Compare and contrast the absolute value of a real number to that of a complex number
Answers
Consider a real number in two dimensional plane that X axis and Y axis having ordered pair : P(x,y) or (3,4).
To find it's absolute value we will find it's Distance from origin.
As Coordinate of Origin = (0,0)
Absolute Value of OP = [tex]\left | OP \right |[/tex]
= [tex]\sqrt{(0-x)^2+(0-y)^2}=\sqrt {x^2+y^2}[/tex]
If the point is Q(3,4)
[tex]\left | OQ \right |=\sqrt{3^2+4^2}=\sqrt{5^2}=5[/tex]
In case of a complex number :
Z = a + bi , we consider two axes Real Axis and Imaginary Axis.
We represent Z that is (a,b) in the same way that we represent point in two dimensional plane.
To find it's absolute value , we will find it's distance from origin.
[tex]\left | Z \right |= \sqrt{a^2+b^2}[/tex]
If [tex]Z_{1}[/tex] = 6 + 8 i
[tex]\left | Z_{1}\right |=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]
Related Questions
how do you solve f + 15 = 35
Answers
So what we do to one side of the equal sign, we must do to the other side as well.
We want to solve for f, so we need to subtract 15 on both sides of the equal sign in order to get f alone by itself on the left side:
[tex] f=20 [/tex]
So now we know that f = 20.
f + 15 = 35
Isolate the variable (f). Note the equal sign. What you do to one side, you do to the other.
Subtract 15 from both sides
f + 15 (-15) = 35 (-15)
f = 35 - 15
Simplify
f = 20
f = 20 is your answer
hope this helps
The cruise control feature on a car is set to maintain a speed of 65 miles per hour. The car’s actual speed never varies by more than three mph. Select the inequality that represents the speed of the car while cruise control is being used.
Answers
Final answer:
The inequality that represents the speed of the car while cruise control is being used is 62 ≤ s ≤ 68, where s is the car's speed and it shows the car's speed will be at least 62 mph and at most 68 mph.
Explanation:
The cruise control feature on a car is designed to maintain a steady speed, in this case, 65 miles per hour. However, it is acknowledged that the car's actual speed can fluctuate slightly. The question asks for an inequality that represents the potential speed of the car while cruise control is in use.
Considering the car's speed can vary by up to 3 mph more or less than the cruise control setting, we can set up an inequality to describe this range of speeds. The car's speed (s) should be no more than 3 mph above 65 mph and no less than 3 mph below 65 mph. Therefore, the inequality that represents the speed s of the car would be:
62 ≤ s ≤ 68
This inequality shows that the car's speed will be at least 62 mph and at most 68 mph, encompassing the 3 mph range of variation allowed by the cruise control setting.
8x-12y=84 into slope intercept form
Answers
in slope intersept form or (y=mx+b) is
y=2/3x-7
What is the value of the expression -225 divided by -15
GIVING BRAINLIEST
Answers
Steps: -225/-15
-(-15)
15
-225 divided by -15 is equal to 15.
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find the value of the expression -225 divided by -15
By means of division we can find this value.
-225/(-15) = 15
Two hundred twenty five is the numerator and fifteen is the denominator.
We get 15
When we divide a negative number by a negative number, the result is a positive number.
Therefore, -225 divided by -15 is equal to 15.
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What is the simplified form of the expression? (2x^6)(3x^(1/2)
Answers
so the answer is 6x^(13/2)
Answer:
[tex](6x^\frac{13}{2})[/tex]
Step-by-step explanation:
[tex](2x^6)(3x^\frac{1}{2})[/tex]
Use property of exponents
a^m * a^n = a^mn
When the exponents with same base are in multiplication then we add the exponents
2 times 3= 6
now we multiply x^6 and x^1/2
[tex](x^6)(x^\frac{1}{2})=x^{6+\frac{1}{2}}[/tex]
Make the denominators same to add the fractions
[tex]\frac{12}{2} +\frac{1}{2} =\frac{13}{2}[/tex]
[tex](6x^\frac{13}{2})[/tex]
Plz help me answer this
Answers
In which situation is the distance traveled proportional to time?
