Answers
Answer:
(d) 7/25 -(24/25)i
Step-by-step explanation:
You want the value of 4-3i divided by its conjugate.
ConjugateThe conjugate of a sum is the same sum with the sign changed.
conjugate of 4-3i is 4+3i
conjugate of 4+√2 is 4-√2
In algebra, a conjugate is often used when squaring one of the terms will make it "rational" or real (or both). That is because the product of a number and its conjugate is the difference of the squares of the parts of the sum.
(a -b)(a +b) = a² -b²
ApplicationYou want the value of (4-3i) divided by its conjugate. Simplifying that expression will also make use of the conjugate.
[tex]\dfrac{4-3i}{4+3i}=\dfrac{(4-3i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{4^2+2(4)(-3i)+(3i)^2}{4^2-(3i)^2}=\dfrac{(16-9)-24i}{16+9}\\\\=\boxed{\dfrac{7}{25}-\dfrac{24}{25}i}[/tex]
Related Questions
Which of the following equations represents a line that passes through the points (5,3) and (-5,-1). Both, neither, 1, or 2.
1. y+1=2/5(x+5)
2. y=-2/5x+1
PLS ANSWER
Answers
Answer:
Both
Step-by-step explanation:
(5, 3) and (-5, -1)
To get the equation of two points(coordinate)
(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)
(5, 3) --- (x₁, y₁)
(-5, - 1) --- (x₂, y₂)
(- 1 - 3)/(- 5 - 5) = (y - 3)/(x - 5)
-4/-10 = (y - 3)/(x - 5)
4/10 = (y - 3)/(x - 5)
⅖ = (y - 3)/(x - 5)
5(y - 3) = 2(x - 5)
5y - 15 = 2x - 10
5y = 2x - 10 + 15
5y = 2x + 5
Divide through by 5
5y/5 = 2x/5 + 5/5
y = ⅖x + 1
Option 2 is correct
let's see if option 1 is correct
y = ⅖x + 1
add 1 to both sides.
y + 1 = ⅖x + 1 + 1
y + 1 = ⅖x + 2
y + 1 = ⅖(x + 5)
So, option 1 is also correct
Answer:
Both
Step-by-step explanation:
(5, 3) and (-5, -1)
To get the equation of two points(coordinate)
(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)
(5, 3) --- (x₁, y₁)
(-5, - 1) --- (x₂, y₂)
(- 1 - 3)/(- 5 - 5) = (y - 3)/(x - 5)
-4/-10 = (y - 3)/(x - 5)
4/10 = (y - 3)/(x - 5)
⅖ = (y - 3)/(x - 5)
5(y - 3) = 2(x - 5)
5y - 15 = 2x - 10
5y = 2x - 10 + 15
5y = 2x + 5
Divide through by 5
5y/5 = 2x/5 + 5/5
y = ⅖x + 1
Option 2 is correct
let's see if option 1 is correct
y = ⅖x + 1
add 1 to both sides.
y + 1 = ⅖x + 1 + 1
y + 1 = ⅖x + 2
y + 1 = ⅖(x + 5)
So, option 1 is also correct
Ann is 4 years older than Julie. 4 years ago Ann was twice as old as Julie. Find their present ages.
Answers
Answer: Julie is 8 years old. Ann is 12 years old.
Step-by-step explanation:
A=Ann's age. J=Julie's age
A=J+4
A-4=(J-4)*2
A-4=2(J-4)
A=2(J-4)+4
2(J-4)+4=J+4
2J-8+4=J+4
2J-4=J+4
2J=J+8
J=8
A=J+4
A=8+4
A=12
Julie is 8 years old. Ann is 12 years old.
Julie's present age (x) is 8 years old, and Ann's present age (x + 4) is 12 years old. Julie is 8 years old and Ann is 12 years old.
Let's denote Julie's age as x.
Since Ann is 4 years older than Julie, her age can be represented as x + 4.
Four years ago, Julie's age was x - 4 and Ann's age was (x + 4) - 4 = x.
Since Ann was twice as old as Julie, we can write the equation
: x = 2(x - 4).
Simplifying the equation, we get: x = 2x - 8.
Rearranging the terms, we find: x - 2x = -8.
Combining like terms, we have: -x = -8.
Finally, solving for x, we get: x = 8.
Therefore, Julie's present age (x) is 8 years old, and Ann's present age (x + 4) is 12 years old.
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i need help with these 2 questions {^_^]
Answers
7) - 14
9) 16 1/2
h(x)=x squared +1 k(x)=x-2 (h+k)(2)
Answers
The value of the function (h+k)(2) is 1
What is a function?
