When dividing complex numbers, why do
you need to multiply the numerator and
denominator by the complex conjugate of the
denominator?
Answer:
Hope this helps..
Step-by-step explanation:
So when you need to divide one complex number by another, you multiply the numerator and denominator of the problem by the conjugate of the denominator. This step creates a real number in the denominator of the answer, which allows you to write the answer in the standard form of a complex number.
Answer:
You have to multiply by the complex conjugate because the denominator has to be a real number. By multiplying the complex conjugate you can transform the denominator in to a real number.
Step-by-step explanation:
With explanations please
1.) A ship leaves port and travels 21km on a bearing of 032° and then 45km on a bearing of 287°
a) Calculate it's distance from the port
b) Calculate the bearing of the port from the ship
2.) A surveyor leaves her base camp and drives 42 km on a bearing of 032°,she then drives 28km on a bearing of 154°. How far is she then from her base camp and what is her bearing from it?
Answer:idk
Step-by-step explanatio
The graph below shows the number of pages Matthew read in x hours. Find the slope of the line. Explain what the slope represents.
Answer: The slope represents the RATE at which Matthew read pages in x hours.
Step-by-step explanation:
While I can not see the graph, I can conclude the representation from your sentence. Slope usually describes cases where an action increases or decreases over time if that makes sense. I can help you with the calculation if you add the graph! I hope this helped a bit!
Which of the following options best represent the equation of a function?
Select all that apply.
Options:
x + y = 16
x2 + y2 = 16
y = 2
x = 2
y = x2 + 2
y = |x + 2|
Please explain how you get your answer, ty
Answer:
y=2
x=2
y=x2+2
y= lx+2l
Step-by-step explanation:
This is because these are the simplest forms of the equation. seeing as a function is f(x) (which is the same as y) when an equation is equal to a single variable, it is "solved" for hat variable and therefore best represents the equation of the function :)
Please help!!! thank youu
Answer:
38.2
Step-by-step explanation:
The total number of people who prefer burgers is
26+42 =68
The number who are female is 26
The fraction of women that prefer burgers is
26/68 =.382352941
Changing to a percent
38.2%
If a taxpayer has an adjusted gross income (AGI) of $75,000, donates
$20,000 to charity, and itemizes deductions on his federal income tax return,
how much of the charitable donation is deductible?
O A. None of the donation is deductible.
B. $20,000
O c. $10,000
O D. $5000
Answer:20000
Step-by-step explanations
Points , , and are collinear. Point is between and . Solve for given the following. =3+3 =−1+2 =11 =
hi whats the answer for this
Answer:
a) square pyramid
b)sphere
c)cube
d) pyramid
Step-by-step explanation:
Answer:
Step-by-step explanation:
A: square based pyramid
B: sphere
C: Cube
D: Tetrahedron
Choose the product. -6p 3(3p 2 + 5p - 1)
Answer:
-18 p^5 - 30 p^4 - 6p^3
Step-by-step explanation:
-6p^3(3p^2 + 5p - 1)
Distribute
-6p^3(3p^2) + -6 p^3*5p - 6p^3
Combine like terms
-18 p^5 - 30 p^4 - 6p^3
Write the first six terms of the sequence.
a1 = 4, an = An-1 +5
Answer:
{4, 9, 14, 19, 24}
Step-by-step explanation:
Best to use the notation a(1) = 4, a(n) = a(n-1) + 5.
a(1) = 4 (given)
a(2) = 9 (here we found a(2) by adding the common difference, 5, to a(1)
a(3) = 14
a(4) = 19
a(5) = 24
Find the volume of the pyramid.
Calculate the surface area of the 3-D composite figure please!! show how you got the surface area
Answer:
1222 ft²
Step-by-step explanation:
11*19*2=41811*9*2=19819*9*2 - 10*9=25213*9*2=2341/2*10*12*2=120418+198+252+234+120=1222 ft²
The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the IQR?
The annual rainfall for two cities, Albany and Zachary, in each of the years from 2002 to 2011 are shown in the tables. Annual Rainfall for Albany (in.) 23.36 18.51 28.54 22.36 30.50 24.74 11.93 15.34 18.07 15.98 Annual Rainfall for Zachary (in.) 27.27 20.11 31.14 25.88 32.97 25.03 18.55 23.91 22.75 19.73 Find the mean for the two cities' annual rainfalls. In which city does it rain more in a year, on average? Drag and drop the correct choices into the boxes to complete the statement. On average, Albany gets _ inches of rain per year and Zachary gets _ inches of rain per year. on average, which city rains more zachary or albany?