A car moving in stop-and-go traffic
A person biking on a trail at 12
miles per hour for 20
minutes
A baseball hit to center field
A race car slowing down after crossing the finish line
Answers
Answer: a person on a trail at 12 miles per hour for 20 minutes
Step-by-step explanation:
just go it right!!!
the diagram show a straight line ABC . Find the value of p
Answers
(13-11)/(-4-(-2))=2/-2=-1. Therefore, the equation is y=-1*x+b. Plugging it into (-4, 13), we note that 13=4+b and b=9 by subtracting 4 from both sides, making the equation y=-x+9. Plugging it into A, we get that
1 (y , the second value) = -x+9. Subtracting both sides by 9, we get 1-9=-x and -8=-x. Multiplying each side by -1, we get x=8
Find the probability of flipping a coin and it showing heads and drawing a diamond from a standard deck of cards.
Answers
The probability of flipping a coin and it showing heads and drawing a diamond from a standard deck of cards is 1/8.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability = (number of sides with a head / number of sides of a coin) x (number of diamonds / number of cards)
1/2 x 13/54 = 1/8
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Final answer:
The probability of flipping a coin and getting heads followed by drawing a diamond from a standard deck of cards is 1/8 or 0.125.
Explanation:
The probability question involves two independent events: flipping a coin and drawing a card from a standard deck. For the coin toss, the probability of getting heads is 0.5 since a coin has two sides and both are equally likely. Now, for drawing a diamond from a standard deck of cards, there are 13 diamonds out of 52 cards, so the probability is 13/52 or 1/4.
To find the probability of both events happening, we multiply the probabilities of each event, because they are independent events. So, the probability of flipping a coin and getting heads and then drawing a diamond is (1/2) * (1/4) = 1/8 or 0.125.
f (x)=4x^2+4x+8, g (x)=4x-7 find (g*f)(x)
Answers
g*f = (2x -6)*(-4x+7) = -8x2 + 14x + 24x - 42 = -8x2 + 38x - 42
Then, (g*f)(1) = -8 (1)2 + 38 (1) - 42 = -12
FIRST CORRECT ANSWER GETS BRAINLIEST!
Answers
By pythagorean theorem, [tex]JK = \sqrt{MK^2 - MJ^2} = \sqrt{20^2 - 12^2} = \sqrt{400 - 144} = \sqrt{256} = 16. [/tex]
After that you just find the perimeter of the rectangle.
[tex]2l + 2w = 2*16 + 2*12 = 32 + 24 = 56[/tex] :)
Determine the 4th term in the geometric sequence whose first term is -2 and whose common ratio is -5
Answers
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number
We are told that a=-2 and r=-5 so:
a(4)=-2(-5)^(4-1)
a(4)=-2(-5)^3
a(4)=250
250.
To determine the 4th term in a geometric sequence, start with the first term and use the common ratio. In this case, the first term is -2 and the common ratio is -5. The formula for finding the nth term of a geometric sequence is an = a1 * r(n-1).
Identify the values: a1 = -2, r = -5, n = 4.
Substitute into the formula: a4 = -2 * (-5)(4-1).
Calculate the 4th term: a4 = -2 * (-5)3 = -2 * (-125) = 250.
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
Answers
to make a polynomial you need to do ax2 + bx + c = 0
4xy^2 + 8x^2y = 2xy( y + 3x)
here you go two forms
but remember here they are asking to make the GCF 2 so the powers can't go greater than 2
hope this helps
Complete the steps in order to write the inverse of f(x) = x + 5
Answers
To find the inverse of a function, replace f(x) with y, swap x and y, then solve for y. Thus, the inverse of f(x) = x + 5 is f^-1(x) = x - 5.
Explanation:To find the inverse of a function like f(x) = x + 5, we use the following steps:
Replace the function notation f(x) with y. So, we get y = x + 5.
