Find the real part and the imaginary part of the following complex number. (sqrt(6) - sqrt(6i))/4
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
(√6 - √6i) / 4
Step 02:
complex numbers:
[tex]\frac{\sqrt{6}-\sqrt{6}i}{4}=\frac{\sqrt{6}}{4}-\frac{\sqrt{6}i}{4}[/tex]real part:
√6 / 4
imaginary part:
- √6i / 4
That is the full solution.
Related Questions
how long will it take for $2700 to grow to $24500 at an interest rate of 2.2% if the interest is compounded quarterly? Round to the nearest hundredth.
Answers
Let n be the number of quarterlies.
Then
[tex]\begin{gathered} 24500=2700(1+0.022)^n \\ \Rightarrow1.022^n=\frac{245}{27} \\ \Rightarrow n=\frac{\log _{10}\frac{245}{27}}{\log _{10}1.022} \end{gathered}[/tex]Hence the number of months = 3n = 304.04 months
and the number of years = n / 4 = 25.34 years
What is the equation in slope-intercept form of the line that passes through the points (-4,8) and (12,4)?
Answers
ANSWER
y = -0.25 + 7
EXPLANATION
The line passes through the points (-4, 8) and (12, 4).
The slope-intercept form of a linear equation is written as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope of the line.
We do that with formula:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{where (x}_1,y_1)\text{ = (-4, 8) } \\ (x_2,y_2)\text{ = (12, 4)} \end{gathered}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m\text{ = }\frac{4\text{ - 8}}{12\text{ - (-4)}}\text{ = }\frac{-4}{12\text{ + 4}}\text{ = }\frac{-4}{16}\text{ = }\frac{-1}{4} \\ m\text{ = -0.25} \end{gathered}[/tex]Now, we use the point-slope method to find the equation:
[tex]\begin{gathered} y-y_{1\text{ }}=m(x-x_1) \\ \Rightarrow\text{ y - 8 = -0.25(x - (-4))} \\ y\text{ - 8 = -0.25(x + 4)} \\ y\text{ - 8 = -0.25x - 1} \\ y\text{ = -0.25x - 1 + 8} \\ y\text{ = -0.25x + 7} \end{gathered}[/tex]That is the equation of the line. It is not among the options.
what is the better buy 4GB flash drive for $8 2 GB for $6 or 8 GB for $13
Answers
In order to find out which of the options would be better to buy we would have to calculate the better unit price that eacho of the following options offer.
So, unit price for the offers would be:
For 4GB flash drive for $8, unit price=$8/4
unit price=$2
For 2 GB for $6, unit price=$6/2=$3
For 8 GB for $13, unit prince=$13/8=$1.625
Therefore, as the unit price of 8 GB for $13 is the lower one, then the better choice to buy would be 8 GB for $13
The floor of a shed has an area of 80 square feet. The floor is in the shape of a rectangle whose length is 6 feet less than twice the width. Find the length and the width of the floor of the shed. use the formula, area= length× width The width of the floor of the shed is____ ft.
Answers
Given:
The area of the rectangular floor is, A = 8- square feet.
The length of the rectangular floor is 6 feet less than twice the width.
The objective is to find the measure of length and breadth of the floor.
Consider the width of the rectangular floor as w, then twice the width is 2w.
Since, the length is given as 6 feet less than twice the width. The length can be represented as,
[tex]l=2w-6[/tex]The general formula of area of a rectangle is,
[tex]A=l\times w[/tex]By substituting the values of length l and width w, we get,
[tex]\begin{gathered} 80=(2w-6)\times w \\ 80=2w^2-6w \\ 2w^2-6w-80=0 \end{gathered}[/tex]On factorizinng the above equation,
[tex]\begin{gathered} 2w^2-16w+10w-80=0 \\ 2w(w-8)+10(w-8)=0 \\ (2w+10)(w-8)=0 \end{gathered}[/tex]On solving the above equation,
[tex]\begin{gathered} 2w+10=0 \\ 2w=-10 \\ w=\frac{-10}{2} \\ w=-5 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} w-8=0 \\ w=8 \end{gathered}[/tex]Since, the magnitude of a side cannot be negative. So take the value of width of the rectangle as 8 feet.
Substitute the value of w in area formula to find length l.
[tex]\begin{gathered} A=l\times w \\ 80=l\times8 \\ l=\frac{80}{8} \\ l=10\text{ f}eet. \end{gathered}[/tex]Hence, the width of the floor of the shed is 8 ft.
