Points z1 and z2 are shown on the graph.Part A: Give the complex conjugate of z2 and explain how to find it geometrically.Part B: Find z2 − z1 geometrically and explain your steps.
Answers
Looking at the graph
we have that
z1=(4,6i) -------> 4+6i
z2=(-5,2i) -----> -5+2i
so
Part a
Conjugate of z2
we know that
z2=-5+2i
the conjugate of z2 is -5-2i
to find out the conjugate change the sign of the imaginary part
(-5,-2i)
Part B
Find out z2-z1
z1=(4,6i)
z2=(-5,2i)
so
z2-z1=(-5-4,2i-6i)
z2-z1=(-9,-4i)
to find out the coordinate of the real axis, subtract the coordinates of the real axis and to find out the coordinate of the imaginary part, subtract the coordinates of the imaginary parts
Related Questions
the variables y and x have a proportional relationship and y=9 when x =2. what is the value of y when x=3
Answers
SOLUTION:
Step 1:
In this question, we have the following:
The variables y and x have a proportional relationship and y=9 when x =2.
What is the value of y when x=3?
Step 2:
Mathematically, we can see that:
[tex]\begin{gathered} y\text{ }\alpha\text{ x } \\ y\text{ = kx ( where k is a constant)} \\ 9\text{ = k ( 2)} \end{gathered}[/tex]Divide both sides by 2, we have that:
[tex]k\text{ = }\frac{9}{2}[/tex]Hence, the relationship between x and y =
[tex]y\text{ = }\frac{9}{2}\text{ x}[/tex]Step 3:
Then, we need to find the value of y when x = 3 , we have that:
[tex]\begin{gathered} y\text{ = }\frac{9}{2}(3) \\ y\text{ = }\frac{9\text{ x 3}}{2} \\ y\text{ = }\frac{27}{2} \end{gathered}[/tex]CONCLUSION:
The value of y when x = 3 is :
[tex]y\text{ =}\frac{27}{2}[/tex]
need helo with this question
Answers
Question:
Solution.
On the x-axis to return to its original position the object must move the displacement to the right, that is:
[tex]x_{2\text{ }}-x_1=7-4\text{ = 3}[/tex]Now, because it moved down. To move in its original position the object must move up the total displacement in the vertical direction (y-axis):
[tex]y_2\text{ }_{}-y_1=2-0\text{ = }2[/tex]Then, the correct solution is:
Translation 3 units right and 2 units up.
Point A is a vertex of a polygon. Point R is the image of A after the dilation. Find the scale factor ofthe dilation.A(-2,-3) and R (-10,-15)
Answers
To find the dilatation factor we can divide the componets so:
[tex]\begin{gathered} \frac{-2}{-10}=0.2 \\ \frac{-3}{-15}=0.2 \end{gathered}[/tex]So the dilatation factor is:
[tex]0.2=\frac{1}{5}[/tex]a statistic class was asked about the city where they live the results are listed below that F equal Fort Pierce P equal Port St Lucie vehicle Vero Beach as equal Sebastian and Zoey equal Okeechobee
Answers
Given:
F = Fort Pierce
P = Port St. Lucie
V = Vero Beach
S = Sebastian
O = Okeechobee
From the details gotten from the class, the frequency of each is given below;
[tex]\begin{gathered} F=5 \\ P=3 \\ V=10 \\ S=7 \\ O=5 \\ \text{Total frequency = 30} \end{gathered}[/tex]To get the relative frequency,
[tex]R\text{ elative frequency = }\frac{frequency}{\text{total frequency}}[/tex]Hence, the relative frequency and percentage for;
Fort Pierce is;
[tex]\begin{gathered} R\text{ elative frequency = }\frac{frequency}{\text{total frequency}} \\ R\text{ elative frequency = }\frac{5}{30}=0.167 \\ \text{Percentage = 0.167}\times100\text{ =16.7\%} \end{gathered}[/tex]Hence, the relative frequency and percentage for;
Port St. Lucie is;
[tex]\begin{gathered} R\text{ elative frequency = }\frac{frequency}{\text{total frequency}} \\ R\text{ elative frequency = }\frac{3}{30}=0.100 \\ \text{Percentage = 0.100}\times100\text{ =10.0\%} \end{gathered}[/tex]Hence, the relative frequency and percentage for;
Vero Beach is;
[tex]\begin{gathered} R\text{ elative frequency = }\frac{frequency}{\text{total frequency}} \\ R\text{ elative frequency = }\frac{10}{30}=0.333 \\ \text{Percentage = 0.333}\times100\text{ =33.3\%} \end{gathered}[/tex]Hence, the relative frequency and percentage for;
Sebastian is;
[tex]\begin{gathered} R\text{ elative frequency = }\frac{frequency}{\text{total frequency}} \\ R\text{ elative frequency = }\frac{7}{30}=0.233 \\ \text{Percentage = 0.233}\times100\text{ =23.3\%} \end{gathered}[/tex]Hence, the relative frequency and percentage for;
Okeechobee is;
[tex]\begin{gathered} R\text{ elative frequency = }\frac{frequency}{\text{total frequency}} \\ R\text{ elative frequency = }\frac{5}{30}=0.167 \\ \text{Percentage = 0.167}\times100\text{ =16.7\%} \end{gathered}[/tex]Olwa is testing the possible rational roots of P(g)=2g^3+4g^2+g+6. She has substituted each value into the function, and none of her results were equal to zero. How should she interpret this information?A. Only one root of the polynomial is rational.B. None of the roots of the polynomial are rational. C. At least 2 of the roots of the polynomial are rational. D. All of the roots of the polynomial are rational
Answers
the answer is B. None of the roots of the polynomial are rational.
