The point (1,1) represents 1+i in the two dimensional complex plane. Absolute value of 1+i = [tex]\sqrt{2}[/tex].
Given the complex number, z = 1+i
The general form of a complex plane is x+iy, where x and y are real numbers.
We can place any complex number into a two-dimensional complex plane with two axes - X and Y.
For z = 1+i, x = 1 and y = 1. So the point (1,1) will represent z = 1+i in the two dimensional complex plane.
The absolute value of a complex number z = x+iy is given by ,
|z| = [tex]\sqrt{x^2+y^2}[/tex]
So for z = 1+i, |z| = [tex]\sqrt{1^2+1^2}=\sqrt{2}[/tex]
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y is less than -2 in inequality notation
Given statement 'y is less than -2 ' in inequality notation would be, y < -2
In this question we have been given a statement 'y is less than -2'
We need to write given statement in inequality notation.
We know that, an inequality is a mathematical expression where two non-equal mathematical expressions or numbers are compared.
We know that we use '<' notation for less than.
Consider given statement:
y is less than -2.
⇒ y < -2
Therefore, given statement 'y is less than -2 ' in inequality notation would be, y < -2
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Convert 5.764764764 ... to a rational expression in the form of a over b , where b ≠ 0
If x = 5.764764764…, then 1000x = 5764.764764764…, so that
1000x - x = 5764.764764764… - 5.764764764…
999x = 5759
x = 5759/999
Which of the following describes a situation in which the total distance a baseball player travels is zero meters from his starting point? (5 points)
Situation (B) best describes how a baseball player travels a total distance of zero meters from his starting point, that is, the player runs 3 meters forward and then 3 meters in the opposite direction.
What is the distance?Distance is a numerical or quantifiable measurement of the distance between two objects or points. The distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over"). Because spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used figuratively to mean a measurement of the amount of difference between two common pieces (such as statistical distance between probability distributions or edit distance between text strings) or a degree of detachment (as exemplified by the distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such notions of distance, both physical and metaphorical.According to the options:
Options (A), (C), and (D) is wrong as there the basketball travels some sought distance from the starting point. It is only in option (B) in which the total distance of the baseball player comes to 0 as he runs 3 meters forward and then runs 3 meters in the opposite direction.Therefore, situation (B) best describes that the total distance a baseball player travels is zero meters from his starting point that is, the player runs 3 meters forward and then runs 3 meters in the opposite direction.
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The complete question is given below:
Which of the following describes a situation in which the total distance a baseball player travels is 0 meters from his starting point? (5 points)
a) The player runs 4 meters forward and then runs 3 meters in the opposite direction.
b) The player runs 3 meters forward and then runs 3 meters in the opposite direction.
c) The player runs 3 meters forward and then runs 4 meters in the opposite direction.
d) The player runs 3 meters forward and then runs 0 meters in the opposite direction.
What are the values of (-2)^4 and -2^4?
8 and -8
16 and 16
-8 and -8
16 and -16
A portion of the periodic table is shown below. Which column of elements would be most likely to chemically combine with sodium in a 1:1 ratio?
Step-by-step explanation:
chlorine cl when combines with sodium na
Nacl will form so chlorine
√-100=____ + _____i
Answer:
[tex]10 + 1i[/tex]
Step-by-step explanation:
[tex]i = \sqrt{-1}[/tex]
[tex]\sqrt{-100} = \sqrt{100} * \sqrt{-1}[/tex]
[tex]\sqrt{-100} = 10 + 1i[/tex]
Please help me it doesn't have to be quickly just help
Answer:
3 to the power of 3
Step-by-step explanation:
Answer:
1. 8x
2.4x^2
3.3^x
Step-by-step explanation:
I took the test
HELPP PLEASE 70 POINTS
Can please anyone help me with this
Answer:
Step-by-step explanation:
im not sure but yea
The diameter of a cylindrical container is 22cm. If the volume of the container is 1331cm³, calculate its height.
Answer:
3.5cm
Step-by-step explanation:
Vol=πr²h
Transposing for h,=vol÷πr²
where r=22/2=11cm and taking π=3.142
h=1331/(3.142×(11)²)=3.5cm
the teacher separated her class of fifty-eight students into two groups. one group has 6 more than thrice as many students as the other group. how many students are in each group?