Transform y f(x) by translating it right 2 units. Label the new functiong(x). Compare the coordinates of the corresponding points that makeup the 2 functions. Which coordinate changes. x or y?
Answers
If we translate y = f(x) 2 units to the right, we would have to sum and get g(x) =f(x+2).
That means the x-coordinates of g(x) are going to have 2 extra units than f(x).
[tex](x,y)\rightarrow(x+2,y)[/tex]Therefore, with the given transformation (2 units rightwards) the function changes its x-coordinates.Miguel made $17.15 profit from selling 7 custom t-shirts through a website. Miguel knows the total profit he earns is proportional to the number of shirts he sells, and he wants to create an equation which models this relationship so that he can predict the total profit from selling any number of t-shirts.
Answers
Let:
[tex]\begin{gathered} P(x)=\text{profit} \\ k=\text{price of each t-shirt} \\ x=\text{Number of t-shirts sold} \end{gathered}[/tex]Miguel made $17.15 profit from selling 7 custom t-shirts, therefore:
[tex]\begin{gathered} P(7)=17.15=k(7) \\ 17.15=7k \\ \text{Solving for k:} \\ k=\frac{17.15}{7}=2.45 \end{gathered}[/tex]Therefore, the equation that models this relationship is:
[tex]P(x)=2.45x[/tex]Write the following number as a fraction:
0.27
Answers
Step-by-step explanation:
27/100 is the fraction of 0.27
What is the value of x? Enter your answer in the box. x =
Answers
The value of x from the given isosceles triangle is 8 units.
The measures of sides of triangle are given AB=4x-10, AC=5x-22 and BC=3x+2.
What is an isosceles triangle?Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.
Here, AC = BC
⇒ 5x-22 = 3x+2
⇒ 5x-3x = 22+2
⇒ 3x = 24
⇒ x = 8 units
Therefore, the value of x from the given isosceles triangle is 8 units.
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Can you explain this math to me please I’ve never seen it before and don’t understand
Answers
For a quadratic function in standard form,
[tex]\begin{gathered} \text{a = coefficient of x}^2 \\ b\text{ = coeffcient of x} \\ c=\text{ the constant term} \end{gathered}[/tex]For the polynomial f(x),
a = 2, b = -3 and c = 4
For the polynomial g(x)
a = 4, b = -6, c = 10
For the polunomial h(x),
a = 7, b = 0, c = 8
For the polynomia p(x),
a = 1, b = -10, c = 0
To the function attached,Is f(x) continuous at x=1? Please explain
Answers
Recall that a function is continuous at a point if the limit as the variable approaches a value is the same as the value of the function at that point.
Now, notice that, using the definition of the function:
[tex]\begin{gathered} \lim_{x\to1^+}f(x)=\sqrt{1}+2=3, \\ \lim_{x\to1^-}f(x)=3, \end{gathered}[/tex]therefore:
[tex]\lim_{x\to1}f(x)=3.[/tex]Given that the limit and the value of the function at x=1 are equal, the function is continuous at x=1.
Answer: It is continuous at x=1.
b. Function h will begin to exceed f and g around x = [. (Round up to the nearest whole number.)
Answers
If we evaluate x = 10 on all the functions, we have:
[tex]\begin{gathered} h(10)=1.31^{10}=14.88 \\ f(10)=1.25(10)=12.5 \\ g(10)=0.1562(10)^2=15.625 \end{gathered}[/tex]and then, evaluating x = 11, we get:
[tex]\begin{gathered} h(11)=1.13^{11}=19.49 \\ f(11)=1.25(11)=13.75 \\ g(11)=0.15625(11)^2=18.9 \end{gathered}[/tex]notice that on x = 10, h(x) does not exceed g(x), but on x = 11, h(x) exceeds the other functions. Therefore, h will begin exceed f and g around 11
the population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the pop ulation in 30 years? how fast is the population growing at t 30?
Answers
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.A differential equation is one that has one or more functions and their derivatives. The derivatives of a function define how quickly it changes at a given location. It is frequently used in disciplines including physics, engineering, biology, and others.The population P after t years obeys the differential equation:
dP / dt = kPWhere P(0) = 500 is the initial condition and k is a positive constant.
∫ 1/P dP = ∫ kdtln |P| = kt + C|P| = e^ce^ktUsing P(0) = 500 gives 500 = Ae⁰.