A function can be defined as an expression or rule that shows relationship between an independent and dependent variable.
Given the functions;
h(x)= x ² +1 k(x)=x-2To determine ( h + k), we have
( h + k) = x² + 1 + x - 2
Then,
(h+k)(2), substitute the value of x as 2
(h+k)(2) = (2)² + 1 - (2) - 2
(h+k)(2) = 4 + 1 - 4
(h+k)(2) = 1
Thus, the value of the function (h+k)(2) is 1
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Does anyone know this answer??
Answers
Stefan drove to work in rush hour traffic, going just 25 miles in 1 hour and 8 minutes. Later that day, he left work early to avoid the rush and was able to take the same route home in 32 minutes. What was Stefan's average speed overall?
Answers
The average speed of stefan is 0.57 miles per hour.
Given, In heavy traffic, Stefan covered just 25 miles in 1 hour and 8 minutes on his way to work.
He left work early to beat the rush hour and made it home in 32 minutes using the same route.
speed of steven in heavy traffic = distance/ time
distance = 25 miles
time = 1 hour and 8 minutes = 68 minutes
therefore, speed = 25/68 = 0.36 miles per hour.
speed of steven while returning back to home.
distance = 25 miles
time = 32 minutes.
speed = 25/32 = 0.78 miles per hour.
average speed = 0.36 ₊ 0.78/2
= 1.14/2
= 0.57 miles per hour.
hence we get the average speed as 0.57 miles.
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35 POINTS Rebecca has 3 paintings to sell. The amount of money Rebecca makes from selling x paintings is represented by a function.
f(x)=25x
What is the domain of the function?
all real numbers
{25, 50, 75}
{0, 25, 50, 75}
{0, 1, 2, 3}
Answers
Answer:
First one because she will not buy it for free so 0 isn't in the domain
Answer:
all real numbers I believe
..・ヾ(。＞＜)シ
identify the set or sets of numbers that belong to -8/5
Answers
The number of the sets is the {1, 2/5,4/5,8/5}.
According to the statement
We have to find that the sets of numbers.
So, For this purpose, we know that the
A set of numbers is a collection of numbers, called elements. The set can be either a finite collection or an infinite collection of numbers.
From the given information:
The set or sets of numbers that belong to -8/5.
For make a set of the numbers we have to find the those number which are the divisible on the number -8/5.
Then
Let the number 1, 2/5,4/5,8/5.
And these are the numbers which are the divisible on the -8/5 and give some perfect value like 1, 2 etc.
The set of the numbers = {1, 2/5,4/5,8/5}
So, The number of the sets is the {1, 2/5,4/5,8/5}.
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15(2x + 3) = 85 + 10x
Answers
Answer:
x = 2
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x15(2x + 3) = 85 + 10x30x + 45 = 85 + 10x 20x + 45 = 8520x = 40x = 2The value of x is 2.
Somone help me on this free 20 poins
Answers
Answer:
T = 3.67 years
Step-by-step explanation:
Compare and order the following numbers:
√11, 2 1/4, -2.5, 3.6 repeating, -3.97621...
Answers
The correct decreasing order of the given numbers is : 3.32 > 2.25 > -2.25 > -3.98
What is Descending Order ?
Descending order is a way to arrange numbers from largest to smallest. When we arrange things in order, from a higher value to a lower value, it is known as the descending order or the decreasing order.
√11 = 3.316 = 3.32 (rounding off to two decimal places)
2 1/4 = 9/4 = 2.25 (by solving mix fraction)
-2.25 (negative number is written in negative x- axis)
-3.97621 = -3.98 (negative number is written in negative x- axis)
arranging the numbers in descending order
3.32 > 2.25 > -2.25 > -3.98
therefore, the highest number is 3.32 and the lowest number is -3.98
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help solve please x^3-2x^2-2=0
Answers
Answer:
x=2.35930...
i hope this is the answer
Find the 9th term of the arithmetic sequence with 9=10 and d= - ½
Answers
The 9th term of this arithmetic sequence is 6.
In an Arithmetic Progression (AP), the nth term is given by the formula-
a9 = a + (n-1)d
where a = first term of the AP
d = common difference
Here, we are given that a= 10 and d = - ½
Let the 9th term of the AP be a9
Therefore, according to the formula for finding the nth term of an AP, we get-
a9 = a + (9-1)d
a9 = a + 8d
Substituting the values of a and d given in the question-
a9 = 10 + 8(-1/2)
a9 = 10 - 4
a9 = 6
Thus, the 9th term of the arithmetic sequence is 6.