Students in one group is 45
Students in another group is 13
teacher separated her class of fifty-eight students into two groups
Number of groups =2
one group has 6 more than thrice as many students as the other group
Let one group has x students
another group has y students
x+ y = 58 . . . . . 1
x= 6+3y
Substitute x= 6+3y in . . . 1
6+3y +y = 58
4y=52
y=13
x=6+3y=6+3(13)
= 6+39
= 45
Students in one group is 45
Students in another group is 13
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Convert the decimal below to a fraction in simplest form.
0.166
(166÷2)
______
(1000÷2) = 83/500
The quotient of 24 and d
Answer:
The quotient of 24 and d would be [tex]\frac{24}{d}[/tex]
Step-by-step explanation:
Quotient is the answer of a division problem. So, you would divide 24 by d.
Do you think it would be better to use breaking apart in the distributive property or compensation to find the product of five times 328? explain why and show how to find the product.
Yes it would be better to use breaking apart in the distributive property or compensation to find the product of 5 x 328 .
what is distributive property?
This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding or substracting the results together .like in subtraction A(B-C)= AB-AC
In other words, an equation of the type A (B+C) can be solved as A (B+C) AB+AC in accordance with the distributive property.
This characteristic also holds for subtraction.
5 x 328
= 5(300+28)
= 5 x 300 + 5 x 28
= 1500 + 140
= 1640
Hence, it would be better to use breaking apart in the distributive property or compensation to find the product of 5 x 328 .
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A rectangle PQRS is dilated about the origin to form a new rectangle P ’Q ’R ’S ’, as shown. What is the scale factor of the dilation?
Answer:
3
Step-by-step explanation:
Point p was on -1, 2
Point p' was on -3, 6
IF you divde p' by p you get 3, so the dialation is 3.
A rectangular hotel room has a perimeter of 72 feet. Its area is 320 square feet. What are the dimensions of the room?
Answer
Step-by-step explanation:
Xochitl earned $94.80 at her job when she worked for 4 hours. What was her hourly
wage, in dollars per hour?
Answer: $23.70/hr
Step-by-step explanation:
x= hourly wage
4= the number of hours worked
$94.80=total earned
4x=$94.80
x=$94.80/4
x= $23.70/hr
She earned $23.70 per hour
Jill's plant is 15 inches tall and grows 0.25 inches each week, Mox's plant is 18 inches fall and grows 0.25 inches each week. At this rate, will Jill's plan! ever be faller than Max's Explain
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -2 ≤ x ≤ 3? -10 Go -8 -6 -4 -2 100 80 60 20 -20 -40 -60 -80 -100 2 8 10
Answer:
1 + 1 = 2 a i esta la respjesta
Step-by-step explanation:jijiji
33/25 as a decimal rounded to the nearest tenth
Answer:1.3
Step-by-step explanation:
33/22=1.32
Round to nearest 10th
1.32=1.3
Kara's Custom Tees experienced fixed costs of $800 and a variable cost of $3 per shirt. Write an equation that can be used to determine the total costs encountered by Kara's Custom Tees when x shirts are produced. Then, determine the total cost of producing 75 shirts.
The total cost of producing 75 shirts will be $1050.
It is given that Kara's Custom Tees experienced fixed costs of $800 and variable cost of $3 per shirt.
We have to find an equation and also the total cost of producing 75 shirts.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , multiplication , etc.
As per the question ;
Fixed cost = $ 800
and
Variable cost per shirt = $3.
If x shirts are produced then ; then equation will be ;
= 800 + 3x
And total cost of 75 shirts will be ;
= 800 + 3 × 75
= 800 + 225
= $ 1050
Thus , the total cost of producing 75 shirts will be $1050.
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Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
The equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation of the parabola is y = 2 · x · (x - 4).
What is the equation of the parabola seen in a graph?