A = 500.Thus, P = 500e^ktFurthermore,
P(10) = 500 × 115% = 575sO575 = 500e^10ke^10k = 1.1510 k = ln (1.15)k = In(1.15)/10 ≈ 0.0140Therefore, P = 500e^0.014t.The population after 30 years is:
P = 500e^0.014(30) = 760.44Therefore, using the differential equation, the population after 30 years is 760.44.
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Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.45. See the figure below.
If the monthly cost for 22 HCF is $45.78, what is the monthly cost for 19 HCF?
Answers
Using a linear function, it is found that the monthly cost for 19 HCF is of $41.43.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the parameters of the function are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the value of y when the function crosses the y-axis(x = 0).As stated in the problem, the slope is of 1.45, hence:
y = 1.45x + b.
The monthly cost for 22 HCF is $45.78, hence when x = 22, y = 45.78, meaning that the intercept b can be found as follows:
45.78 = 1.45(22) + b
b = 45.78 - 1.45 x 22
b = 13.88.
Then the function is:
y = 1.45x + 13.88.
And the cost for 19 HCF is given by:
y = 1.45(19) + 13.88 = $41.43.
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Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.A) Create an equation to represent their total earnings in each situation. Explain what each of the variables represent.
Answers
Given:-
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.
To find:-
An equation to represent their total earnings in each situation.
Find the y-intercept of the line represented by the equation: -5x+3y=30
Answers
We need to find the y-intercept of the equation.
For this, we need to use the slope-intercept form:
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
Now, to get the form, we need to solve the equation for y:
Then:
[tex]-5x+3y=30[/tex]Solving for y:
Add both sides 5x:
[tex]-5x+5x+3y=30+5x[/tex][tex]3y=30+5x[/tex]Divide both sides by 3
[tex]\frac{3y}{3}=\frac{30+5x}{3}[/tex][tex]\frac{3y}{3}=\frac{30}{3}+\frac{5x}{3}[/tex][tex]y=10+\frac{5}{3}x[/tex]We can rewrite the expression as:
[tex]y=\frac{5}{3}x+10[/tex]Where 5/3x represents the slope and 10 represents the y-intercept.
The y-intercept represents when the graph of the equations intersects with the y-axis, therefore, it can be written as the ordered pair (0,10).
The length of a rectangle is 2 inches more than its width.If P represents the perimeter of the rectangle, then its width is:oAB.O4Ос. РOD.P-2 별O E, PA
Answers
Given:
a.) The length of a rectangle is 2 inches more than its width.
Since the length of a rectangle is 2 inches more than its width, we can say that,
Width = W
Length = L = W + 2
Determine the width with respect to its Perimeter, we get:
[tex]\text{ Perimeter = P}[/tex][tex]\text{ P = 2W + 2L}[/tex][tex]\text{ P = 2W + 2(W + 2)}[/tex][tex]\text{ P = 2W + 2W + }4[/tex][tex]\text{ P = 4W + }4[/tex][tex]\text{ P - 4 = 4W}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = }\frac{\text{4W}}{4}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = W}[/tex]Therefore, the answer is D.
A yogurt stand gave out 200 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 115 people tasted the vanilla and 137 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?
Answers
So we are to find x
[tex]137-x+x+115-x=200[/tex][tex]\begin{gathered} 137+115-x=200 \\ 252-x=200 \\ -x=200-252 \\ -x=-52 \\ x=52 \end{gathered}[/tex]The final answer52 people chose chocolate and vanilla twistDalia works mowing lawns and babysitting. She earns $8.40 an hour for mowing and $7.90 an hour for babysitting . How much will ahe earn for 7 hours of mowing and 1 hour of babysitting?
Answers
Given that she earns $8.40 an hour for mowing then for 7 hours of mowing, the amount earned
= 7 * $8.40
=$58.80
Furthermore, given that she earns $7.90 for baby sitting for an hour
Hence for mowing for 7 hours and baby sitting for 1 hour, the total amount she will earn
= $58.80 + $7.90
= $66.70
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After
driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads
23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
I need helppp with example pliss
Answers
Answer:
15.6 MPG
Step-by-step explanation:
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads 23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
You went 23,927 - 23,672 = 255 miles
Because you started on a full tank, you went 255 miles on 16.5 gallons
to figure MPG:
255/16.5 = 15.4545... MPG
rounded to nearest 10th of gallon:
15.6 MPG
1 pts
4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
A: neither
B: perpendicular
C: parallel
Answers
Answer:
B
Step-by-step explanation:
[tex]m_{\overline{AB}}=\frac{4-0}{-2-2}=-1 \\ \\ m_{\overline{CD}}=\frac{-2-4}{-3-3}=1 [/tex]
Since the slopes are negative reciprocals of each other, and since they intersect, they are parallel.
