Plot the complex number, then write the complex number in polar form. You may express the argument in degrees.
Answers
DEFINITIONS
To represent a complex number we need to address the two components of the number.
Consider the complex number:
[tex]a+bi[/tex]Complex numbers are the points on the plane, expressed as ordered pairs (a, b), where a represents the coordinate for the horizontal axis and b represents the coordinate for the vertical axis.
Note that the imaginary part is plotted out on the vertical axis while the real part is on the horizontal axis.
QUESTION
The complex number is given to be:
[tex]4\sqrt[]{3}-4i[/tex]This means that the ordered pair representing the complex number is given to be:
[tex](a,b)=(4\sqrt[]{3},-4)[/tex]This means that the point will be positive on the real axis and negative on the imaginary axis. Therefore, the point will be in the 4th quadrant.
The correct option is OPTION B.
Related Questions
please help me understand how to find the average rate of change of the function over the given interval and please show me work.
Answers
To answer this, you'll need to recall a formula for finding the rate of change of one variable with respect to another. Given f(x)=x^2 + x +1, the rate of change of the variable with respect to x is given by:
[tex]\begin{gathered} \frac{\differentialD yy}{\square}y}{dx}=n(ax^{n-1}),\text{ where n is the power of variable term, and a is the coefficient.}y}{\square}yy}{dx}=\text{nax}^{n-1} \\ So\text{ when f(x)=x\textasciicircum 2+x+1 is differentiated, we will arrive at } \\ \\ \frac{dy}{dx}=2x+1\text{ The average rate of change of the function within the range (-3,-2) means, we have to use x as -3 and also x as -2 into the derivative function } \\ x=-3 \\ \frac{\differentialD yy}{\square}y}{dx}=2(-3)+1=-6+1=-5y}{\square}y}{dx}=2(-3)+1=-6+1=-5 \\ \text{Also, } \\ x=-2 \\ \frac{\differentialD yy}{\square}y}{dx}=2x+1\text{ becomes}y}{\square}yy}{dx} \\ \\ \end{gathered}[/tex]Does anyone know the answer to this?
Answers
The most appropriate choice for equation of line in slope intercept form will be given by
x + 2y = -16 is the required equation of line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
[tex]m=tan\theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
The line passes through (0, -8) and (-2, -7)
Slope =
[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]
The line passes through (0, -8)
Equation of line
[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]
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A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
Answers
Answer: 15cm
Step-by-step explanation:
Your welcome
Which points are separated by a distance of 4 units?A. (3,6) (3,9)B. (2,7) (2,3)C. (1,5) (1,3)D. (4,2) (4,7)
Answers
let us take the point (2,7) and (2,3) the distance between these two is
[tex]\begin{gathered} d=\sqrt[]{(2-2)^2+(7-3)^2} \\ d=\sqrt[]{4^2} \\ d=4\text{ unit} \end{gathered}[/tex]Hence these two points are separated by 4 units.
So option B is correct.
if two angles measure 90 and are complementary and congruent, the measure of each angle is
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Leonardo, the answer is
45 degrees.
Divide 8 A) 3 B) 0) 7 16 D) 7. 32
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Answer
3(1/2) or (7/2) or 3.5
Step-by-step Explanation
The question wants us to divide (7/8) by (1/4).
[tex]\frac{7}{8}\div\frac{1}{4}[/tex]The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.
That is, in changing ÷ into ×, (1/4) changes to (4/1)
So,
[tex]\begin{gathered} \frac{7}{8}\div\frac{1}{4} \\ =\frac{7}{8}\times\frac{4}{1} \\ =\frac{28}{8} \\ =\frac{7}{2} \\ =3\frac{1}{2} \end{gathered}[/tex]Hope this Help!!!
a standard Normal distribution, what percentage of observationnd the z-table here.4.95%5.48%6.06%95.05%
Answers
SOLUTION:
Case: Z-scores and probabilities
Given: z-score of standard normal distribution, z= 1.65
Required: To get the percentage of observation
Method: We will be reading it off the z-score table
Step 1: First we see what the table looks like
Step 2: From the table, we trace 1.65 by looking at 1.6 on the column title and 0.05 on the row title
Step 3: We observe the value is 0.4505
This translates to 45.05%.