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A research group surveyed 250 students. The students were asked how often they go to the movies and whether they prefer comedies or dramas
Answers
A percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
The percentage of the students who go to the movies three times a month or more is given by:
Total students = 30 + 55 = 85 students.
Percentage = 85/250 × 100
Percentage = 0.34 × 100
Percentage = 34%.
The percentage of the students who prefer dramas is given by:
Total students = 85 + 55 = 140 students.
Percentage = 140/250 × 100
Percentage = 0.56 × 100
Percentage = 56%.
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Complete Question:
A movie club surveyed 250 high school students. The students were asked how often they go to the movies and whether they prefer comedies or dramas. Their responses are summarized in the following table.
(a) What percentage of the students go to the movies three times a month or more?
(b) What percentage of the students prefer dramas?
-4 66/100 greater or less than -4 3/4
Answers
After the conclusion we can conclude that the fraction [tex]-4\frac{66}{100} < -4\frac{3}{4}[/tex].
What are fractions?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.First, we need to make both denominators the same in order to find which fraction is greater and less than.
So,
[tex]-4\frac{66}{100} , -4\frac{3}{4} \\[/tex](-400+66)/100, (-16+3)/4-334/100, -13/4(-334×4)/(100×4), (-13×100)/(4×100)-1336/400, -1300/400Hence, -1336/400 < -1300/400
So, we can conclude that: [tex]-4\frac{66}{100} < -4\frac{3}{4}[/tex]Therefore, the fraction [tex]-4\frac{66}{100} < -4\frac{3}{4}[/tex].
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Write equations for the horizontal and vertical lines passing through the point (1,6) .
Answers
Answer:
the horizontal and vertical lines passing through the point (1,6)
y-6=
x-1=
Step-by-step explanation:
Answer:
x=1 and =
Step-by-step explanation:
estimate the cube root of 1100
Answers
Answer:
Step-by-step explanation:
∛1100
Answer:
10.324
Step-by-step explanation:
I doesn't have a perfect cube root
Factor completely
2x^5-7x^5/2+6
Answers
after simplifying yhe expression 2 x ⁵ - 7 x ⁵ / 2 + 6, we get the result as - 3 / 2 ( x⁵ - 4).
We are given the expression :
2 x ⁵ - 7 x ⁵ / 2 + 6
We need to factorize the expression completely.
Taking LCM, we get that,
4 x⁵ - 7 x⁵ + 12 / 2
combining the like terms, we get that,
- 3 x ⁵ + 12 / 2
taking - 3 common from the expression, we get that
- 3 / 2 ( x⁵ - 4)
Therefore, after simplifying yhe expression 2 x ⁵ - 7 x ⁵ / 2 + 6, we get the result as - 3 / 2 ( x⁵ - 4).
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Which of the following represents the sum of the polynomials below?
(6x³ +2ײ +9x)+(-2x³ +5x² +3x)
OA. 4x³ +7x² +12x
OB. 4x³ +7x² +12
OC. 8x³ +7x² +12x
OD. 4x³ +7x² +6x
Answers
Answer:
A
Step-by-step explanation:
First, you have to align the like terms next to each other so that it will be easier to combine like terms. (Like terms have the same variables and powers)
[tex]6x^3+(-2x^3)+2x^2+5x^2+9x+3x[/tex]
Combine like terms:
(When combining like terms all you have to do is add/subtract the coefficients, number in front of variables, and leave the variable and exponents)
[tex]6x^3+(-2x^3)= > 6x^3-2x^3=4x^3[/tex]
[tex]2x^2+5x^2=7x^2[/tex]
[tex]9x+3x=12x[/tex]
So, we get [tex]4x^3+7x^2+12x[/tex]
The sum of the angle measures of a quadrilateral is 360°. In Exercises 7 and 8,
write and solve an equation to find the value of x. Use a protractor to check the
of your answer.
reasonableness
7.
110°
90⁰
to
80⁰
Answers
The value of the angle of the quadrilateral is 80° .
A quadrilateral in geometry is represented as a four-sided polygon with four corners (vertices) and four sides .
The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name. In reference to other polygons, it is also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon). Since "gon" is an anagram for "angle," it is also known as a quadrangle or 4-angle.There are two types of quadrilaterals: simple (not self-intersecting) and complex (self-intersecting, or crossed). Convex or concave quadrilaterals are simple quadrilaterals.The sum of all the angle measures of a quadrilateral is 360°Given angles of the quadrilateral are 110° ,90⁰ and 80⁰.
Now let us consider the fourth angle be x.
∴110°+ 90⁰ + 80⁰ + x = 360°
or, x = 360° - (280°)
or, x = 80°.