Determine whether a tangent line is shown in this figure
Answers
Given:
Required:
To determine whether a tangent line is shown in the given figure.
Explanation:
By the definition of tangent line, we know that tangent line is a straight line that touches the circle at one point.
Now consider the given figure, there is a tangent line in the given figure.
Final Answer:
Yes.
Determine the required value of a missing probability to make the distribution a discrete probability distribution… p(4) =
Answers
The table given showed the discrete probability distribution for random variables 3 to 6 and their corresponding probability except for the probability of 4
It should be noted that for a probability distribution, the cummulative probabibility (that is the sum of all the probability) must be equal to one.
This means that
[tex]P(3)+P(4)+P(5)+P(6)=1[/tex]From the given table, it can be seen that
[tex]\begin{gathered} P(3)=0.32 \\ P(4)=\text{?} \\ P(5)=0.17 \\ P(6)=0.26 \end{gathered}[/tex]Then, p(4) is calculated below
[tex]\begin{gathered} P(3)+P(4)+P(5)+P(6)=1 \\ 0.32+P(4)+0.17+0.26=1 \\ P(4)+0.32+0.17+0.26=1_{} \\ P(4)+0.75=1 \\ P(4)=1-0.75 \\ P(4)=0.25 \end{gathered}[/tex]Hence, P(4) is 0.25
currently, Yamir is twice as old as pato. in three years, the sum of their ages will be 30. if pathos current age is represented by a, what equation correctly solves for a?
Answers
The given situation can be written in an algebraic way.
If pathos age is a, and Yamir age is b. You have:
Yamir is twice as old as pato:
b = 2a
in three years, the sum of their ages will be 30:
(b + 3) + (a + 3) = 30
replace the b = 2a into the last equation, and solve for a, just as follow:
2a + 3 + a + 3 = 30 simplify like terms left side
3a + 6 = 30 subtract 6 both sides
3a = 30 - 6
3a = 24 divide by 3 both sides
a = 24/3
a = 8
Hence, the age of Pato is 8 years old.
In how many ways can the letters in the word PAYMENT be arranged using 4 letters?A. 42B. 840C. 2520D. 1260
Answers
The word PAYMENT has 7 letters. They can be arranged in groups of 4 like shown below:
PYNT, TA
I wondered if you could teach me how to do this so I can do these problems independently.
Answers
Answer
a)
A' (-2, 6)
B' (7, 3)
C' (4, 0)
b)
D' (3, 3)
E' (-5, 0)
F' (2, 2)
c)
G' (3, 1)
H' (0, 4)
P' (-2, -3)
Explanation
For the coordinate (x, y)
A transformation to the right adds that number of units to the x-coordinate.
A transformation to the left subtracts that number of units from the x-coordinate.
A transformation up adds that number of units to the y-coordinate.
A transformation down subtracts that number of units from the y-coordinate.
For this question,
a) The coordinates are translated to the right by 4 units and upwards by 1 unit
That is,
(x, y) = (x + 4, y + 1)
A (-6, 5) = A' (-6 + 4, 5 + 1) = A' (-2, 6)
B (3, 2) = B' (3 + 4, 2 + 1) = B' (7, 3)
C (0, -1) = C' (0 + 4, -1 + 1) = C' (4, 0)
When a given point with coordinates P (x, y) is reflected over the y-axis, the y-coordinate remains the same and the x-coordinate takes up a negative in front of it. That is, P (x, y) changes after being reflected across the y-axis in this way
P (x, y) = P' (-x, y)
For this question,
b) The coordinates are reflected over the y-axis
D (-3, 3) = D' (3, 3)
E (5, 0) = E' (-5, 0)
F (-2, 2) = F' (2, 2)
In transforming a point (x, y) by rotating it 90 degrees clockwise, the new coordinates are given as (y, -x). That is, we change the coordinates and then add minus to the x, which is now the y-coordinate.
P (x, y) = P' (y, -x)
For this question,
c) The coordinates are rotated about (0, 0) 90 degrees clockwise.
G (-1, 3) = G' (3, 1)
H (-4, 0) = H' (0, 4)
I (3, -2) = P' (-2, -3)
Hope this Helps!!!
