[tex]\frac{11z}{z+3}=13-i,z\in\mathbb{C}[/tex]
First, multiply both sides by [tex]z+3[/tex],
[tex]11z=(13-i)(z+3)[/tex]
[tex]13z+39-iz-3i=11z[/tex]
Collect terms and put z on the left,
[tex]2z-iz=3i-39[/tex]
[tex]z(2-i)=3i-39[/tex]
[tex]z=\frac{3i-39}{2-i}[/tex]
Division of complex numbers is defined by multiplying both denominator and numerator with complex conjugate of the denominator,
[tex]z=3\frac{(i-13)(2+i)}{(2-i)(2+i)}[/tex]
Multiply out,
[tex]z=3\frac{2i-1-26-13i}{5}[/tex]
[tex]z=3\frac{-11i-27}{5}[/tex]
The result is,
[tex]z=-\frac{81}{5}-\frac{33}{5}i[/tex]
Hope this helps :)
In this triangle, which of the following is true?
We know that this is a right triangle, so one of the sides has to be 90 (indicated by the square on the corner) The angles of all triangles must add to exactly 180. Subtract 90 and 35 from 180
If we do that, we get 55. We know that the unknown angle is 55 now. Now, it asks us for b. We can pythagoras theorem which states that (a^2 + b^2 = c^2) We already know c (c is 20) It does not tell us 2 of the sides but we do know that the answer is either B or D.
The side opposite of 90* should be the largest. The size opposite of 55 would be the second largest one. The side opposite of 35 would be the smallest one. Using pythagoras theorem again, I can try plugging in both 11.47 and 16.38 with c^2 - b^2 = a^2
11.47:
400 - 132 =268 (sq root now = 16.37) this would mean that A is larger than B. B should be larger than A. Try the other one
16.37:
400 -268 = 132 (sq root = 16.37) this would mean that B is larger than A which is what we want.
Thus, 16.37 = B and the last option would be correct (D)
Hope this helps, give an honest rating for me please
Write 12 more than r as an expression
Answer:
12+r
Step-by-step explanation:
"more than" means Addition.
Find the zeros of the quadratic function f(x) = 1/2(x- 7)^2 – 8
Answer:
x = 11 or 3
Step-by-step explanation:
f(x) = (1/2)(x- 7)² – 8
to find the zeros, we equate f(x) = 0
f(x) = 0
(1/2)(x- 7)² – 8 = 0 (add 8 to both sides)
(1/2)(x- 7)² = 8 (multiply both sides by 2)
(x- 7)² = (8)(2)
(x- 7)² = 16
x-7 = ±√16
x-7 = ±4
hence,
x - 7 = 4
x = 4 + 7
x = 11
or
x - 7 = -4
x = -4 +7
x = 3
Answer:
x = 11 or 3
Step-by-step explanation:
I confirmed the answer in grandpoint.
Judy got 27 546 points and 34 668 points in the first two rounds of a
game. How many points did Judy get in all?
Answer:
62 214Step-by-step explanation:
Given,
Points got by Judy in 1st round = 27 546
Points got by Judy in 2nd round = 34 668
Therefore,
Total points Judy got in the first two rounds
= 27 546 + 34 668
= 62 214 (Ans)
Which best describes the relationship between the line that passes through the points (8, 2) and (3,
5) and the line that passes through the points (-3,-7) and (0, -12)?
Answer:
C
Step-by-step explanation:
They are neither perpendicular nor parallel since line 1 has slope=-3/5 and line 2 has slope=-5/3. They are neither equal nor have a product equal to - 1.
The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Which of the following is the graph of the quadratic parent function
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
1 Dorji
ran 2km in 20 minutes. A that rake how far would he
run in an hour?
-->
Answer:
8km
Step-by-step explanation:
if he took 20km in 20min how about 1h
do cross multiplication( use 60min instead of 1h)1h = 60min
a department store regularly sells a pair of pants for $49.95. they are having a sale where clothing 30% off.
after including an 8% sales tax, how much do the pants cost on sale?