I need help with this question I also really don’t understand the topic
Answers
STEP - BY - STEP EXPLANATION
What to find?
The mileage in which company A charge no more than company B.
Given:
Note :
50 cents =50/100 = $0.5
70 cents = 70/100 = $0.7
First, we will set - up the equation for company A charges.
Let m be the number of mileage.
Company A
40 + 0.5m
Next, set up an equation for company B charges.
Company B
30 + 0.7m
Now, company A charge no more than company B when;
company B charges is greater or equal to company A charges.
That is;
company B charges ≥ company A charges.
Substitute the set - up equations.
30 + 0.7m ≥ 40 + 0.5m
Collect like term
[tex]0.7m-0.5m\ge40-30[/tex][tex]0.2m\ge10[/tex]Divide both-side of the equation by 0.2
[tex]\frac{0.2m}{0.2}\ge\frac{10}{0.2}[/tex][tex]m\ge50[/tex]ANSWER
m ≥ 50
Add.Your answer should be an expanded polynomial in standard form.(-m2 + 6) + (-4m² + 7m + 2)
Answers
As given by the question
There are given that the expression:
[tex](-m^2+6)+(-4m^2+7m+2)[/tex]Now,
Simplify the given expression:
[tex](-m^2+6)+(-4m^2+7m+2)=-m^2+6-4m^2+7m+2[/tex]Then,
[tex]\begin{gathered} -m^2+6-4m^2+7m+2=-m^2-4m^2+7m+8 \\ =-5m^2+7m+8 \end{gathered}[/tex]Hence, the value of the expression is shown below:
[tex]-5m^2+7m+8[/tex]7) The formula for finding the area of a square is A = 5^2. How could you rewrite this formula to solve for s?
Answers
This is the area of a square formula, where
A is the Area
s is the length of the sides
To solve for the variable s, we need to isolate it.
The "s" is squared. To get rid of the square, we need to take the square root of both the sides.
Thus,
[tex]\begin{gathered} A=s^2 \\ \sqrt[]{A}=\sqrt[]{s^2} \\ \sqrt[]{A}=s \end{gathered}[/tex]We can re-arrange and write:
[tex]s=\sqrt[]{A}[/tex]Hello, I need help with this 8th Grade Math Problem. Thank You!
Answers
Step 1;
To find the slope of a line, pick two points from the line and find the slope.
Points ( 2, 1 ) , (10 , 13 ) { Reason because the two points have both x and y coordinates)
Step 2
[tex]\begin{gathered} Slope\text{ formula m = }\frac{y_2-y_1}{x_2-x_1} \\ x_1\text{ = 2} \\ y_1=1_{} \\ x_2\text{ = 10} \\ y_2\text{ = 13} \\ m\text{ = }\frac{13\text{ - 1}}{10\text{ - 2}} \\ \text{m = }\frac{12}{8} \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]The slope of the line = 3/2
Step 3:
Equation of the line:
To find the equation of a line, use two-point forms equation of a line
[tex]\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 1}}{x\text{ - 2}}\text{ = }\frac{13\text{ - 1}}{10\text{ - 2}} \\ \frac{\text{y - 1}}{x\text{ - 2}}\text{ = }\frac{3}{2} \\ 2(y\text{ - 1) = 3(x - 2)} \\ 2y\text{ - 2 = 3x - 6} \\ 2y\text{ = 3x - 6 + 2} \\ \text{2y = 3x - 4} \end{gathered}[/tex]Step 4:
To find b, plug x = 6 and y = b in the equation of a line formula.