The missing angle of the quadrilateral is 80°
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Macmillan Learning
The summer monsoon rains bring 80% of India's rainfall and are essential for the country's agriculture. Records going back
more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution that is
approximately Normal with mean 852 millimeters (mm) and standard deviation 82 mm. Use the 68-95-99.7 rule to answer the
questions.
Between what values do the monsoon rains fall in the middle 95% of all years? Enter your answer as an interval "(lower bound.
upper bound)" and as a whole number.
The middle 95% of the distribution of moonsoon rainfall amount:
How small are the monsoon rains in the driest 2.5% of all years? Give your answer as a whole number.
The driest 2.5% of monsoon rainfall amount are less than:
MD
688
Sep 8
mm
mm
10:30
Answers
Using the Empirical Rule, it is found that:
The middle 95% of the distribution of moonsoon rainfall amount: (688 mm, 1016 mm).The driest 2.5% of monsoon rainfall amount are less than: 688 mm.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Hence, the middle 95% of values is within 2 standard deviations of the mean, with bounds given as follows:
852 - 2 x 82 = 688 mm.852 + 2 x 82 = 1016 mm.The middle 95% of the distribution of moonsoon rainfall amount: (688 mm, 1016 mm).
For the driest 2.5% of years, considering the symmetry of the normal distribution, we have to look at 2 standard deviations below the mean, as 5/2 = 2.5%, hence:
The driest 2.5% of monsoon rainfall amount are less than: 688 mm.
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12/7 divided by 3/2 =
A. 18/7
B. 7/8
C. 7/18
D. 8/7
Answers
Answer:
Step-by-step explanation:
D
12/7 divided by 3/2 becomes 12/7 times 2/3
Multiplied out you get 24/21 which reduces by dividing both the denominator and numerator by 3 giving you 8/7 or letter D
Given f(x) = -x - 9 and g(x) = 3x + 8, find (f + g)(−8).
Answers
Answer: -17
Step-by-step explanation:
f(x) = -x - 9 and g(x) = 3x + 8
(f + g)(−8)=
f(-8)+g(-8)=
-(-8)-9+3(-8)+8=
8-9-24+8=
-1-16=-17
Two negative consecutive integers have a sum of -45. What are the two integers?
Answers
Answer:
-23+-22=-45
Step-by-step explanation:
In this type of question if he wants the consequtive divided number over 2 and choose the result number and pervious or next one it is depend on the questions
Answer:
The two integers will be/ are - 23 and - 24
The reciprocal of x is 0.25. The reciprocal of y is 10.
Work out the value of xy.
The book says the answer is 5/6 but I can’t get the same answer. Please help.
Answers
Answer:
XY=2/5
Step-by-step explanation:
Given the reciprocal of x is 0.25, that is then
x = 1/ 1/4 = 4
Given the reciprocal of y is 10 then
y = 1/10
xy = 4 ×1/10 =4/10 = 2/5
18. C(−8, −6) and D(−4, 10)
Answers
Answer:
I'm assuming you want to find the slope.
If so, the answer is: m = 4
Hope this helps! <3
first steps in factoring a polynominal with four terms
Answers
Answer:
Subtract two sides
Step-by-step explanation:
What is 3.81704*10^5?
Answers
Answer: 381704, because math
chemical property is__________. a. a property that does not change the chemical composition of the matter. b. a characteristic of matter that indicates whether or not the piece of matter can undergo specific changes c. a property that changes with the physical location of the matter sample, d. a characteristic of matter that can be measured without changing the identity of the material
Answers
Answer:
Physical Property
Step-by-step explanation:
Physical Property. A physical property is a characteristic of a substance that can be observed or measured without changing the identity of the substance. Silver is a shiny metal that conducts electricity very well.
What is 8 x 1 plus 5 x 1/1000 plus 9 x 1/1000
Answers
The value of the expression 8 × 1 plus 5 × 1/1000 plus 9 × 1/1000 is 8.014.
Consider the expression,
8 × 1 plus 5 × 1/1000 plus 9 × 1/1000
Now,
8 × 1 = 8 and;
5 × 1/1000 = 5/1000
and;
9 × 1/1000 = 9/1000
Now,
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + 5/1000 + 9/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + [ ( 9 + 5 ) / 1000 ]
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + 14 / 1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = ( 8 / 1 ) + ( 14 / 1000 )
Now, LCM of 1 and 1000 is 1000.
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 × ( 1000/1000) + 14/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8000/1000 + 14/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = ( 8000 + 14 ) / 1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8014/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8.014
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