A. $30.97
B. $38.96
C. $37.76
D. $32.17
Answer:
C. $37.76
Step-by-step explanation:
30% of $49.95
=30/100×49.95
=$14.99
selling price = 49.95 -14.99
= $34.96
8% sales tax included
=8/100×34.96
=$2.80
new price= 34.96+2.80
=$37.76
What is 40 % of 50?????????????????????????????????????/
Answer:
20
Step-by-step explanation:
Of means multiply
40% * 50
Change to decimal form
.40 * 50
20
Plz help quick quick quick
Step-by-step explanation:
[tex]\angle 3[/tex] and [tex]\angle 16[/tex] are alternate exterior angles so they are equal to each other, which means
[tex]5x - 30 = 3x + 10 \Rightarrow x = 20[/tex]
Solving for the measure of [tex]\angle 16[/tex], we get
[tex]m\angle 16 = 5(20) - 30 = 70°[/tex]
Since [tex]\angle 12[/tex] and [tex]\angle 16[/tex] are supplementary,
[tex]m\angle 12 = 180° - 70° = 110°[/tex]
Answer:
ur image wont load
Step-by-step explanation:
(5.5 * 10^-6 + 6.3 * 10^-6)^2
9514 1404 393
Answer:
exact: 1.3924×10^-10rounded to 2 sf: 1.4×10^-10Step-by-step explanation:
The factor 10^-6 can be brought out:
((5.5 +6.3)×10^-6)^2 = (11.8^2)×10^-12 = 1.3924×10^-10
Often, a problem like this wants you to round to a precision appropriate to the given values. Here, that is 2 significant figures:
≈ 1.4×10^-10
_____
Additional comment
Your scientific or graphing calculator can do this nicely, even showing you the result in scientific notation. A spreadsheet can do the same.
The usual rules of exponents apply.
(a^b)(a^c) = a^(b+c)
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
the diameter of Earth's moon is on average 3.8 x 10^8m. Use the formula A=4π² to find the approximate surface area. (Use 3.14 for the value of π)
Answer:
The answer is
[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]
Step-by-step explanation:
Since the Earth's moon is a sphere
Surface area of a sphere from the question is given by
A = 4πr²
where r is the radius
To find the radius using the diameter we use the formula
radius = diameter / 2
[tex]radius \: = \frac{3.8 \times {10}^{8} }{2} [/tex]
[tex]radius = 1.9 \times {10}^{8} \: m[/tex]
π = 3.14
Substitute these values into the above formula
That's
[tex]A = 4 \times 3.14 \times ({1.9 \times {10}^{8} })^{2} [/tex]
We have the final answer as
[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]
Hope this helps you
If a textbook costs £7.80, how many can be bought for £101.40?
Answer:
13 textbook can buy.
Step-by-step explanation:
13 textbook can buy.
Divide total by price per book:
101.40 / 7.80 = 13
13 books can be bought
-58.58 is equal to the rational number
Answer:
This is true
Step-by-step explanation:
Because a rational number can be expressed as going on forever.
Given the function f(x) = 3x - 1, explain how to find the average rate of change between x = 1 and x = 4.
Step-by-step explanation:
f(1) = 3×1 - 1 = 2
f(4) = 3×4 - 1 = 12-1 = 11
so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.
the average change rate is the total change across the x interval relative to the interval length.
that is
9/3 = 3
which is the slope (= the factor of x) in the line equation.
for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.
if the change rate would be different for different parts of the function, it would not be a straight line.
Answer:
3
Step-by-step explanation:
The average rate of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 1, 4 ] , then
f(b) = f(4) = 3(4) - 1 = 12 - 1 = 11
f(a) = f(1) = 3(1) - 1 = 3 - 1 = 2
average rate of change = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3
3 1/2 ft into inches
Answer:
42 inches
Step-by-step explanation:
1 ft = 12 inch
Answer:
42 inches.
Step-by-step explanation:
Unit of measurement:
1 foot = 12 inches.
3 ft x 12 inches = 36 inches.
1/2 foot x 12 inches = 12/2 = 6 inches.
36 inches + 6 inches = 42 inches
42 inches is your answer.
~
giving brainliest to whoever finishes this correctly! :)
The number of times a player has golfed in one's lifetime is compared to the number of strokes it takes the player to complete 18 holes. The correlation coefficient relating the two variables is -0.26. Which best describes the strength of the correlation and what is true about the causation between the variables?
Answer: It is a weak negative correlation and it is not likely causal.
Step-by-step explanation:
Given: The number of times a player has golfed in one's lifetime is compared to the number of strokes it takes the player to complete 18 holes. The correlation coefficient relating the two variables is -0.26.
Variables : "number of times a player has golfed in one's lifetime" and "number of strokes it takes the player to complete 18 holes".