However, we are interested in the values above the 45.05%. So everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score
To get the z-score above this, we do:
1 - 0.9505
P(> z) = 0.0495 or 4.95%
Final answer:
A) The answer is 4.95%
The angle of elevation to the top of a Building in New York is found to be 7 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
_________ feet
Answers
The height of the building is 649.44 feet
Given,
The angle of elevation of the building from ground = 7°
The distance from base of the building to the angle = 1 mile
We have to find the height of the building:
As this information are noted, we will get a right angled triangle(image attached).
So, by trigonometry:
Tanθ = opposite side / adjacent side
here,
θ = 7 degree
opposite side = x
adjacent side = 1 mile
Then,
Tanθ = opposite side / adjacent side
tan(7°) = x / 1
x = tan(7°) × 1
x = 0.123 × 1
x = 0.123 miles
1 mile = 5280 feet
Then,
0.123 miles = 0.123 × 5280 = 649.44 feet
That is,
The height of the building is 649.44 feet.
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Darell made a scale drawing of a shopping center. The parking lot is 4 centimeters wide in the drawing. The actual parking lot is 40 meters wide. What scale did Darell use?
Answers
Answer:
1 cm to 10 m
Step-by-step explanation:
4 cm to 40 m = 1 cm to 10 m
p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)
Answers
1) Let's find the roots of the equation: 5x² -7x +1
5x² -7x +1
2) Calling x_1 =p and x_2= q
Plugging them into the (p/q)+(q/p) expression, dividing the fractions. And then rationalizing it we'll have finally:
[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. The total value of the coins was $7.90. The number of Dimes was 7 less than triple the number of Quarters. Write a system of equations that represents this situation. Use N, D, and Q.
Answers
A Nickel is 5 cents = 5/100 = $0.05
A dime is 10 cents = 10/100 = $0.1
A quarter is 25 cents = 25/100 = $0.25
Let N represent the number of nickels
Let D represent the number of dimes
Let Q represent the number of quarters
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that
N + D + Q = 81
The total value of the coins was $7.90. It means that
0.05N + 0.1D + 0.25Q = 7.9
The number of Dimes was 7 less than triple the number of Quarters. It means that
D = 3Q - 7
The system of equations is
N + D + Q = 81
0.05N + 0.1D + 0.25Q = 7.9
D = 3Q - 7
Solve the inequality: y-5-20Which of the following is the graph of the solution?
Answers
Given the inequality:
[tex]y-5>-20[/tex]Let's select the graph which represents the solution.
Let's solve the inequality.
Add 5 to both sides of the inequality:
[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.
Therefore, the graph of the solution is:
ANSWER:
A
I believe the answer to be c but I'm not the best at word problems this is a practice study guide.
Answers
In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:
Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.
Now, we can calculate the values that define the interval using the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -1.96=\frac{x-8.1}{1.47} \\ x-8.1=-2.88 \\ x=-2.88+8.1 \\ x=5.22 \\ \\ 1.96=\frac{x-8.1}{1.47} \\ x-8.1=2.88 \\ x=2.88+8.1 \\ x=10.98 \end{gathered}[/tex]Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)
Find the coordinates of each point under the given rotation about the origin (-5, 8); 180
Answers
As given by the question
There are given that the point, (-5, 8).
Now,
The given coordinate of point (-5, 8) which is lies on the second quadrant.
Then,
According to the question,
Rotate it through 180 degree about the origin
Then,
The given coordinate move from 2nd quadrant to 4th, where the value of x is positive and y is negative
Then,
The new coordinat will be, (5, -8).
