Answer:
The correct statements describing the process of converting z = 2 + 3i to polar coordinates using technology are:
Write the complex number as a point in the complex plane: (2, 3i)
Substitute a = 2 and b = 3 for the real and imaginary parts respectively.
Using radians for θ, record the result as r = 3.606 and θ = 0.983 as your answer in polar coordinate form: (3.606, 0.983).
To convert a complex number in the form of z = a + bi to polar coordinates using technology, we can use the following steps:
Write the complex number as a point in the complex plane, with the real part as the x-coordinate and the imaginary part as the y-coordinate.
Substitute a for the real part and b for the imaginary part.
Using the Pythagorean theorem, we can find the distance from the origin to the point, which is the magnitude or modulus of the complex number, represented by r.
Using the tangent function, we can find the angle of the point from the positive x-axis, which is the argument or phase of the complex number, represented by θ.
Record the result in polar coordinates as (r, θ), where r is the magnitude and θ is the argument, given in radians.
It's also worth noting that polar coordinates can also be represented in the form of (r, θ ) or (r, arg(z)) or (r, angle(z))
Answer:
z = 2 + 3i
Step-by-step explanation:
1 decimal place. (2 marks) In a 4x400m relay competition, a team of athletes each completed their round in 45 sec. 43 sec. 44 sec and 45 sec respectively. If the race started at 1:35:31 p.m., find the time when the team completed the race. (3 marks)
What is the longest side of a triangle opposite of?.
The hypotenuse is the longest side of a triangle which is opposite to the right angle.
A right triangle's hypotenuse is always the side that faces the right angle. This side is longest in a right triangle. The other two sides are those that are opposed and close by. The labels on these sides relate to an angle.
The word "hypotenuse," which refers to the longest side, is derived from two Greek roots that mean "to stretch." One side is across from another at a particular angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side.
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What is a cross section cut to the angle of the base of a rectangle prim
Answer:
In a right rectangular prism, a cross section can be cut on a slant to produce a variety of additional shapes. Depending on the angle of the cut, the cross section can be a triangle, quadrilateral, pentagon, or hexagon. The maximum number of "sides" of a cross section (plane section) equals the number of faces (surfaces) of the solid
Answer:
a rectangle
Step-by-step explanation:
When a geometric plane slices a prism so that the cut is parallel to the plane of the base, the cross section will have the shape of the base. So, in the case of a right rectangular prism, the cross section is a rectangle.
Select the solution for the system of linear equations y = 3x + 4 and y = x + 2.
The value of x from the given linear equation is -1 and y = 1
A linear polynomial over a field, from which the coefficients are taken, can be equalized to zero to produce a linear equation.
A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from
It is given that y = 3x+4 (i) and y = x+2 (ii)
Put equation i) = ii)
Then, we get 3x+4 = x+2
2x = -2
x = -1.
Put the value of x in equation ii)
y = -1+2
y = 1
Hence, the value of x from the given linear equation is -1 and y = 1
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A traveler flies from Charlotte, North Caroline to Los Angeles, California. At the same time, another traveler flies from Lost Angeles to Charlotte. The air speed of each plane is the same. The ground speed of the first plane is 550 mi/ hour and the ground speed of the second plane is 495 mi/hr. What is the air speed? What is the wind speed? Step 1: Write a system of equations Step 2: Choose a method to solve the system BE GOOD IN THE ANSWER
Answer:
Air speed of planes is 522.5 mi/hr,Wind speed is 27.5 mi/hr.----------------------------------
Let the air speed of the planes be s and the speed of the wind be w.
The two equations are:
550 - w = s495 + w = sAdd up the two equations, it will eliminate w and we'll solve it for s:
550 + 495 = s + s1045 = 2ss = 1045/2s = 522.5The air speed of planes is 522.5 mi/hr.
Find the wind speed:
550 - w = 522.5w = 550 - 522.5w = 27.5The wind speed is 27.5 mi/hr.
On March 8, 2017, one U.S. dollar was worth 19.61 Mexican pesos.
(a) On that date, how many dollars was 150.68 pesos worth? Round your answer to the nearest hundredth of a dollar. dollars
(b) On that date, how many pesos was 98.27 dollars worth? >Round your answer to the nearest hundredth of a peso. 0 pesos
Answer:
(a) 7.68 dollars
(b) 1927.07 pesos
Step-by-step explanation:
Setting up a conversion factor will be helpful in helping us solve this problem. A conversion factor shows the relationship between two different units, and and is used to convert from one unit to the other.