[tex]\begin{gathered} 2y\text{ = 3x - 4} \\ 2b\text{ = 3}\times\text{6 - 4} \\ 2b\text{ = 18 - 4} \\ 2b\text{ = 14} \\ b\text{ = }\frac{14}{2}\text{ = 7} \\ \text{b = 7} \end{gathered}[/tex]Step 5
To find a, plug x = a and y = 10 in the equation of a line formula.
[tex]\begin{gathered} 2y\text{ = 3x - 4} \\ 3\text{ }\times\text{ 10 = 3a - 4} \\ 30\text{ = 3a - 4} \\ 3a\text{ = 30 + 4} \\ 3a\text{ = 34} \\ \text{a = }\frac{34}{3} \end{gathered}[/tex]Two factory plants are making TV panels. Yesterday, Plant A produced 2000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 8%?
Answers
Let x be the number of panels produced in Plant B, with the given information we can set the following equation:
[tex]2000\cdot0.03+x\cdot0.10=(2000+x)\cdot0.08.[/tex]Simplifying the above equation, we get:
[tex]60+0.10x=160+0.08x\text{.}[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} 0.10x-0.08x=160-60, \\ 0.02x=100, \\ x=5000. \end{gathered}[/tex]Answer:
[tex]5000.[/tex]For the given rectangular equation, give its equivalent polar equation.
Answers
ANSWER
[tex]\text{ r = }\frac{\text{ 5}}{\text{ cos}\theta\text{ - sin }\theta}[/tex]EXPLANATION
Given that;
[tex]x\text{ - y = 5}[/tex][tex]\text{ The rectanguar equation is x - y = 5}[/tex][tex]\begin{gathered} \text{ for polar form of equation} \\ \text{ x= rcos}\theta \\ \text{ y = rsin}\theta \\ \end{gathered}[/tex]Find r
[tex]\begin{gathered} \text{ rcos}\theta\text{ - rsin}\theta\text{ = 5} \\ r(cos\text{ }\theta\text{ - sin }\theta)\text{ = 5} \\ \text{ Isolate r} \\ \text{ r = }\frac{5}{(cos\theta\text{ - sin }\theta)} \end{gathered}[/tex]February is sale month at the clothing store. All items are marked down 20 percent. If the sale price for a purse is $42, what was the price before the markdown?
Answers
According to the statement the item has been marked down 20%, write an equation for the sales price letting x be the original price and writing the percentage in decimal form.
[tex]SP=x\cdot(1-0.2)[/tex]if you have the sales price find the value of x
[tex]\begin{gathered} 42=0.8x \\ x=\frac{42}{0.8} \\ x=52.5 \end{gathered}[/tex]the purse had an original value of $52.5
1 1 Find the Area: 13 in 4 in 7 in 24 in
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the area will be the area of the rectangle plus the area of the trapezoid, then:
[tex](7\times24)+\frac{(13+24)}{2}\times4=(168)+74=242[/tex]then the answer is 242 square inches.6(p+6)-(p-6) I need help
Answers
Answer:
[tex]6(p+6)-(p-6)_{}=5p+42[/tex]Explanation:
Given the expression:
[tex]6(p+6)-(p-6)_{}[/tex]To simplify this, we need to first remove the brackets. Doing that, we have:
[tex]6p+36-p+6[/tex]Next, we collect like terms
[tex]6p-p+36+6[/tex]Finally, we evaluate
[tex]5p+42[/tex]Mark thinks the equation y= 4+6x will match the red solid graph. Mia thinks it will match the blue dotted graph. Who’s right? Mark. Or. Mia
Answers
Given:
The given equation is
[tex]y=4+6x[/tex]Solution:
Now, for x=0 we have
[tex]y=4+6(0)=4[/tex]And, for y=0 we have
[tex]\begin{gathered} 0=4+6x \\ x=\frac{-4}{6}=\frac{-2}{3} \end{gathered}[/tex]which shows that the vlue dotted graph is the correct graph of the equation.
