangle's length is how many times its width?
Answer:
The rectangles length is 2 times as much as its width.
Step-by-step explanation:
8 x 10⁴ = 80,000
4 x 10⁴ = 40,000
40,000 x 2 = 80,000
cost for babysitting services
Answer:
$14.82/hr
It depends on where you are though.
The midpoint of line segment AB is M(3,-1). If the coordinates of A(8,4), what are the coordinates of B?
The coordinate B are (-2, -6)
Given that, the coordinates of the midpoint of line segment AB are (3,-1). Also, coordinates of A are (8,4).
Let the coordinates of B be (a,b)
We know that,
Midpoint of two points (x1,y1) and (x2,y2) is calculated by the formula
[tex]\frac{x1+x2}{2} ,\frac{y1+y2}{2}[/tex]
Hence, midpoint of AB= [tex]\frac{8+a}{2} ,\frac{4+b}2}[/tex] = (3,-1)
[tex]\frac{8+a}{2}= 3 ,\frac{4+b}2} = -1[/tex]
8+a = 6, 4+b= -2
a = -2 b = -6
Hence the coordinate B are (-2, -6)
What do you mean by midpoint?In geometry, a centroid is the mid point of a segment. It is equidistant from both endpoints and is the mid point of both the segment and the endpoints. This divides the segment into two.
mid point can be calculated by [tex]\frac{A+B}{2}[/tex]
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OF THE STUDENTS IN KAREN'S CLASS, 4/5 OF THEM OWN A BIRD. OF THE STUDENTS WHO OWN A BIRD, 1/2 ALSO OWN A HAMSTER. WHAT FRACTION OF THE STUDENTS IN KAREN'S CLASS OWN A BIRD AND A HAMSTER?
Answer:
the fraction is 2/5
Step-by-step explanation:
4/5 + 1/2
=2/5
Melissa rented a Segway, a stand up scooter, in downtown Austin, Tx. The store charges a $3.25 initial charge plus $2.50 per mile. Which equation can be used to find y, the total cost of the rental, if x represents the number of miles Melissa rode on the Segway?
Answer:
y = 2.50× + 3.25
Step-by-step explanation:
For example if Melissa rode 8 miles:
y = 2.50(8) + 3.25
y = 20.00 + 3.25
y = $23.25
How do you Make Seven an even number?
Just take off the "S" from Seven.
"Even" is formed.
How to make Seven an even number?Just take the "S" out of Seven. It becomes "even."
An even number is one that divides by two and leaves a 0 as the final result.
2, 4, 6, 8, 10, and other even numbers are examples.
To really make 7 an even number, add 1.
7 + 1 = 8
It becomes 8, which is even.
Another way to make it even is to subtract 1.
7 - 1 = 6
It becomes 6, which is even.
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Tony went on holiday to Canada.
His flights cost a total of £1600
Tony stayed for 12 nights.
His hotel cost $184 per night.
Tony used wifi for 9 days.
Wifi cost $6 per day.
Tony took a taxi 6 times costing a mean average of $27 per taxi journey.
The exchange rate was $1.83 to £1
Work out the total cost of the flights, the hotel room, the wifi and 6 taxi journeys.
Give your answer in pounds.
Answer:
Step-by-step explanation:
(12 nights)($184) = $2208
(9 nights)($6) = $54
(6 taxi rides)($27) = $162
$2208 + $54 + $162 = $2424
We will use a ratio to calculate American dollars to pounds
2424/x = 1.83/1
Cross multiply
1.83x=2424
Divide
= ~£1324.59
£1324.59 + £1600 = £2924.59
The answer is ~2924.59 pounds
The total cost of the flights, the hotel room, the wifi, and 6 taxi journeys for Tony's holiday in Canada is approximately £2925.13.
Given that Tony is vacationing in Canada, his flight cost is £1600, he stayed for 12 nights, his hotel cost $184 per night, Tony used wifi for 9 days. Wifi cost $6 per day. Tony took a taxi 6 times costing a mean average of $27 per taxi journey.
The exchange rate was $1.83 to £1.
We need to find the total cost his spend in the vacation.
To calculate the total cost of Tony's holiday, we need to convert all the expenses to pounds and then sum them up.
Flights cost: £1600
Hotel cost per night: $184
Hotel cost for 12 nights: 12 nights x $184/night = $2208
Wifi cost per day: $6
Wifi cost for 9 days: 9 days x $6/day = $54
Taxi cost per journey (mean average): $27
Total taxi cost for 6 journeys: 6 journeys x $27/journey = $162
Now, we need to convert the costs from dollars to pounds using the exchange rate of $1.83 to £1.