Our conversion factor is 1 U.S. Dollar = 19.61 Mexican pesos. To convert units, we can turn the conversion factor into a ratio (U.S. dollar ÷ 19.61 Mexican pesos or vice versa) and then multiply the given amount by the ratio. The unit that we want to end up with should always be in the numerator, and the unit we want to convert from should always cancel out in the denominator. This will be demonstrated when we solve the problems below:
(a) We want to convert from pesos to dollars, so we will multiply by the conversion factor (1 dollar / 19.61 pesos).
150.68 pesos (1 dollar / 19.61 pesos) = 7.68 dollars(b) Now we want to convert from dollars to pesos, so we will multiply by the conversion factor (19.61 pesos / 1 dollar).
98.27 dollars (19.61 pesos / 1 dollar) = 1927.07 pesosWhat ordered pair represents the location of Home?
options:
(-2,-4)
(2, 3)
(-2, 3)
(2, -5)
Answer:
(-2, 3)
Step-by-step explanation:
Is there a square root of 1?.
Yes. There is the square root of 1. The square root of 1 is 1. The square root of 1 is always taken with positive sign. Square root of 1 is a rational number.
The square root of any number is an inverse mathematical operation of a square. square root is the the value which gives the number when it is multiplied by itself. The symbol √ is used to indicate the square root. A number is said to be a rational number that can be made by dividing an integer by an integer. It can be written as a fraction. There are so many ways to find square roots. whose square and the square root are equal is 1. It is neither prime nor composite. Square root of 1 is never be a negative number. It always taken as positive. From the natural numbers only perfect squares have square roots and negative numbers aren’t members of the set.
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Use the equation below to find V, if i=6, w=7 , and h=2 V=iwh
Answer:
84
Step-by-step explanation:
V = IWH
V = (6)(7)(2)
[84]
Grace aw 16 bird habitat at the zoo aviary the ign aid each habitat had 12 bird how many bird were in the aviary in all
There were 192 birds in the aviary in total.
There were 16 habitats in the aviary at the zoo, and each habitat had 12 birds. To find out how many birds were in the aviary in total, we need to multiply the number of habitats by the number of birds in each habitat.
16 habitats * 12 birds/habitat = 192 birds
So there were 192 birds in the aviary in total.
This is done by using the distributive property of multiplication. Basically, if you have a certain number of groups, each containing a certain number of items, and you want to find the total number of items, you can multiply the number of groups by the number of items in each group. In this case, the number of groups is the number of habitats (16) and the number of items in each group is the number of birds (12). So by multiplying those two numbers together, we get the total number of birds in the aviary.
Therefore, There were 192 birds in the aviary in total.
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16 areas with 12 birds each equals 192 birds.
Thus, there were 192 animals in all in the aviary.
Utilizing multiplication's distributive principle, this is accomplished. Basically, you can increase the total number of groups by the total number of items in each group if you have a certain number of groups, each of which contains a specific number of items. In this instance, the number of objects in each group equals the number of birds, and the number of groups equals the number of habitats (16). (12). We can calculate the overall number of birds in the aviary by multiplying those two numbers.
Consequently, there were 192 animals in all in the aviary.
What is 15x+48=120 what is the x value
So the value of x is 4.8
15x + 48= 120
Now we send the 48 on the right side.
15x= 120-48.
Here we subtract 48 from 120 we get
15x= 72
In the next step we divide the both sides with 15
15x/15= 72/15
x=4.8
So the value of x is 4.8
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Which equation repreent the ame line a the point in the table? Input (x) Output (y) −4 5 0 2 83 0
The equation which represents the same line as the points in the table is y = -3/4 x + 2. (Option C)
The equation of the points given in the table can be determined by using the slope-intercept form which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
The slope of the line can be determined by:
m = rise/run = Δy/ Δx = (y2 – y1)/(x2 – x1)
Hence, taking two points from the table say (-4, 5) and (0, 2)
m = (2 – 5)/(0 – (-4)) = -3/4
y intercept is the value of y when x = 0
From the table, y-intercept b = 2
Hence, the equation of the line is: y = -3/4 x + 2
Note: The question is incomplete. The complete question is attached.
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The difference between 2 number i 2. When each number i rounded to the nearet hundred, the difference i 100. What number could they be?
When each number is rounded to the nearest hundred, the difference I 100 the number could be 14,499 less 13,500 or 999
To the closest hundred, the biggest number that can be named 14,000 is 14,050. To the closest hundred, the least number that can be named 14,000 is 13,950. There is a 100 difference between the two.
This claim may be generalized as follows.
The difference between the upper and lower limits is m for any integer N that has been rounded to the nearest m.
The maximum is N+m/2.
N-m/2 is the lower limit.