2(3x-2)=5x make x the subject of the formula
Answers
We need to make x the subject of formula in the given equation;
[tex]2(3x-2)=5x[/tex]Firstly we need to expand the bracket.
[tex]\begin{gathered} 2(3x-2)=5x \\ 2\times3x-2^{}\times2=5x^{} \\ 6x\text{ - 4 }=5x^{} \end{gathered}[/tex]Then we can subtract 5x from both sides.
[tex]\begin{gathered} 6x-4-5x^{}\text{ }=5x-5x^{} \\ 6x-5x^{}-4=0^{} \\ x\text{ - 4 }=0 \end{gathered}[/tex]finally, we also need to add 4 to both sides, so that we will be left with x on one side.
[tex]\begin{gathered} x-4+4=0^{}+4 \\ x=4^{} \end{gathered}[/tex]We have our answer.
So, making x the subject of formula;
[tex]x=4^{}[/tex]A training field is formed by joining a rectangle and two semicircle, as shown below. The rectangle is 100 m long and 7 m wide. What is the length of the training track running around ( use the 3.14 for pie , and do not round your answer)
Answers
The answer will be the sum of the longer sides of the rectangle plus the perimeter of the full circumferencem then:
[tex]2(100)+2\pi(35)=200+70\pi=200+70(3.14)=419.8[/tex]then the answer will be
[tex]419.8\text{ m}[/tex]can you put 1.59, 2.1, 1.73, 2.061 in order from least to greatest
Answers
the given numbers are,
1.59, 2.1, 1.73, 2.061
so, the increasing order is,
1.59 < 1.73 < 2.061 < 2.1
this is for my friends extra coins for y'all...
"8 ÷ 2 × (2 + 2) = ?
please do work and no web site too as well.
Answers
Answer:
its 16
Step-by-step explanation:
because 8 divided by 2 equals 4 and 2+2=4 also so if we times 4x4 it would equal 16
I hope that makes sense :)
I need the answer as fast as possible I have to go right now
Answers
Given:
The objective is to choose the correct inequality for the graph.
From the graph, the y intercept is 4 and the x intercept is 3. Since both intercepts are at positive values, the equation of inequality will have positive coefficients.
Also, the shaded region is on the left side of the graph, then the symbol used for inequality will be,
[tex]4x+3y\le C[/tex]Here, C represents the constant.
Consider option (A).
[tex]4x+3y\le12[/tex]The graph of the above inequality will be,
Conider the next inequality,
[tex]x\le0[/tex]Then, the graph of the inequality will be,
On combining the graphs,
Thus, the correct inequality of the given graph is,
[tex]\begin{gathered} 4x+3y\le12, \\ x\ge0 \end{gathered}[/tex]Hence, option (1) is the correct answer.
Find the missing side. Roundto the nearest tenth.17y440Xy = [?]
Answers
Given:
Angle =44 degrees, the hypotenuse side =17, and opposite side = y.
Recall the formula for the sine
[tex]\sin \theta=\frac{Opposite\text{ side }}{\text{Hypotenuse}}[/tex][tex]\text{ Substitute opposite side =y, hypotenuse =17 and }\theta=44^o,\text{ we get}[/tex][tex]\sin 44^o=\frac{y}{17}[/tex][tex]17\times\sin 44^o=y[/tex][tex]\text{ Use }\sin 44^o=0.6947.[/tex][tex]y=0.6947\times17=11.8099[/tex]Round off, we get
[tex]y=11.8[/tex]The value of y is 11.8 units.
1 b. Sarah roller skates with a constant speed of 16 miles per hour. How far can she travel in 150 minutes?
Answers
Given:
Speed, s=16 miles/hour
Time, t=150 minutes.
The objective is to find the distance d.
Let's convert the speed as miles/minute.
It is known that 1 hour=60 minutes.
[tex]\begin{gathered} \text{speed, s=}\frac{16}{60} \\ s=\frac{16}{60}\text{ mile/minute} \end{gathered}[/tex]Now, find the distance.
