Plot the complex number and find its absolute value 2−i
Answers
The absolute value of the complex number is √2. The graph is plotted and attached.
What is the complex number?A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given complex number as;
2−i
The absolute value is found as;
[tex]\rm R = \sqrt{1^2 +(-1)^2 } \\\\ R = \sqrt 2[/tex]
The graph for the complex number is attached.
Hence the absolute value of the complex number is √2.
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Related Questions
*Will give 30pts*Consider function f. f(x)=2x^2.What is the value of (f•f)(x)?
Answers
Answer:
[tex]\textbf {B}[/tex]
Step-by-step explanation:
f(x) = 2x²
f [f(x)]
f [2x²] = 2(2x²)²
f[f(x)] = 2(4x⁴)
f[f(x)] = 8x⁴
3(x-5)² +14(x-5)-24
Answers
Answer:
3x^{2} -16x-19
Step-by-step explanation:
If we are going to be simplying this problem, then we need to take it step by step.
Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.
Answer:
(3x - 19) • (x + 1)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((3•((x-5)2))+14•(x-5))-24
STEP
2
:
Equation at the end of step 2
(3 • (x - 5)2 + 14 • (x - 5)) - 24
STEP
3
:
Trying to factor by splitting the middle term
Factoring 3x2-16x-19
The first term is, 3x2 its coefficient is 3 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is -19
Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57
Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .
-57 + 1 = -56
-19 + 3 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3
3x2 - 19x + 3x - 19
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-19)
Add up the last 2 terms, pulling out common factors :
1 • (3x-19)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x-19)
Which is the desired factorization
The dot plot shows the number of books lent by a school library during a 10-day period.
What was the mean absolute deviation of the number of books?
F. 0
G.
H.
J.
1.04
1.96
..
23 24 25 26 27 28 29 30 31 32 33
2.19
Answers
The mean absolute deviation of the number of books is 1.84
How to determine the mean absolute deviation?The dot plot of the number of books is in the attached figure.
From the figure, we have:
x f
1 1
2 2
3 2
4 3
5 1
6 2
7 3
8 1
Start by calculating the mean using:
[tex]\bar x= \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}[/tex]
Evaluate the sum and products
[tex]\bar x= \frac{69}{15}[/tex]
Divide
[tex]\bar x= 4.6[/tex]
The mean absolute deviation is then calculated as:
[tex]|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}[/tex]
So, we have:
[tex]|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}[/tex]
Evaluate the absolute difference
[tex]|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}[/tex]
Evaluate the sum of products
[tex]|\bar x|= \frac{27.6}{15}[/tex]
Divide
[tex]|\bar x|= 1.84[/tex]
Hence, the mean absolute deviation of the number of books is 1.84
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A shop advertises a 24% off sale. The coat sold for $258 fins the decrease in price and the sale price
Answers
Answer:
339.47
Step-by-step explanation:
100 - 24 = 76
258 = 76 percent
3.39473684211 = 1 percent
339.47 = 100 percent
Answer:
The decrease in price is $61.92
The sale price is $196.08
Step-by-step explanation:
24% × 258 = 61.92
258 decrease 24% =
258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08
The volume of a cubical box is
54.872 cm3. The length of the side of
the box is
(b) 3.6 cm
(c) 3.8 cm
(a) 3.4 cm
(d) 3.2 cm
Answers
The sides length of the cubical box is 3.8 cm if the volume of a cubical box is 54.872 cm³ option second is correct.
What is a cube?It is defined as three-dimensional geometry that has six square faces and eight vertices.
We have a volume of a cubical box is 54.872 cm³
V = 54.872 cm³
As we know the volume of the cube:
V = side³
54.872 = side³
Taking cube root on both sides:
side = 3.8 cm
Thus, the sides length of the cubical box is 3.8 cm if the volume of a cubical box is 54.872 cm³ option second is correct.
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In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.
Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3.
To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and
∠DFE is 4 times greater than ∠GFH.
∠FHG is One-fourth the measure of ∠FED.
∠DFE is congruent to ∠GFH.
∠FHG is congruent to ∠EFD.
Answers
To prove that △DFE ~ △GFH by SAS similarity theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.The correct answer is option C.
The image of the triangle is attached with the answer below:-
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:
By comparing ΔDEF and ΔGFH
DF = DG + GF
= 12 + 4
DF = 16
Also,
EF = EH + HF
= 9 + 3
EF = 12
Comparing the sides of ΔDEF and ΔGFH, we have;
[tex]\dfrac{DF}{GF}[/tex] = [tex]\dfrac{EF}{HF}[/tex]
[tex]\dfrac{16}{4}=\dfrac{12}{3}[/tex]
4 = 4
Thus, the two triangles have similar sides.
Comparing the included angle <DFE and <GFH, then;
∠DFE is congruent to ∠GFH
Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;
[tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
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Answer:
C
Step-by-step explanation:
Edg
Tim earns 96pounds for 16 hours. Tim earns 'time and a half' for overtime. he works 4 hours of overtime in addition to his normal 16 hours. how much does he earn altogether
Answers
find hourly rate:
96 / 16 = 6 pounds per hour
6 x 1.5 = 9 pounds per hour for overtime.
9 x 4 = 36 pounds
96 + 36 = 132 pounds total
196/16 = 6 per hr
overtime = 6*1.5=9
96 + (9*4) = 132
Suppose a population parameter is 0.8, and many large samples are taken
from the population. If the sample proportions are normally distributed, with
95% of the sample proportions falling between 0.684 and 0.916, what is the
standard deviation of the sample proportions?
Answers
Using the Empirical Rule, it is found that standard deviation of the sample proportions is of 0.058.
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.0.684 and 0.916 is within 2 standard deviations of the mean(below and above), hence there are 4 standard deviations between these measures, so:
4s = (0.916 - 0.684)
s = (0.916 - 0.684)/4
s = 0.058.
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The graphs below have the same shapes. What is the equation for the red graph?
Answers
The equation for the red graph will be g(x) = x² + 3.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function f(x) is given below.
f(x) = x²
Then the function g(x) will be given as
g(x) = x² + 3
Then the equation for the red graph will be g(x) = x² + 3.
The missing graph is given below.
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In the following month 10% savings on other costs are expected. What is the total other costs target for next month for the five locations
Answers
Answer:
The given question is incomplete. The graphs for the question are attached below.
Total savings on other costs expected in the following month is 13,950.
Total other costs targeted for next month for the five locations:
Washington Place = 14,850
Lincoln Square = 9,900
Millienium Concourse = 18,000
The old mill = 13,500
CWG Tenton = 0
Step-by-step explanation:
According to the graphs, there are two parts to this question
1. In the following month, 10% savings on other costs are expected.
The graph is attached below for reference
10% savings on other costs are expected in the following month:
=> (4,000 + 2,000 + 5,000 + 2,000 + 2,500) * (1-10%)
=> 15,500 * [tex](1-\frac{10}{100})[/tex]
=> 15,500 * [tex]\frac{90}{100}[/tex]
=> 13,950
Total savings on other costs expected in the following month is 13,950
2. Total other costs target for next month for the five locations are:
Washington Place = 6,000+3,000+3,500+ 4,000 = 16,500 * 0.9 = 14,850
Lincoln Square = 5,000+ 2,000+ 2,000+2,000= 11,000 * 0.9 = 9,900
Millienium Concourse =7,000+3,000+5,000+5,000= 20,000 * 0.9 = => 18,000
The old mill = 6,000+ 5,000+ 4,000=15,000 * 0.9 = 13,500
CWG Tenton = 0 * 0.9 = 0
Total other costs target for next month for the five locations:
Washington Place = 14,850
Lincoin Square = 9,900
Millienium Concourse = 18,000
The old mill = 13,500
CWG Tenton = 0
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A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is
Answers
Answer:
0.5km or 500m
Step-by-step explanation:
Given Distance = Speed x Time
In this case, we should use the difference in speed and time of the 2 scenarios.
Difference in Time = 20 mins(late) + 10 mins(early)
= 30 mins or 0.5 hour
Difference in Speed = 4km/h - 3km/h = 1km/h
Distance = 1km/h x 0.5 hr = 0.5km or 500m.
Which expressions are equivalent to 9b?
Choose all answers that apply
A. b+2(b+2b)
B. 3b+b
C. 2(2b)
Answers
Answer:
A. b+2(b+2b)
b + 2b + 4b = 7b
B. 3b + b = 4b
C. 2(2b) = 4b
None of them are equal to 9b
Answer:
[tex]\fbox {None}[/tex]
Step-by-step explanation:
A
b + 2(b + 2b)b + 2(b) + 2(2b)b + 2b + 4b7bB
3b + b4bC
2(2b)4b
Given the following equation of a circle in general form, find the equation in standard form by completing the square.
4x² + 8x + 4y² + 32y +52 = 0
Provide your answer below:
Answers
The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have an equation that represents the circle:
4x² + 8x + 4y² + 32y +52 = 0
Divide by 4 on both the sides:
x² + 2x + y² + 8y + 13 = 0
x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0
x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13
(x + 1)² + (y + 4)² = 4
(x + 1)² + (y + 4)² = 2²
Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
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question is in the image below please help
Answers
Answer:
p= 80
Step-by-step explanation:
p+8 = 8 x 11
p+8 = 88
p= 88-8
p= 80
Andres rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase
describes the probability that he will roll a number greater than or equal to 1?
Answers
I don't know what the word or phrase is, but with the parameters you've given, 100%
two sides and an angle are given below. determine whether the given information results in one triangle, two triangles, or no triangle at all. solve any resulting triangle(s). b = 8, c= 7, b = 170°
Answers
Answer:
A. single triangle. C = 8.74°, A = 1.26°, a = 1.01
Step-by-step explanation:
When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.
Law of SinesThe law of sines tells us the sides and angles have the relation ...
sin(A)/a = sin(B)/b = sin(C)/c
We can use this first to find angle C:
sin(C) = c/b·sin(B)
C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°
∠C ≈ 8.74°
Remaining measuresNow that we know two angles, we can find the third:
A = 180° -B -C = 180° -170° -8.74° = 1.26°
∠A = 1.26°
Using the law of sines again, we can find the measure of side 'a'.
a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346
The measure of segment 'a' is about 1.01 units.
__
Additional comment
If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.
Determine the distance between two points. (9,-9) and (-6,-7)
Answers
1. EL precio a la venta de una impresora de inyección de tinta es de $285.000 incluida una Ganancia del 35%. ¿cuánto le cuesta a la tienda cada impresora?
Answers
Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.
¿Cómo encontrar el precio de una impresora sin ganancia?
En el enunciado tenemos el precio de una impresora para el consumidor, el cual comprende el dinero invertido por vendedor más la ganancia esperada. Este indicador observa la siguiente fórmula:
C' = C · (1 + r/100) (1)
Donde:
C - Coste asumido por el vendedor, en unidades monetarias.C' - Coste para el consumidor, en unidades monetarias.r - Tasa de ganancia, en porcentaje.Si sabemos que C' = $ 285.000 y r = 35 %, entonces el coste asumido por el vendedor es:
285.000 = 1,35 · C'
C' ≈ 211.111,11
Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.
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Solve: 8 + x/3 = 1/6 (x-6) -1
A. x = 60
B. x = -60
C. x = -36
D. There are infinitely many solutions
Answers
Answer: B -60
Step-by-step explanation: When you plug in -60 into the equation it all equals out into -12 = -12, which is true. All of the other solutions don't work.
Answer:
B. x = -60
Step-by-step explanation:
8 + x/3 = 1/6 (x-6) - 1
Multiply both sides by 6.
48 + 2x = x - 6 - 6
x = -12 - 48
x = -60
Jacob invests a sum of money in a savings account with an interest rate of 9% compounded
continuously. After 6 years, the balance reaches $11,303.34. What was the amount of the initial
investment?
Answers
Answer:
6587
Step-by-step explanation:
Formula is
A= P(1+r/n)^nt
A = 11303.34
r = .09
n = 365 compounded daily
t = 6 years
solve for P
What is the slope of the line shown below?
A. 2/7
B.-7/2
C.-2/7
D. 7/2
Answers
(WORK SHOWN BELOW)
Answer:
-2/7
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 1-3)/( 3 - -4)
= (1-3)/( 3+4)
= -2/7
Using a rounded version of a conversion ratio allows for a quick estimate of a unit conversion
using mental math or paper and pencil (no calculator or phone). Show an example of a unit cuz
conversion estimation using this strategy.
Answers
The conversion ratio that can be illustrated will be converting 2030m to kilometers.
How to illustrate the conversion?The unit conversion that can be illustrated based on the information can be convert 2030m to kilometers.
It should be noted that 1000 meters makes 1 kilometer. Therefore, rounding up 2030m mentally will be 2000m and the conversion to kilometers will be:
= 2000/1000
= 2 km
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jessica has 4/8 of a bottle of roitussun on hand the pharmacist instructs to reduce it by 1/2 how much robitussun does the pharmacist need to prepare the prescription
Answers
Answer:
1/4
Step-by-step explanation:
4/8 = 1/2
1/2 x 1/2 = 1/4
Which relation below is NOT a function?
A. {(-2, 4), (1,3), (0,4)}
B. {(5,5), (4,4), (3,3) }
C. {(-4,0), (-7,0), (11, 0)}
D. {(1,4), (2,5) (1,7)}
Answers
D has two possible values of y when x = 1 therefore it is NOT a function
ON ECRIT SUR LES DUN DE EQUILIBRE CHACUNE DES LETTRES AMURES
Answers
Answer:
oh.
Step-by-step explanation:
How to translate a graph of y= absolute value of x to obtain the graph of y= absolute value of x-6
Answers
Answer: Translate the graph of y=|x| 6 units to the right.
The ratio of the number of laps Andy swam to the number of laps Ben swam
on the first day of a swimming lesson was 5: 6. The ratio of the number of
laps Andy swam to the number of laps Ben swam on the second day of the
swimming lesson was 9: 5. If Ben swam 33 laps on both days, how many laps
did Andy swim on the second day of the swimming lesson?
Answers
Answer:
10
Step-by-step explanation:
Three out of every 20 students in ms. jones’ Math class earned a grade of A. What percent of the students earned a grade of A?
Answers
Answer:
15%
Step-by-step explanation:
3/20x100=15
Which expressions are completely factored?
30a^6-24a^2=3a^2(10a^4-8)
Answers
The factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].
The given expression is [tex]30a^{6} -24a^{2}[/tex].
We need to factorise the given expression.
What are the factors?Each of these numbers and expressions is referred to as a factor of algebraic expressions if it is possible to express algebraic expressions as the product of numbers, algebraic variables, or algebraic expressions.
Now, [tex]30a^{6} -24a^{2}=6a^{2} (5a^{4}-4 )[/tex]
Therefore, the factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].
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What mistake did he make ?! I need everybody Anwser
Answers
Answer:
he subtracted the wrong coordinates to find the horizontal leg
Step-by-step explanation:
It should be 4-(-3) but he labeled 4-(-1)