Hence, the coordinate is (5, -8).
Question 3 (9 points)Find Pred then green)What is the probability that you select a red marble, then a green marbleP (red) -P (then Green) - (Total of marbles will be 1 less)P (red then green) = *Hint: Multiply
Answers
Solution
Step 1
Write out an expression for the probability
[tex]\text{The probaility of an event occurring= }\frac{\text{Number of required events}}{\text{Total number of events}}[/tex]Step 2
Define terms
Total number of events = 8 marbles
Number of required events = red then marble
Number of red = 2 marbles2
Number of green = 2 marbles
Note: The question is without replacement.
Step 3
Get the required probabilities and the answer
[tex]\begin{gathered} Pr(\text{red marble) = }\frac{2}{8} \\ Pr(\text{green marble without replacement) =}\frac{2}{7} \end{gathered}[/tex]Hence the Pr(of red then green) is given as
[tex]\begin{gathered} =Pr(\text{red) }\times Pr(green\text{ without replacement)} \\ =\frac{2}{8}\times\frac{2}{7}=\frac{1}{14} \end{gathered}[/tex]Hence the probability of picking a red marble then a green marble = 1/14
what does -1 3/4+4.7=
Answers
-1 3/4 + 4.7 = -1.75 + 4.7 = 2.95
3/4 = 0.75, so -1 3/4 is -1.75
-1.75 + 4.7 = 2.95
Answer: 2.95
In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.
Answers
Explanation
Step 1
the sum of the internal angles in a triangle equals 18o, so
[tex]\begin{gathered} (2x+16)+(6x-14)+(2x+8)=180 \\ 2x+16+6x-14+2x+8=180 \\ \text{add similar terms} \\ 10x+10=180 \\ \text{subtract 10 in both sides} \\ 10x+10-10=180-10 \\ 10x=170 \\ \text{divide both sides by 10} \\ \frac{10x}{10}=\frac{170}{10} \\ x=17 \end{gathered}[/tex]Step 2
now, replace the value of x in angle Q to find it
[tex]\begin{gathered} \measuredangle Q=(2x+8) \\ \measuredangle Q=(2\cdot17+8) \\ \measuredangle Q=(34+8) \\ \measuredangle Q=42 \end{gathered}[/tex]I hope this helps you
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answers
[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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composition of functions, interval notation
Answers
Given the functions:
[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]I would like to find their domain as well and then complete the answers:
[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]For the first question: g(x) / m(x)
[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is
[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]For the second domain g(m(x)), let's find out what is the function:
[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]This means that x cannot be among the interval -2,2:
[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]For the last domain m(g(x)) we perfome the same procedure:
[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]For this domain it is obvious that x cannot take the zero value but anyone else.
[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]8) What is the mass of the teddy bear if the toy car has a mass of 375 grams? 10 .S 0 4kg 3kg 1kg 2kg 000
Answers
The mass of the teddy is 1,225 grams
Here, we want to get the mass of the teddybear given the mass of the toy car
Since boith are on the scale, then it means they contribute to the mass on the scale
By reading the scale, we can see that the mass on the scale is 1.6 kg
As we know, 1000 g is 1 kg
It means 1.6 kg in g will be 1.6 * 1000 = 1,600 g
So, we can now subtract the mass of the toy car from this total to get the mass of the teddy
Mathematically, we have this as;
[tex]1600\text{ g - 375 g =1,225 g}[/tex]If 6 is subtracted from the third of three consecutive odd integers and the result is multiplied by 2, the answer is 23 less then the sun if the first and twice the second of the integers
Answers
Ken wants to install a row of cerámic tiles on a wall that is 21 3/8 inches wide. Each tile is 4 1/2 inches wide. How many whole tiles does he need?