Answer:
On average, Albani gets 20.933 inches of rain per year.
On average, Zachary gets 24.734 inches of rain per year.
On average, Zachary gets more rain than Albani.
Step-by-step explanation:
Mean is given by:
[tex]Mean = \frac{Sum}{Total}[/tex]
For Albani :
Sum of total number of terms = 23.36+18.51+28.54+22.36+30.50+24.74+11.93+15.34+18.07+15.98
Sum of total number of terms = 209.33
Number of terms = 10
[tex]Mean=\frac{209.33}{10}\\\\Mean=20.933\\[/tex]
For Zachary :
Sum of total number of terms = 27.27+20.11+31.14+25.88+32.97+25.03+18.55+23.91+22.75+19.73
Sum of total number of terms = 247.34
Number of terms = 10
[tex]Mean=\frac{247.34}{10}\\Mean=24.734[/tex]
a group of 43 children, with some adults, travelled by coach on a trip to a zoo
The total cost of the trip was £516
the entrance fee was £12.75 for each adult and£8.25 for each child
the cost of hiring the coach was £123
How many adults were in the group?
you must show your working
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516 - 123 = 393
8.25 x 43 = 354.75
393 - 354.75 = 38.25
38.25 / 12.75 = 3
There were 3 adults
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Answer:
3 adults
Step-by-step explanation:
(each child)£8.25×(total children)43=£354.75(total amount paid for children)
£354.75+£123=£477.75
£516-£477.75=£38.25
£38.25÷£12.75=3
please help!!
it’s due today
Answer:
this is a little late haha but the last one
Step-by-step explanation:
cus the slope is 2 and the y intercept is -1
six copies of the sum of nine fifths and three.
Answer:
9/5+3/1
24/5 24/5 24/5 24/5 24/5 24/5
i think copies is a multiplication and sum is to add together so
6x(9/5+3)
9/5 is 1 whole and 4/5. 1 whole plus 3 wholes is 4 Wholes so it is 4 wholes and 4/5 which is 24/5.
6x24/5 is (6x24 is 144) so its 144/5 so its 28 wholes and 4/5.
Quadrilateral RSTU is a parallelogram. Which is the LEAST additional information needed to prove that RSTU is a rectangle?
a
The diagonals are congruent, and one angle is a right angle.
b
c
All four angles are right angles.
d
Both pairs of opposite sides are congruent, and all angles are right angles.
Answer:
B
Step-by-step explanation:
Which figure shows an example of symmetry?
OA
O B
o
O D
Answer:
C.
Step-by-step explanation:
symmetry means that when you fold the paper along the line of symmetry shape is overlapping
Determine whether the forces in the pair are pulling at right angles to each other. For the values a = 1.6 and b = 5.8, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth
Answer:
Approximetly 6
Step-by-step explanation:
a^2 + b^2 = c^2
1.6^2 + 5.8^2 = c^2
2.56 + 33.64 = c^2
36.2 = c^2
c=6 (approximetly)
can 20 degrees 60 degrees and 100 degrees be a triangle
Answer: Yes
Step-by-step explanation: The area of a triangle equals 180°
100+60+20=180
Answer: Yes
Explanation: The sum of the measures of the angles is always 180°
This idea is known as the (Triangle Sum Theorem).
Since 20 + 60 + 100 is equal to 180, we know
that these measures can form a triangle.
which of the following are true statements about a 30-60-90 triangle? cheack all that apply
Answer:
C and F
Step-by-step explanation:
Using this those are the only two that make sense
Answer:
Step-by-step explanation:
In right triangle ABC, ∠C is a right angle, m∠A=52∘, AC=10.01, and AB=c.
sin52∘≈0.788
cos52∘≈0.616
tan52∘≈1.280
What is the measurement of AB?
In right triangle GHI, ∠H is a right angle, m∠I=42∘, and GH=11.
sin42∘≈0.67
cos42∘≈0.74
tan42∘≈0.90
What is the measurement of HI?
9514 1404 393
Answer:
AB = 16.25HI = 12.22Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relevant relationships.
__
1. Cos = Adjacent/Hypotenuse
cos(52°) = AC/AB
AB = AC/cos(52°) = 10.01/0.616
AB = 16.25
__
2. Tan = Opposite/Adjacent
tan(42°) = GH/HI = 11/HI
HI = 11/tan(42°) = 11/0.90
HI ≈ 12.22
if an atom has 12 positively charged protons and 12 negatively charged electrons, what is it's total charge?
[tex]+12+(-12)\\=0[/tex]
A pen cost $0.89 yesterday. It is on sale today for $0.65.
How much less does the pen cost today?