Since -0.26 is more closer to 0 as compared to 1 , so it describes a weak negative correlation.
Also, it is not likely causal as number of times a player has golfed in one's lifetime not cause number of strokes it takes the player to complete 18 holes.
Answer: B) It is a weak negative correlation, and it is likely casual
Correct on edge 2020!
Please find the answer !
Answer:
ring volume is 12cm3
Step-by-step explanation:
Lr ccm=volume of water and ring - Volume of water
ring cubic centimeters =x
x=9.2cm*4.5cm*7cm - 8.8cm*4.5cm*7cm
x=289.2cm3 - 277.2cm3
x=12cm3
If you owe your friend $3 and you have $15, which expression would help you find out how much money you would have left?
Answer:
12
Step-by-step explanation:
15 - 3 = 12
Answer:
both of them are right
Step-by-step explanation:
You are considering the services of three different employment agencies, all of which can get you a job that starts at $2,000 a month. Agency A charges 50 percent of the first month's gross salary. Agency B charges 10 percent of your monthly salary for the first six months. Agency C charges a $100 up-front fee and a flat fee of $500 when you are placed. Compare the three choices. Which of these offers the least expensive overall fee?
Answer:
Agency C offers the least expensive overall fee
Step-by-step explanation:
Alone from gross salary, you would make 24000 a year.
Agency A
24000 - ( 2000 x 0.5)
= 23,000
$1000 fee
Agency B
24000 - ( 2000 x 0.1 ) x 6
= 24000 - 200 x 6
= 24000 - 1200
= 22,800
$1200 fee
Agency C
24000 - (500 + 100)
= 24000 - 600
= 23,400
$600 fee
Can somebody help me please?
Answer:
[tex]\boxed{x \geq 353}[/tex]
Step-by-step explanation:
Hey there!
Info Given
- Dot is solid
- Line goes to the right
- Dot is at 353
So by using the given info we can conclude that the inequality is,
x ≥ 353
Hope this helps :)
Answer:
Inequality: 100 + 50w ≥ 18000
What to put on graph: w ≥ 358
Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.
Answer:
Margin of Error = z∝/2 * Standard Error
Step-by-step explanation:
The formula for standard error is given by
SE = [tex]\sqrt{\frac{pq}{n} }[/tex]
Where p is the probability or proportion of success q=1-p and n is the number of trials or samples.
Now Margin of Error is given by
ME = z∝/2 * Standard Error
The confidence level is used to estimate the value of alpha.
For example 90% confidence means alpha= 1-0.9= 0.1 and alpha by 2 would be 0.05 . So the value for alpha by 2 would be 1.96
in the diagram EF and GH are straight lines. Find the values of a,b,c and d
How do i work out the area of a circle that equals 5000
Answer:
Radius is 39.89422804 units
Step-by-step explanation:
Area of circle can be calculated with the formula: [tex]\pi r^{2}[/tex]
The area of the circle is 5000.
[tex]\pi r^{2}[/tex]= 5000
If you're looking for the radius, solve for r.
[tex]r^{2}[/tex]= [tex]\frac{5000}{\pi }[/tex]
r= [tex]\sqrt{\frac{5000}{\pi} }[/tex]
r= 39.89422804 units
Please answer this correctly without making mistakes
Answer:
151 9/19
Step-by-step explanation:
Step-by-step explanation:
Option A is the correct answer because it is equal to 151.47
What does it mean when the resulting temperature is above 0 on the number line? What does it mean when a temperature is below 0?
Answer:
It means that above 0 degrees Celsius the water does not freeze, whereas 0 degrees are freezing teperatures of water.
Step-by-step explanation:
Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?
0° - 7° = -7°
Transform the Cartesian (rectangular) equation to a polar equation: x = -9. The selected answer is incorrect.
Answer:
Solution : Option C
Step-by-step explanation:
We have the equations r² = x² + y², x = r cos(θ), and y = r sin(θ) that can be used to solve this problem. In this case we only need the second two equations ( x = r cos(θ), and y = r sin(θ) ) as we don't need to apply the concept of circles etc here.
Given : x = - 9,
( Substitute r cos(θ) for x )
r cos(θ) = - 9,
r = - 9 / cos(θ)
( Remember that sec is the reciprocal of cos(θ). Substitute sec for 1 / cos(θ) )
r = - 9 sec(θ)
Therefore the third option is the correct solution.