(N+m/2) is the difference between the two. (N-m/2) = (N-N) +m/2 - (N-N) -m/2
= 0 + m/2 + m/2
= 2(m/2)
= m.
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Can anyone help me with this pls..?
The expression (3z⁴)² is equivalent to 9z⁸
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The law of exponents states that raising a number with an exponent is equal to multiplying the exponent times the power. It is given as:
(xᵃ)ᵇ = xᵃᵇ
Given that:
(3z⁴)²
Applying the law of exponents:
= (3)²(z⁴)²
= 9z⁸
(3z⁴)² is equal to 9z⁸
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You walk into a store and see a sign that says "Tv: 47% off, only pay $1,500 today!" What was the original price of the TV?
The original price of the TV is $4691.5
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that You walk into a store and see a sign that says "Tv: 47% off, only pay $1,500 today!"
We have to find the original price of the TV.
Convert 47% to decimal value.
47/100=0.47
Now multiply 0.47 with x which gives 1500
0.47x=1500
Divide both sides by 0.47
x=1500/0.47
x=$3191.48
Now add $1500 and $3191.5 to find the original price.
1500+3191.5
$4691.5
Hence, the original price of the TV is $4691.5
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If Gina tosses the coins 40 times, what is the
approximate relative frequency that she
will get 2 heads?
Answer:
20 times
Step-by-step explanation:
40 / 2 = 20?? sorry if im wrong
a man is x years old and his son is y years old . what is their average ?
Find negative absolute value of negative two fifths.
(A) −2.5
(B) 2.5
(C) two fifths
(D) negative two fifths
Answer: d
Step-by-step explanation:
-2/5 is the absolute value of - |- 2/5|
What is Expression?An expression is combination of variables, numbers and operators.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
Given that negative absolute value of negative two fifths.
- |- 2/5|
Solving the modulus we get;
|- 2/5| = 2/5
Then negative,
- 2/5
Hence - 2/5 is the absolute value
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Heather made $156 for 12 hour of work at the ame rate how many hour would he have to work to make it 65 dollar
Heather would have to work 4.6 hours to make $65.
Time and work is a branch of mathematics that deals with the relationship between the time required to complete a task and the amount of work done. The basic formula used in time and work is:
Work = Time x Rate
Where,
Work = amount of work done
Time = time taken to complete the work
Rate = the rate at which the work is done
We can calculate this by using the formula:
Hours = (Money earned / Hourly rate)
In this case, you can use the proportion:
(x hours) / (65) = (12 hours) / (156)
Solving for x you get:
x = (65 * 12) / 156 = 4.6 (approximately, rounded to the nearest tenth)
Therefore, Heather would have to work 4.6 hours to make $65.
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In this case, you can use the proportion:
(x hours) / (65) = (12 hours) / (156)
Solving for x you get:
x = (65 * 12) / 156 = 4.6 (approximately, rounded to the nearest tenth)
square root of (x-15)(x-15)
Answer: x - 15
Step-by-step explanation:
The answer is x - 15
Answer:
x-15
Step-by-step explanation:
In Triangle RMC, RM = 19. MC = 27. and CMR = 27°. What is the area of RMC? Round to the nearest tenth.
The area of the RMC triangle is 43.4.
What is a triangle?3 sides, 3 corners, 3 corners form a closed triangle. The mathematical sign of a three-sided triangle is RMC. Triangle-shaped sandwiches and signs are the most common triangles.
Three sides and three interior angles together define a triangle (a rectilinear polygon). This symbol is used to represent one of the basic geometric shapes with three connected vertices.
Triangles are classified in different shapes depending on their sides and angles. Different parts form a triangle. It consists of 3 corners, and 3 sides.
If we round the area to the nearest 10th digit then it will be 116.
Use the Law of Cosines to find the length of the third side RC: RC = [tex]sqrt(19^2 + 27^2 - 2(19)(27)cos(27))[/tex]
Compute the semi-perimeter s = (19+27+RC)/2
Compute the area of the triangle with Heron's formula
A = [tex]sqrt(s(s-a)(s-b)(s-c))[/tex]
After the calculation, we can get the area is approximately 43.4
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In February, the amount of snowfall was 225 feet. In March, the amount of snowfall was 513 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.
Answer:738
Step-by-step explanation:
What characteristics of parallel lines and perpendicular lines create different requirements?.
The Parallel lines never intersect, but they must be in the same plane and the perpendicular lines intersect at right angle and must be coplanar .
The Parallel lines are defined as the two lines which are in the same plane that are at equal distance from each other and never intersect or meet .
The Characteristics are :
(i) Parallel liens are always parallel and are at equidistant from each other. (ii) Parallel lines are non-intersecting lines.