Answer:
The pen costs 24 cents less today than yesterday
Step-by-step explanation:
0.89-0.65=0.24
Answer:
It costs $0.24 less
Step-by-step explanation:
0.89 - 0.65=0.24
examine the number patter below 1,2,3,5,8,13,21
The sequence is the Fibonacci sequence!
It works like this.
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
and so on.
Answer:
Step-by-step explanation:
Ad the last two for the next
(1+2)= 3. 3+5=8.......
so 13+21= 34
21+34= 55
34+55= 89
not sure what you are looking for but I hope that helps.
Please answer this !
Answer:
50
Step-by-step explanation:
Using the experimental probability, first we have to find total amount paint then to find the amount of good quality forever paint we have to subtract the amounts of other paints from total amount.
Let x represents the amount of good quality forever paint sold.
Total amount of paint [tex]=48+45+35+39+33+x=200+x[/tex] ...(i)
Experimental probability of paint sold will be better quality durable paint is
[tex]P=\dfrac{\text{Amount of better quality durable paint}}{\text{Amount of total paint}}[/tex]
[tex]P=\dfrac{45}{\text{Amount of total paint}}[/tex]
It is given that experimental probability of paint sold will be better quality durable paint is [tex]\frac{9}{50}.[/tex]
[tex]\frac{9}{50}=\dfrac{45}{\text{Amount of total paint}}[/tex]
[tex]\text{Amount of total paint}=\dfrac{45\times 50}{9}[/tex]
[tex]\text{Amount of total paint}=250[/tex] ...(ii)
From (i) and (ii), we get
[tex]200+x=250[/tex]
[tex]x=250-200[/tex]
[tex]x=50[/tex]
Therefore, 50 gallons good quality forever paint is sold.
I need help, please.
Answer:
a
Step-by-step explanation:
11-9=2 and 2 times 7 is 14, 14 plus 12 is 26 ,and 26=26 is a true statement
work out (8x10^-3) x (2x10^-4)
Answer:
[tex]1.6 \times 10^{-6}[/tex]
Step-by-step explanation:
[tex](8 \times 10^{-3}) \times (2 \times 10^{-4})[/tex]
[tex]8 \times 2 \times 10^{-3} \times 10^{-4}[/tex]
[tex]16 \times 10^{-3+(-4)}[/tex]
[tex]16 \times 10^{-3-4}[/tex]
[tex]16 \times 10^{-7}[/tex]
[tex]1.6 \times 10^{-6}[/tex]
Answer:
(8 × 10^-3)× ( 2× 10 ^-4)
reorder the terms
You will get
(8 × 2) ( 10^ -3 × 10^-4)
Multiply
16 ( 10^ -3 × 10^-4)
Use the rules of indices
a^ b × a^ c = a^b+c
16(10^-3-4)
16(10^-7)
= 16 × 10^-7 or 1.6 × 10^-6 or 0.0000016
Hope this helps.
PLS I NEED HELP...THE PICTURES ARE IN ORDER (13 POINTS ) Question 1 Solve the following equation. Explain or show your reasoning. ---------------------------------------------------------------------------------------- Question 2 Solve the following equation. Explain or show your reasoning. ------------------------------------------------------------------------------------------ Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Clare's mistake and what is the solution to the equation?
Answer:
1 . x = 9,
2 . n = 4,
3 . Clare made an error in the 2nd step; Correct answer is y = - 65 / 11
Step-by-step explanation:
1 .
[tex]2 * ( x + 5 ) = 3x + 1 - Apply Distributive Property,\\\\2x + 10 = 3x + 1 - Subtract 2x from Either Side,\\10 = x + 1 - Subtract 1 from Either Side,\\\\x = 9,\\Conclusion; x = 9[/tex]
2 .
[tex]3 * ( n + 2 ) = 9 * ( 6 - n ) - Apply Distributive Property,\\\\3n + 6 = 54 - 9n - Add ( 9n ) on Either Side,\\12n + 6 = 54 - Subtract 6 from Either Side,\\\\12n = 48 - Divide Either Side by 12,\\n = 4,\\\\Conclusion; n = 4[/tex]
3 . Clare made an error in the second step ( 72 + 24y = 4y - 5 - 9y ) and to derive the correct solution, see the following steps below;
[tex]12 * ( 5 + 2y ) = 4y - ( 5 - 9y ),\\60 + 24y = 4y - 5 + 9y,\\65 + 24y = 4y + 9y,\\65 + 24y = 13y,\\\\65 = - 11y,\\y = - 65 / 11\\\\Conclusion; y = - 65 / 11[/tex]