Swap the roles of x and y. This changes the equation to x = y + 5.
Solve for y to get the inverse function. By subtracting 5 from both sides, we acquire y = x - 5.
This implies that the inverse of the function f(x) = x + 5 is f-1(x) = x - 5.
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Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parentheses 6 minus 6 i close parentheses.
Answers
randy made a business trip of 204 miles. he averaged 52 mph for the first part of the trip and 50 mph for the second part. if the trip took 4 hours, how long did he travel at each rate?
Answers
x+y = 4
x=4-y
52x+50y=204
52(4-y)+50y=204
208-52y+50y=204
208-2y=204
-2y=-4
y=2
x= 4-2=2
check 52*2=104
50*2 = 100
104+100=204
so he traveled 2 hours at both 50 and 52 mph
The following information is obtained from two independent samples selected from two normally distributed populations.
n1 = 18 x1 = 7.82 σ1 = 2.35
n2 =15 x2 =5.99 σ2 =3.17
A. What is the point estimate of μ1 − μ2? Round to two decimal places.
B. Construct a 99% confidence interval for μ1 − μ2. Find the margin of error for this estimate.
Round to two decimal places.
Answers
A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:
μ1 − μ2 = x1 – x2 = 7.82 – 5.99
μ1 − μ2 = 1.83
B. The formula for confidence interval is given as:
Confidence interval = (x1 –x2) ± z σ
where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58
and σ is calculated using the formula:
σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]
σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]
σ = 0.988297
Going back to the confidence interval:
Confidence interval = 1.83 ± (2.58) (0.988297)
Confidence interval = 1.83 ± 2.55
Confidence interval = -0.72, 4.38
The tickets in a box are numbered from 1 to 20 inclusive. If a ticket is drawn at random and replaced, and then a second ticket is drawn at random, what is the probability that the sum of their numbers is even?
Answers
Answer:
1/2
Step-by-step explanation:
no guarantees but the guy before me said 10/20 and of course if you divide 10 and 20 you get 0.5, and 0.5 is equal to 1/2.
A survey has a margin of error of 4%. In the survey, 67 of the 110 people interviewed said they would vote for candidate A. If there are 9570 people in the district, what is the range of the number of people who will vote for candidate A?
Answers
67/100 = x/9570
x denotes the number of voters for candidate A when the actual number of total voters are 9,570. Solving for x, we find that x = 6,411.9. In approximation, that is equal to 6,412 voters.
However, you should take not of the margin of error. It means that the number of voters is not exactly 6,412. There is a room for the range which is 4%.
6,412(0.04) = 256
So, the number of voters is 6,412+/-256.
6,412 + 256 = 6,668
6,412 - 256 = 6,156
Thus, the range of voters is between 6,668 to 6,156 people.
what else would you need yo show that ABC DEF by ASA APEX ?
Answers
You are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). A small square of the same size is cut from each corner, and each side folded up along the cuts to from a box with no lid. 1. Anya thinks the cut should be 1.5 inches to create the greatest volume, while Terrence thinks it should be 3 inches. Explain how both students can determine the formula for the volume of the box. Determine which student's suggestion would create the larger volume. Explain how there can be two different volumes when each student starts with the same size cardboard. 2. Why is the value of x limited to 0 in. < x < 4.25 in.?
Answers
We can solve for the value of x using the formula:
V = l w h
where,
h = x the size of the cut since it would form the walls of the rectangle
w = 8.5 – 2x = it is subtracted by 2x since two sides will be cut
l = 11 – 2x
Substituting:
V = x (8.5 − 2x) (11 − 2x)
Expanding the expression:
V = 93.5 x – 39 x^2 + 4 x^3
To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:
dV / dx = 93.5 – 78 x + 12 x^2
0 = 93.5 – 78 x + 12 x^2
We get:
x ≈ 1.585 in and x ≈ 4.915 in
Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.
There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.