(iii) We can say that Parallel lines meet at infinity.
The Perpendicular lines are formed when the two lines meet each other at a right angle or 90 degrees.
The Characteristics are :
(i) The Perpendicular lines always intersect at the right angle.
(ii) If the two lines are perpendicular to a same line, then they both are said to be parallel to each other and never intersect.
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find the principal of interest 3415 naira ,rate 5% and time 4 yrs 3 months
Answer:
Rs16.968
Step-by-step explanation:
solution
given
i=3415
r=5%
time=4yrs 3 months
=4.25 yrs
we know,
p=Ix100/tr
= 3415x100/4.25x5
=Rs16.98
©Thank You
Answered By Solution 49
If O is the centre of the circle in the figure, find the value of x.
If O is the center of the circle in the figure, the value of x. is 80°.
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry.
Given: ∠ BAC = 35°, ∠ DBC = 65°,
∠BDC = ∠BAC = 35° (Angle in same section).
∠BDC + ∠BCD + ∠DBC = 180° in ABCD.
35° + x + 65° = 180°
⇒ 100° + x = 180°
. '. x = 80°
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Complete question -
Is 32 a co-prime number?.
No, thirty-two is not a prime number i.e., it is a composite number.
A prime number is a number that has only two divisors that is 1 and the number itself. Consider the number 7, which has only two factors, 1 and 7 so it is a prime number. As another example, let's take the example of 8, which has two or more divisors of 1, 2, 4, and 8. This means that 8 is not prime i.e., it is a composite number. I have a number 32 and I need to check if it is prime. To do this, we need to determine 32 factors. The factors of 32 are 1,2,4,8,32, so 32
= 1×2×2×2×2. Here we see that 2, 4, and 8 are factors of 32 that are different from 1 and 32. So there are more than two factors. Therefore it is not prime.
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Complete question:
Is 32 a prime number?
Is a 100 degree angle a right angle?.
No, A right angle is equal to 90 degrees.
In geometry and trigonometry, a right attitude is an angle of precisely ninety stages radians similar to 1 / a 4 turn. If a ray is placed in order that its endpoint is on a line and the adjacent angles are equal, then they may be right angles. The time period is a calque of Latin angulus rectus; here rectus manner "upright", regarding the vertical perpendicular to a horizontal baseline.
Closely related and crucial geometrical concepts are perpendicular strains, which means lines that form right angles at their factor of intersection, and orthogonality, which is the assets of forming right angles, usually implemented to vectors. The presence of a proper angle in a triangle is the defining factor for right triangles, making the proper perspective basic to trigonometry.
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A recipe for cinnamon rolls calls for 2 cups of flour for every 4/1 cup of water. Using the same recipe, how much water will you need for 9 cups of flour?
Rio walked 5 tep forward,8 tep backward,9 tep forward,and 3 tep backward. How many tep i rio from where he tarted?
This indicates that Rio has advanced 3 steps from his starting position.
Rio advanced five steps.Rio has now advanced five steps from his starting position.
8 backward steps.
Rio has moved 5 - 8 = - 3 steps from his starting place, according to this calculation.
Nine steps ahead.Rio has now advanced (-3 + 9) = 6 steps from his starting place.
3 backward steps.
This indicates that Rio has advanced 6 – 3 = 3 steps from his starting position.
Note: Include the stages as you proceed.
Subtract the steps while moving backward.If the outcome is negative, for instance, (-3) steps forward from the beginning position equals (backward) 3 steps from the starting point.Know more about Steps
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Provide numerical measures of individuals. The measures can be added or subtracted, and provide meaningful results.
Its called quantitative variables.
Examples of quantitative variables
Numerical measures of individuals are including:
Age: measured in yearsHeight: measured in inches or centimetersWeight: measured in pounds or kilogramsIncome: measured in dollars or another currencyEducation level: measured in years of schooling completedBlood pressure: measured in mmHgBody Mass Index (BMI): calculated as weight in kg divided by height in meters squaredHeart rate: measured in beats per minute (bpm)These are examples of quantitative variables because their values can be added, subtracted, and mathematically manipulated to provide meaningful results.
Numerical Measures of IndividualsThe primary numerical measure for qualitative data is called the proportion, and it is expressed as a percentage of the total data values in each category. The most frequent numerical measurements for quantitative data are the mean, median, mode, range, variance, and standard deviation. Other numerical measures include the percentiles and range.
The quantitative variables offer numerical measurements of the people being studied. On the values of a quantitative variable, arithmetic operations such as addition and subtraction can be done, and the resulting meaningful results can be interpreted in a variety of ways.
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