[tex]\begin{gathered} d=s\cdot t \\ d=\frac{16}{60}\cdot150 \\ d=\frac{240}{60} \\ d=4 \end{gathered}[/tex]Hence, the distance travelled by sarah is 4 miles.
find the mean of 25 numbers if the mean of 15 of them is 18 and the mean of the rest is 13
Answers
Given the mean of 15 of them is 18 and the mean of the rest is 13
And the total numbers are 25
So,
First, we need to find the sum of all numbers
the mean of 15 of them is 18
so, the sum of the 15 numbers are = 18 * 15 = 270
The rest of the numbers = 25 - 15 = 10
the mean of the rest is 13
so, the sum of the rest = 13 * 10 = 130
so, the sum of all numbers = 270 + 130 = 400
so, the mean of the all numbers =
[tex]\frac{400}{25}=16[/tex]So, the answer is, mean = 16
Question 12 of 40 Find the domain of the graphed function. -5 A. x is all real numbers. B. -45X34 C. X=-4 D. -45 x 2
Answers
A graph is given and it is required that you find the domain of the graphed function.
Recall that the domain of a relation or a function is the set of all possible values for input in that function.
Note that the set of possible values for input is the set of x-values of the function.
Hence, to find the domain from the graph, check the interval of x-values from the given graph.
Notice from the graph that the x-values start at x=-4 to x=2 (both inclusive).
It follows that the domain of the function is:
[tex]-4\leqslant x\leqslant2[/tex]The correct option is D.
Given that sin A =3/5 and tan B= -12/5 where A is an acute angle and B is an obtuse angle. Without using tables or calculators, find the value of (a) tan A(b) cos (A+B)
Answers
The given angles are sin A =3/5 and tan B= -12/5 where A is an acute angle and B is an obtuse angle.
a. To determine tan A
First find the cos A with the help of trigonometric property
[tex]\cos A=\sqrt[]{1-\sin ^2A}[/tex][tex]\cos A=\sqrt[]{1-\frac{9}{25}}=\frac{4}{5}[/tex][tex]\tan A=\frac{\sin A}{\cos A}=\frac{3}{4}[/tex]b. To determine cos(A+B)
[tex]\cos (A+B)=\cos A\cos B-\sin A\text{ sin B}[/tex]We have to find sin B and cosB, it is given that tan B= -12/5
[tex]\sec ^2B=1+tan^2B[/tex][tex]\sec ^2B=1+\frac{144}{25}=\frac{169}{25}[/tex][tex]\sec B=\frac{13}{5}[/tex]Then the value of cos B is 5/13.
Determine the value of sinB
[tex]\sin B=\sqrt[]{1-\frac{25}{169}}=\frac{12}{13}[/tex]The value of cos (A+B) i
The lines shown below are perpendicular. If the green line has a slope of
Answers
SOLUTION:
For perpendicular lines, the product of slopes;
[tex]m_1m_2=-1[/tex]So, we have;
[tex]\begin{gathered} \frac{1}{7}\times m_2=-1 \\ m_2=-1\div\frac{1}{7}=-7 \end{gathered}[/tex]Thus, the answer is;
[tex]-7[/tex]what is the scale factor of 76 and 1
Answers
The scale factor of 76 and 1 will be 76.
Given,
76 and 1
We have to find the scale factor of 76 and 1.
Scale factor = Dimension of the new shape Dimension of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.
Scale calculator;
Measurements can be converted from one scale to another using a scale converter. One inch to one mile can be entered, and vice versa. The scale converter will then provide you a conversion table once you've completed this.
Here,
The greatest common factor of 76 and 1 is 76.
So, the scale factor of 76 and 1 will be 76.
Learn more about scale factor here;
https://brainly.com/question/14474492
#SPJ1
The slope of a straight line changes depending on which points on the line you choose to compare. True or false
Answers
The slope of the line is determined by the ratio of vetical change to the horizontal change.
Thus the ratio of changes doesnot change with change in point considered.
Thus the answer is False.
With a sphere with a diameter of six centimeters what is the volume?
Answers
We have that the equation for the volume of the sphere is:
[tex]V=\frac{4}{3}\pi\cdot r^3[/tex]in this case, we have that:
[tex]\begin{gathered} \pi=3.14 \\ r=3\operatorname{cm} \end{gathered}[/tex]then, using the formula, we have:
[tex]V=\frac{4}{3}(3.14)(3)^3=\frac{4}{3}(3.14)(27)=113.04\operatorname{cm}^3[/tex]therefore, the volume is 113.04cm^3
what is 30/100 = ?/10
Answers
SOLUTION
In this question, we are meant to find the missing number in the equivalent fractions:
30/100 = X / 10
Cross- multiply, we have:
30 x 10 = 100 x X
300 = 100 X
Divide both sides by 100, we have :
X = 3