It is restricted to 0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.
solve the system of equations using elimination. 3p+9q=6 5p-5q=30
Answers
15p+45q=30
Solving this will get 60p=300 so p=5
Plug it in and we get 15+9q=6 so q=-1
The answer is p=5 q=-1
5p-5q=30
3(5)+9(-1)=6
15-9=6✔
5(5)-5(-1)=30
25+5=30✔
p=5
q=-1
If trap is an isosceles trapezoid, what is the value of x
Answers
Answer:
Option E ⇒ x = 19
Step-by-step explanation:
See the attached figure.
TRAP is an isosceles trapezoid
The shown angles are supplementary angles
So, the sum of (5x+9) and (4x) is 180
So, 5x+9 + 4x = 180
solve for x
9x + 9 = 180
9x = 180-9 = 171
x = 171/9 = 19
The answer is option E
Rounded to the nearest some, What is the greatest amount of money that rounds to $105.40? What is the least amount of money that rounds to $105.40?
Answers
The greatest amount of money that rounds to $105.40 is $105.41, while the least amount that rounds to $105.40 is $105.39.
Explanation:The greatest amount of money that rounds to $105.40 would be the amount slightly greater than $105.40. Since rounding to the nearest cent, we would look at the hundredths place. Any amount greater than $105.405 would round up to $105.41. So the greatest amount of money that rounds to $105.40 would be $105.41.
The least amount of money that rounds to $105.40 would be the amount slightly less than $105.40. Again, looking at the hundredths place, any amount less than $105.395 would round down to $105.39. So the least amount of money that rounds to $105.40 would be $105.39.
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Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
Answers
x^2-x-2=0
a=1
b=-1
c=-2
How do you turn 1/8 into a fraction
Answers
hope it helps, xx
A girl wants to count the steps of a moving escalator which is going up. If she is going up on it, she counts 60 steps. If she is walking down, taking the same time per step, then she counts 90 steps. How many steps would she have to take in either direction, if the escalator were standing still?
Answers
So let,
V the speed of the girl per step
v the speed of the escalator per step
L the length between ground and floor in number of steps
V*60+v*60 = L => V+v=L/60
V*90-v*90 = L => V-v=L/90
By adding the equations V+v = L/60 and V-v=L/90 we get:
2V = L(3+2)/180
V = 5L/360
V = L/72
Time to climb (in steps) with v=0 (escalator standing still) is:
V*t = L
t = L/V
t = L/(L/72)
t = 72 steps
The girl will count 72 steps.
When adding or subtracting two decimals, what is the first thing you must do
Answers
What is the simplified form of √10000x^64 ? 5000x^32 5000x^8 100x^8 100x^32
Answers
Answer:
Option (d) is correct.
[tex]\sqrt{10000x^{64}}=100x^{32}[/tex]
Step-by-step explanation:
Given : Expression [tex]\sqrt{10000x^{64}}[/tex]
We have to write a simplified form of the given expression [tex]\sqrt{10000x^{64}}[/tex]
Consider the given expression [tex]\sqrt{10000x^{64}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]
[tex]=\sqrt{10000}\sqrt{x^{64}}[/tex]
Factor 10000 as [tex]10000=100^2[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
[tex]\sqrt{100^2}=100[/tex]
also, [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
We have,
[tex]\sqrt{x^{64}}=x^{\frac{64}{2}}=x^{32}[/tex]
Thus, [tex]\sqrt{10000x^{64}}=100x^{32}[/tex]
Answer: D. 100x32
Step-by-step explanation:
What is the constant term in the expression 4x3y + 8x2 + 6x + 5? (Input a numeric value only.)
Answers
Answer:
Answer is 5.
Step-by-step explanation:
The given expression is :
[tex]4x^{3}y+8x^{2} +6x+5[/tex]
We have to tell the constant term here.
A constant term is one that remains same and does not change with change in values of x and y.
Here, other terms contains either x or y or both, that will change with change in x and y. Only 5 is the single term that will remain constant.
So, the answer is 5.