Answers
We have the following:
[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}[/tex]therefore:
[tex]\begin{gathered} 21\frac{3}{8}=\frac{21\cdot8+3}{8}=\frac{168+3}{8}=\frac{171}{8} \\ 4\frac{1}{2}=\frac{4\cdot2+1}{2}=\frac{8+1}{2}=\frac{9}{2} \end{gathered}[/tex]now, we divde to know the amount:
[tex]\frac{\frac{171}{8}}{\frac{9}{2}}=\frac{171\cdot2}{8\cdot9}=\frac{342}{72}=4.75\cong4[/tex]Therefore, the answer is 4 whole tiles
I need help with a word problem in algebra 2 please
Answers
We were given the following information:
Plan 1
Cost = $175
It has unlimited call & texts as well as 15gb
Plan 2
Cost = $50 per month
It has unlimited call & texts as well as 6gb
After 6gb, data is charged $5 per gb
From this we have the following equations:
[tex]undefined[/tex]What is the prime factorization of 84.(A)2 x 3 x 7(B)2^2 X 3 X 7(C)2 X 21
Answers
Answer:
84=2^2 x 3 x 7
Explanation:
A prime number is any number that has only two factors: 1 and itself.
To find the prime factorization of 84, we are required to express it as a product of its prime factors.
[tex]\begin{gathered} 84=2\times42 \\ 84=2\times2\times21 \\ 84=2\times2\times3\times7 \\ =2^2\times3\times7 \end{gathered}[/tex]
Therefore, the prime factorization of 84 is:
84=2^2 x 3 x 7
having trouble solving quadratic equations using factoring, examples are fine
Answers
Let's solve the quadratic equation using factorization:
x²-9x -22= 0
In order to solve using this method, we should beforehand factorize the polynomial:
The middle number is -9 and the last number is -22.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks? Let's think about two numbers that add up to -9 and multiply together to -22...
These numbers will be -11 and 2:
-11 +2= 9
-11*2= -22
So the factorization is:
(x+2)*(x-11) = 0
That means:
x + 2 =0
and
x - 11 = 0
Solving the equations:
x= -2
x= 11
S= {-2, 11}
Please help nobody knows the answer to my question. Round to 2 decimal places.
Answers
To answer this question we will use the z-score.
Recall that the z-score is given as follows:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]The z-score of 54 is:
[tex]z=\frac{54-50}{5}=\frac{4}{5}=0.8.[/tex]The z-score of 56 is:
[tex]z=\frac{56-50}{4}=\frac{6}{5}=1.2.[/tex]Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:
[tex]P(0.8Now, recall, that:[tex]P(aNow, from the given table we get that:[tex]\begin{gathered} P(0.8)=0.7881, \\ P(1.2)=0.8849. \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} P(0.8Answer: 0.10.720÷5 WORK OUT NEEDED
Answers
144
Explanation:[tex]720\text{ }\div\text{ 5}[/tex]working the division:
The process:
7 ÷ 5 = 1 R 2
add the 2 to the next number: this gives 22
22 ÷ 5 = 4 R 2
add 2 to the next number: this gives 20
20 ÷ 5 = 4 R 0
The result of 720 ÷ 5 = 144
simplify -5m²n³ × 15m⁴ n⁶
Answers
To simplify the given expression we will use the following property of exponents:
[tex]a^n\times a^m=a^{n+m}.[/tex]Using the above property we get:
[tex]-5m^2n^3\times15m^4n^6=(-5\times15)m^{2+4}n^{3+6}=-75m^6n^9.[/tex]Answer:
[tex]-5m^2n^3\times15m^4n^6=-75m^6n^9.[/tex]what is 234,181 rounded to the nearest thousand
Answers
The figure 234,181 has the digit 4 in the thousands place.
Rounding to the nearest thouand would therefore be
234,000
This is because, the digit 1 that follows is not up to 5 and therefore is insignificant. So the digit 1 and the others after it are all rounded up to zeros.
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Answers
50 X 5 X 3
answer divide
by 36