Hi, I need help on this. the sentence says Write the Numbers that represent each Expression
Answers
H = 1, P =2, R = 3 B = -1, C = -2, A = -3, Q = -5
Explanation:
For the first number line:
From the tick mark to the tick mark with 4, there are 4 tick marks
Distance from 0 to 4 = 4 - 0 = 4
Each tick mark = 4/4 tick marks
Each tick mark = 1
This means each tick mark increases by 1 to the right after 0 and decreases by one to the left before zero.
H, P and R are after 0
H = 0 + 1 = 1
P = 1 + 1 = 2
R = 2 + 1 = 3
B, C, A and Q are all before 0
B = 0 - 1 = -1
C = -1 - 1 = -2
A = -2 - 1 = -3
Q = -4 - 1 = -5
For the 2nd number line:
from 0 to 100, there 5 tick marks
Distance from 0 to 100 = 100 - 0 = 100
Each tick mark = 100/5 tick marks
Each tick mark = 20
This means each tick mark after zero increases by 20 to the right and decreases to the before 0 by 20.
A, L and M are after zero
Number before A is 20, increasing the number by 20
A = 20 + 20 = 40
L = 40 + 20 = 60
M = 60 + 20 = 80
J, P, T, V are before zero
Number before J = 0, decreasing by 20
J = 0 - 20 = -20
P = -20 - 20 = -40
T = -40 - 20 = -60
V = -60 - 20 = -80
There are 3 consecutive even integers that have a sum of 6. What is the value of the least integer?
Answers
We can express this question as follows:
[tex]n+(n+2)+(n+4)=6[/tex]Now, we can sum the like terms (n's) and the integers in the previous expression. Then, we have:
[tex](n+n+n)+(2+4)=6=3n+6\Rightarrow3n+6=6[/tex]Then, to solve the equation for n, we need to subtract 6 to both sides of the equation, and then divide by 3 to both sides too:
[tex]3n+6-6=6-6\Rightarrow3n=0\Rightarrow n=\frac{3}{3}n=\frac{0}{3}\Rightarrow n=0_{}[/tex]Then, we have that the three consecutive even integers are:
[tex]0+2+4=6[/tex]Therefore, the least integer is 0.
6. A line goes through these two points, (-4, -1) anti (-9,-5).A. Find an equation for this line in point slope form.B. Find the equation for this line in slope intercept form. Be sure to show your work.C. If the y-coordinate of a point on this line is 7, what is the x-coordinate of this point?
Answers
A. In order to find the equation, first we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]m is the slope
(-4, -1)=(x1,y1)
(-9,-5)=(x2,y2)
we substitute the values
[tex]m=\frac{-5+1}{-9+4}=\frac{-4}{-5}=\frac{4}{5}[/tex]then we use the point-slope form
[tex]y-y_1=m(x-x_1)[/tex]we substitute the values
[tex]y+1=\frac{4}{5}(x+4)[/tex]B. in order to find the slope-intercept form we need to isolate the y
[tex]y=\frac{4}{5}x+\frac{11}{5}[/tex]C. if the y coordinate is 7
[tex]7=\frac{4}{5}(x)+\frac{11}{5}[/tex]then we isolate the x
[tex]\frac{4}{5}x=7-\frac{11}{5}[/tex][tex]\begin{gathered} \frac{4}{5}x=\frac{24}{5} \\ x=\frac{5\cdot24}{5\cdot4} \\ x=6 \end{gathered}[/tex]the value of the x-coordinate is 6 when the y-coordinate is 7
5. Joseph Cheyenne is earning an annual salary of $24,895. He has been offered the job in the ad. How much more would he earn per month if he is paid: a. the minimum? b. the maximum
Answers
Joseph has an annual salary of $24895 dollars and she get the new job that is between 28000-36000 dollars so:
the minimum will be:
[tex]24895+28000=52000[/tex]and the maximun will be:
[tex]24895+36000=60895[/tex]which expressions are equivalent to 9 divided by 0.3
Answers
Answer:
Step-by-step explanation:
So the answer would be 90 divided by 3 because all you have to do is multiply 0.3 times 10 and 9 times 10 simple hope this was understandable30 will be the expressions that are equivalent to 9 divided by 0.3.
What is an equivalent expression?In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in maths are those that hold true even when they appear to be distinct. However, both forms provide the same outcome when the values are entered into the formula.
An expression is equivalent even when both sides are multiplied or divided with the same non-zero value.
The expression 9 divided by 0.3 can be written as 9/0.3
The expression that will be equivalent will be determined as:
= 9/0.3
= 90/3
= 30
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