Flights cost in pounds: £1600
Hotel cost in pounds: $2208 / $1.83 = £1207.10
Wifi cost in pounds: $54 / $1.83 = £29.51
Taxi cost in pounds: $162 / $1.83 = £88.52
Finally, we can calculate the total cost in pounds:
Total cost = Flights cost + Hotel cost + Wifi cost + Taxi cost
Total cost = £1600 + £1207.10 + £29.51 + £88.52
Total cost = £2925.13
So, the total cost for Tony's holiday in Canada is approximately £2925.13.
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|−4| Choose... equal to |4|. |−4| is the distance from −4 to Choose... on a number line.
the height of a is approximately normally distributed. duncan and shane are duncan is 32.0 inches tall and is at the 32nd percentile of the distribution which is closest to the mean
Duncan's height is the closest to the mean for the given normal distribution.
What is termed as the normal distribution?The normal distribution, also recognized as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.The probability density function for just a continuous random variable in such a system defines the Normal Distribution. Assume that f(x) is the probability density function as well as X is a random variable.We learn from the question that
Given that 3-year-old boys' heights are roughly normally distributed, the mean will be the 50th.
Thus, comparing Duncan's height in the 32th percentile and Shane's height in the 62nd percentile with the mean height in the percentile 50.
i.e
50 - 32 = 18
and
62 - 50 = 12
Duncan's height is the closest to the mean.
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The complete question is -
The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3 year old boys. Duncan is 32.0 inches tall and is in the 32nd percentile. Shane is 34.0 inches tall and is at the 62nd percentile. Which is the closest to the mean
Can 6 1/5 be turned into a decimal
Answer: Yes, 6.20
Step-by-step explanation:
1/5 is equal to 0.20, so 6 1/5 equals 6.20
Find real x and y such that:
(x+yi)^2=x-yi
NEED HELP NOW PLEASE
Answer:
y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))
x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))
Step-by-step explanation:
Solve for y:
(x + (0 + i) y)^2 = x + (0 - i) y
Subtract -i y + x from both sides:
-x + (i y + x)^2 + i y = 0
Expand and collect in terms of y:
-x + x^2 + y (2 i x + i) - y^2 = 0
Multiply both sides by -1:
x - x^2 + y (-2 i x - i) + y^2 = 0
Subtract -x^2 + x from both sides:
y (-2 i x - i) + y^2 = x^2 - x
Add 1/4 (-2 i x - i)^2 to both sides:
1/4 (-2 i x - i)^2 + y (-2 i x - i) + y^2 = 1/4 (-2 i x - i)^2 - x + x^2
Write the left hand side as a square:
(1/2 (-2 i x - i) + y)^2 = 1/4 (-2 i x - i)^2 - x + x^2
Take the square root of both sides:
1/2 (-2 i x - i) + y = sqrt(1/4 (-2 i x - i)^2 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)
Subtract 1/2 (-2 i x - i) from both sides:
y = 1/2 (2 i x + i) + sqrt((((-2 i) x - i)^2)/4 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)
1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:
y = 1/2 (2 i x + i) + sqrt((-2 x - 1/4)) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)
Subtract 1/2 (-2 i x - i) from both sides:
y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((((-2 i) x - i)^2)/4 - x + x^2)
1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:
Answer: y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))
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Solve for x:
(x + (0 + i) y)^2 = x + (0 - i) y
Subtract -i y + x from both sides:
-x + (i y + x)^2 + i y = 0
Expand and collect in terms of x:
x^2 + x (2 i y - 1) + i y - y^2 = 0
Subtract -y^2 + i y from both sides:
x^2 + x (2 i y - 1) = y^2 - i y
Add 1/4 (2 i y - 1)^2 to both sides:
x^2 + x (2 i y - 1) + 1/4 (2 i y - 1)^2 = 1/4 (2 i y - 1)^2 - i y + y^2
Write the left hand side as a square:
(x + 1/2 (2 i y - 1))^2 = 1/4 (2 i y - 1)^2 - i y + y^2
Take the square root of both sides:
x + 1/2 (2 i y - 1) = sqrt(1/4 (2 i y - 1)^2 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)
Subtract 1/2 (2 i y - 1) from both sides:
x = 1/2 (-2 i y + 1) + sqrt((((2 i) y - 1)^2)/4 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)
1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:
x = 1/2 (-2 i y + 1) + sqrt(((-2 i) y + 1/4)) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)
Subtract 1/2 (2 i y - 1) from both sides:
x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((2 i y - 1)^2)/4 - i y + y^2)
1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:
Answer: x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))
Answer:
Step-by-step explanation: