Given:
There are given the complex equation:
[tex]2(1-i)z^2+(1+i)z+3(1-i)=0[/tex]Explanation:
To find the value, we need to put the standard value of z into the above-given complex function:
[tex]\begin{gathered} 2(1-\imaginaryI)z^2+(1+\imaginaryI)z+3(1-\imaginaryI)=0 \\ 2(1-\imaginaryI)(x+yi)^2+(1+\imaginaryI)(x+yi)+3(1-\imaginaryI)=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2(1-\imaginaryI)(x+y\imaginaryI)^2+(1+\imaginaryI)(x+y\imaginaryI)+3(1-\imaginaryI)=0 \\ (2x^2-2y^2+4xy+x-y+3)+i(-3+x+y-2x^2+2y^2+4xy)=0 \end{gathered}[/tex]Then,
[tex](2x^2-2y^2+4xy+x-y+3)+\imaginaryI(-3+x+y-2x^2+2y^2+4xy)=0+0i[/tex]So,
[tex]\begin{gathered} (2x^2-2y^2+4xy+x-y+3)+\imaginaryI(-3+x+y-2x^2+2y^2+4xy)=0+0i \\ 2x^2-2y^2+4xy+x-y+3=0 \\ -3+x+y-2x^2+2y^2+4xy=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} x=0,y=-\frac{3}{2} \\ x=0,y=1 \end{gathered}[/tex]Final answer:
Hence, the value of the given complex function is shown below:;
[tex]\begin{gathered} z=-\frac{3}{2}i \\ z=i \end{gathered}[/tex]2/3×4/5 in fraction bar
Answer:
8/15
Step-by-step explanation:
Multiply the numerators:
2*4 = 8
Multiply the denominators:
3*5 = 15
Now we have 8/15.
This cannot be simplified, so this is our final answer.
[tex]\frac{2}{3} \times\frac{4}{5}[/tex]
Multiply numerator by numerator and denominator by denominator:
[tex]2*4=8\\3*5=15[/tex]
[tex]\frac{8}{15}[/tex] would be your final answer.
So my grades keep going down
Whats the best way to study
Answer:
Step-by-step explanation:
study
Rectangles ABCD and DEFG are congruent
AB=7cm
AD=17cm
Work out the length of CE
The length of CE is 7cm
How to determine the lengthTo determine the length, we need to consider the properties of a rectangle, we have;
It is a quadrilateralOpposite sides are known to be parallel and congruent to each otherThe interior angles are equal to 90 degreesDiagonals bisect each other at right anglesThe two diagonals have the same lengthRectangle having side lengths of x and y has the perimeter as 2x+2y unitsA rectangle with side lengths x and y has its area as: xy sin 90 = xy square unitsA diagonal of a rectangle is said to be the diameter of its circumcircleFrom the information given, we have that;
AB = 7cm
AD = 17cm
Then, line CE = line AB
But line AB = 7cm
CE = 7cm
Hence, the length is 7cm
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Help me and be a real g pls!!!
Answer: 1. C=43.96 in A=153.86 in²
2. C=56.52 in A=254.34 in²
Step-by-step explanation:
1.
R=7 in
C=2πR
C=2*3.14*7
C=43.96 in
A=πR²
A=3.14*7²
A=3.14*7*7
A=153,86 in²
2.
R
D=18 in
⇒ R=D/2
⇒ R=18/2
⇒ R=9 in
C=2πR
C=2*3.14*9
C=56.52 in
A=πR²
A=3.14*9²
A=3.14*9*9
A=254.34 in²
Find the equivalent expression using the
same bases.
(71.81)4.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
A similar expression can be found in what way?X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.
Consequently, (f + g)(4) is equal to f(4) + g(4)
If two systems of equations have the same solution, they are equivalent (s).
Simplify
(71 . 81) 4 = 287.24
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1. Graph the system of constraints and find the value of x and y that maximize the objective function.
Constraints { x ≥ 0; y ≥ 0; y ≤ 1/5 x + 2; 5 ≥ y + x
Objective Function: C = 7x - 3y
A. (0, 0)
B. (2, 3)
C. (5, 0)
D. (0, 3)
The point in the feasible region maximizes the objective function is (5, 0)
How to determine the feasible region?The given parameters are
Objective function: C = 7x - 3y
Subject to (i.e. the constraints)
x ≥ 0, y ≥ 0
y ≤ 1/5x + 2, 5 ≥ y + x
Next, we plot the graph of the constraints (see attachment)
This is done by entering the inequalities in a graphing calculator
From the graphing calculator, we have the feasible regions to be
(5, 0), (2.5, 2.5) and (0, 5)
Substitute (5, 0), (2.5, 2.5) and (0, 5) in the objective function: C = 7x - 3y
So, we have
(5, 0): C = 7(5) - 3(0)
C = 35
(2.5, 2.5): C = 7(2.5) - 3(2.5)
C = 10
(0, 5): C = 7(0) - 3(5)
C = -15
The value 35 is greater than 10 and -15
The coordinates at this value are (5, 0)
Hence, the coordinates is (5, 0)
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The measures of the interior angles of four regular polygons are shown below. Which expression best represents the measure in degrees of the interior angle of a regular polygon having n sides?
ANSWER
[tex]\frac{180(n-2)}{n}[/tex]EXPLANATION
We want to find the expression that best represents the measure of the interior angle of a regular polygon with n sides.
The general formula for finding the total angle in a regular n sided polygon is given as:
[tex]180(n-2)[/tex]Therefore, to find the measure of each interior angle of the polygon, we have to divide the total angle by the number of sides.
That is:
[tex]\frac{180(n-2)}{n}[/tex]Hence, that is the expression that best represents the measure in degrees of the interior angle of a regular polygon having n sides.
A box of cereal states that there are
78 calories in a
3
4
-cup serving. What is the unit rate for calories per cup? How many calories are there in
4 cups of the cereal?
The unit rate for the cereal is 104 calories per cup and there are 416 calories in 4 cups
How to determine the unit rate for the cereal?From the question, the given parameters are
Calories = 78 calories
Size of cups = 3/4-cup
The unit rate of the calories per cup is calculated as
Unit rate = Number of Calories/Size of cup
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 78/(3/4)
Evaluate the quotient
So, we have the following equation
Unit rate = 104
So, the unit rate is 104 calories per cup
For four cups of cereal, we have
Calories = 104 x 4
Evaluate
Calories = 416
So, the number of calories is 416 calories
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A grain tank on a farm is composed of a storage portion in the shape of a cylinder anda cone-shaped dispensing area at the bottom. The bottom cone portion has a slantheight of 5.5 feet. The entire exposed surface of the tank is to be painted. What is theapproximate amount of surface area that will receive the painting?8.4 ft12 ft5.5 ft
To fidn the surface area of the grain tank you need to find the area of:
Cylinder (without one of the bases as there are just one base exposed), use the next formula:
[tex]A_1=\pi\cdot r^2+h(2\pi r)[/tex]You have for the given cylinder:
h=12ft
r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft
[tex]\begin{gathered} A_1=\pi(4.2ft)^2+12ft(2\pi(\text{4}.2ft)) \\ =17.64\pi ft^2+100.8\pi ft^2 \\ =118.44\pi ft^2 \end{gathered}[/tex]Cone (without the base as the base is not exposed), use the next formula:
[tex]A_2=\pi\cdot r\cdot s[/tex]You have for the given cone:
r= 4.2ft
s= 5.5ft
[tex]\begin{gathered} A_2=\pi(4.2ft)(5.5ft) \\ =23.1\pi ft^2 \end{gathered}[/tex]The entire exposed surface of the tank is:
[tex]\begin{gathered} A_T=118.44\pi ft^2+23.1\pi ft^2 \\ \\ =141.54\pi ft^2 \\ \\ \approx444.66ft^2 \end{gathered}[/tex]The approximate amount of surface area that will receive the painting is 444.66 squared feetsUse identities to find tan, csc, sec, and cot. Where necessary, rationalize denominators
We are given:
[tex]sin\text{ }\theta=\frac{3}{5},cos\text{ }\theta=\frac{4}{5}[/tex]The tangent is defined as the ratio of the sine and the cosine:
[tex]tan\text{ }\theta=\frac{sin\text{ }\theta}{cos\text{ }\theta}[/tex]Calculating:
[tex]\begin{gathered} tan\text{ }\theta=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{5}\cdot\frac{5}{4} \\ \\ tan\text{ \theta}=\frac{3}{4} \end{gathered}[/tex]The cotangent is the reciprocal of the tangent:
[tex]\begin{gathered} \cot\theta=\frac{1}{\tan\theta} \\ \\ \cot\theta=\frac{1}{\frac{3}{4}}=\frac{4}{3} \end{gathered}[/tex]The secant is the reciprocal of the cosine:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{1}{\frac{4}{5}} \\ \\ \sec\theta=\frac{5}{4} \end{gathered}[/tex]The cosecant is the reciprocal of the sine:
[tex]\begin{gathered} \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{3}{5}} \\ \\ \csc\theta=\frac{5}{3} \end{gathered}[/tex]HELP ME PLEASE I NEED HELP I DONT KNOW HOW TO DO THIS
Answer:
convert miles to kilometers by multiply by 1.61 covert kilometers to miles by devide by 0.62(if am not wrong)
Please helppp as fast as possible 20 points ***
FIND THE DOMAIN & RANGE OF THE FUNCTION
g(x)=|x + 4|
Please helppp as fast as possible
Answer:
Domain: (−∞,∞),{x | x ∈ R}
Range: [0,∞),{y|y≥0}
Step-by-step explanation:
Morgan can make 4 cupcakes with 1 cup of flour. How many cupcakes can she make with 18 cups of flour?
Answer: She can make 72 cupcakes.
Step-by-step explanation:
Graphs present information to the reader
True
False
Answer:True
Step-by-step explanation:Graphs show information about information about the topic you are reading\researching so true they show you a lot of info on the topic.
Answer:True
Step-by-step explanation:Graphs show information about information about the topic you are reading\researching so true they show you a lot of info on the topic.
a ball was dropped from the empire state building observatory. the height of the ball in feet is described by the function f(x)=1048-16x^2 where x is time in seconds
Find the time when the ball hits the ground. round your answer to the nearest tenth
The time when the ball hits the ground is 8. 09 seconds
What is a function?A function can be defined as an expression, theorem, law, or rule that elaborates, explains or holds true for the relationship between two variables.
These variables are namely;
The dependent variablesThe independent variablesFrom the information given, we have that;
f(x) = 1048 - 16x²
Where;
f(x) is The height of the ball in feetx is the time in secondsTo determine the time, we have;
collect like terms
- 16x² = - 1048
Divide both sides by the coefficient of x²
-16x²/-16 = -1048/-16
x² = 65.5
Find the square root of both sides, we have;
x = √65.5
x = 8. 09 seconds
Hence, the value is 8. 09 seconds
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What is the area of the triangle?
Solve for x. Show your work.
Answer:
x = 35°
Step-by-step explanation:
Hello!
The sum of the two angles is 90°, so if we set the sum of the two angles to 90, we can solve for x.
Solve for x90 = 32 + 2x - 1270 = 2x35 = xThe value of x is 35°.
to
low
ing
Guess my number.
My number is a 2-digit number.
It is multiple of 5 but not a multiple
of 10.
It has an odd tens digit.
The digit total is less than 10.
What is my number?
Answer:60 and 80
Step-by-step explanation:
what is the median of this data set?[13,13,13,15,15,16,16,17,17]
Given the following data set:
[13,13,13,15,15,16,16,17,17]
Let's determine the median.
Step 1: Arrange the data points from smallest to largest.
The set is already arranged in ascending order.
[13,13,13,15,15,16,16,17,17]
Step 2:
a.) If the number of data points is odd, the median is the middle data point in the list.
b.) If the number of data points is even, the median is the average of the two middle data points in the list.
There are 9 data in the set, it is odd. The middle data is the 5th data.
[13,13,13,15,15,16,16,17,17]
The 5th data is 15.
Therefore, the median of the given set of data is 15.
PLS HELP ME< WILL APPRICIATE
Answer:
<F=74
Step-by-step explanation:
No explanation just asked my teacher
Given g(x)=−23(x−4)2+3, g ( x ) = − 2 3 ( x − 4 ) 2 + 3 , what is the value of g(–5)? *Type in your answer. g(–5) =
The output value of g( -5 ) in the function g( x ) = −23( x - 4 )2 + 3 is 417.
What is the output value of g(-5) in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
g( x ) = −23( x - 4 )2 + 3g( -5 ) = ?To find the g( - 5 ), replace all the occurrence of x with -5 in the function and simplify.
g( x ) = −23( x - 4 )2 + 3
g( -5 ) = −23( -5 - 4 )2 + 3
g( -5 ) = −23( -9 )2 + 3
g( -5 ) = −23( -9 × 2) + 3
g( -5 ) = −23( -18) + 3
g( -5 ) = ( -23 × -18) + 3
g( -5 ) = ( 414 ) + 3
g( -5 ) = 414 + 3
g( -5 ) = 417
Therefore, the output value of g( -5 ) is 417.
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Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
Option D which is [tex](3^{5} )^{2}/3^{4}[/tex] doesn’t have a value less than 1 .
What are exponential power?A number's exponent demonstrates how many times we are multiplying a given number by itself. 34, for instance, indicates that we are multiplying 3 by four. 3333 is its expanded form. The power of an integer is another term for an exponent. A whole number, fraction, negative number, or decimal are all acceptable. How frequently a number is multiplied by itself is indicated by its exponent. As 2 is multiplied by itself 4 times, 2222 might be expressed as 24, for instance. The "base" in this case is 2 and the "exponent" or "power" is 4. The general definition of xn is "x multiplied by itself n times."
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2/3×4/5 by using fraction bar step bystep
Answer: 8/15
Step-by-step explanation:
2/3 x 4/5, multiply numerators and denominators
8/15 or 0.533
For his science project, Spencer needs to photocopy his 21-page
presentation. There are 37 students in his class, and he will need copies for
each person, including his teacher. Each photocopy is $0.12.
How much will Spencer spend at the copy center?
A $77.70
B $93.24
C $95.76
D $100.3
Answer: $95.76
Explantion: Spencer spend $95.76 dollars at the copy center.
Then your done
The difference between 75% of a number and 20% of the same number is 378.4 what is 40% of that number?
Answer:
40% of the number is 275.2.
Step-by-step explanation:
I am going to call the number x.
75% of the number: 0.75x
20% of the same number: 0.2x
The difference between 75% of a number and 20% of the same number is 378.4:
This means that:
0.75x - 0.2x = 378.4
0.55x = 378.4
x = 378.4/0.55
x = 688
40% of the number:
0.4*688 = 275.2
40% of the number is 275.2.
kid had 10 apples and he gic
Answer:
The meal cost $14.51 per person.
Step by step explanation:
Meal cost: 46.72
Sales tax: 8%
Then.
then we take out 8% of the value
[tex]46.72\text{ x 0.08 =3.74}[/tex][tex]46.72+3.74\text{ = 50.46}[/tex]Tip : 15% (meal and sales tax)
[tex]50.46\text{ x 0.15 = 7.57}[/tex][tex]50.46\text{ + 7.57 = 58.03}[/tex]There are 4 people.
[tex]\frac{58.03}{4}=14.51[/tex]Solve for d.
4d - 5 = 11
Answer:
d = 4
Step-by-step explanation:
4d - 5 = 11
a) Subtract 5 from both sides.
-5 + 5 = 11 + 5
4d = 16
b) Divide both sides by 4.
4d/4 = 16/4
16/4 = 4
Therefore, you're answer will be 4.
arie is driving from the usa into canada. she notices that all of the canadian speed limit signs are in kilometers per hour; her odometer only displays miles per hour. how many kilometers per hour is she driving when the odometer reads 19 miles per hour?
5(23)=5(20)+ what property is being used help please i have till monday
The property used here is the distributive property of the multiplication.
What property is being used?Here we have the expression:
5*23 = 5*20 + 5*3
This is the distributive property of the multiplication, it says that:
A*(B + C) = A*B + A*C
Now, the original expression can be rewritten as:
5*23 = 5*(20 + 3)
And now we apply the above property to get:
5*23 = 5*(20 + 3) = 5*20 + 5*3
5*23 = 5*20 + 5*3
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someone include steps if you can
Using the concept of the equation, it can be concluded that Levi answered the first question wrong and the last two correctly. Thus,
No
Yes
Yes
How to check whether the value of x satisfies the equation?To check the value of x satisfies the equation, put the value of x and if it matches the resultant, it is correct.
Now solving the first part, x/4=20;x=5
So, putting x=5 in the equation 5/4=1.25 is not matching with the resultant ie. 20.
Therefore, this is the incorrect value of x.
Now solving the second part, 1.5x-8=7;x=10
So, putting x=10 in equation 1.5*10-8= 15-8=7
It matches with the resultant.
Therefore, this is the correct value of x.
Now solving the third part, 4x+6=58; x=13
So, putting x=13 in equation 4(13)+6= 52+6=58
It matches with the resultant.
Therefore, this is the correct value of x.
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