Herein we find a representation of a quadratic function on a Cartesian plane, whose formula in vertex form is presented below:
y - k = C · (x - h)²
Where:
(h, k) - Vertex of the parabola.C - Vertex constantBy direct inspection we find that the equation of the parabola has a vertex at (h, k) = (2, - 8) and the point (x, y) = (4, 0). Then, the vertex constant is:
C = (y - k) / (x - h)²
C = (0 + 8) / (4 - 2)²
C = 8 / 4
C = 2
Then, the equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation is determined by algebra:
y + 8 = 2 · (x - 2)²
y = 2 · (x - 2)² - 8
y = 2 · (x² - 4 · x + 4) - 8
y = 2 · x² - 8 · x + 8 - 8
y = 2 · x² - 8 · x
y = 2 · x · (x - 4)
The factored form of the equation of the parabola is y = 2 · x · (x - 4).
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annie measured a city park and made a scale drawing. the scale of the drawing was 1 millimeter : 4 meters. the soccer field is 28 millimeters long in the drawing. how long is the actual field?
Answer:
Step-by-step explanation:
34 millimeter
what’s the answer to this???
you have to find where it increases, decreases, and where it’s constant….
help..
Diana usually drives at an average rate of 30 mph. If Diana drives at an average rate of x mph, how long will it take her to get to Tony's house?
Diana drives for two hours at a speed of 30 mph, covering a total distance of 60 miles to get to Tony's house.
What exactly is average speed?Average speed is described as the ratio of a body's total distance traveled to the total time required to reach its destination.The total distance covered by the element in a given time interval is the average speed. A scalar quantity is average speed. It is depicted by magnitude and lacks direction.Diana drives for two hours at a speed of 30 miles per hour.
To calculate the distance she will travel
Average speed = total distance / total time
Total time = two hours and the average speed = 30 mph
30 mph = total distance / two hours
Total distance = 30 × 2
Total distance = 60 miles
Therefore, Diana drives for 2 hours at a speed of 30 mph, so the total distance traveled is 60 miles to get to Tony's house.
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a medical researcher obtains a sample of adults suffering from diabetes. she randomly assigns people to a treatment group and to a placebo group. the treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. at the end of three months the patients' symptoms are evaluated.
This is an example of an experimental study since the researcher chose who would get medicine and who would receive a placebo.
What is Experimental Study?a quantitative research technique that controls other pertinent variables while observing the effects of changes in the study's key variables The Impact of Product Modularity on Supplier Integration: A Multi-Objective Approach2 provides further information. In experimental research, participants are randomly divided into distinct groups (such as experimental and control groups) in order to ascertain the causal relationship between a given condition (an independent variable) and a certain outcome (dependent variable).An illustration of an experimental research on the subject would be to assign people at random to either spend 10 minutes on their page as the experimental treatment, or spend the same amount of time on other websites (control group).
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what is the answer for b?
Answer:
4
Step-by-step explanation:
2+2=4 dummy
whats the pattern of 1,1,11,6,6,16,11,11,21,16
The pattern is 1, 1, 11, 6, 6, 16, 11, 11, 21, 16, 16, 26.
Given,
The pattern: 1, 1, 11, 6, 6, 16, 11, 11, 21, 16.
Here,
First and second term:
1,1 = same number repeat for two times.
Third term:
11 = preceding term + 10
That is, 1 + 10 = 11: That is the third term.
As follows:
Fourth and fifth term:
6, 6 = same number repeat for two times.
Sixth term:
6 + 10 = 16
Seventh and eighth term:
11, 11 = same number repeat.
Ninth term:
11 + 10 = 21
Tenth term is given: 16
Now we have to find eleventh and twelth terms:
Tenth and eleventh should be same number repeat for two times:
16, 16
Twelth term:
16 + 10 = 26.
Now we can complete the pattern:
1, 1, 11, 6, 6, 16, 11, 11, 21, 16, 16, 26.
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A town's population is 42,975 . About 125 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
The number of months when they will be equal is 45 months.
How to calculate the equation?The equation for the first town will be:
= 42975 + 125x
The equation for the second town will be:
= 45225 + 175x
The number of months when the populations of the towns will be equal will be:
42975 - 125x = 45225 - 175x
- 125x + 175x = 45225 - 42975
50x = 2250
x = 2250 / 50
x = 45
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On a shopping trip, Jeffery buys 3 sweaters and 5 pairs of jeans for $160. Eric also purchases 6 sweaters and two pairs of jeans for the same price. What is the difference in price of a sweater and one pair of jeans?
Answer:
Step-by-step explanation:
It would most likely be 0, but I am not sure.