Step-by-step explanation:
This is the trigonometric form of a complex number where
|
z
|
is the modulus and
θ
is the angle created on the complex plane.
z
=
a
+
b
i
=
|
z
|
(
cos
(
θ
)
+
i
sin
(
θ
)
)
The modulus of a complex number is the distance from the origin on the complex plane.
|
z
|
=
√
a
2
+
b
2
where
z
=
a
+
b
i
Substitute the actual values of
a
=
4
and
b
=
−
2
.
|
z
|
=
√
(
−
2
)
2
+
4
2
Find
|
z
|
.
|
z
|
=
2
√
5
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
θ
=
arctan
(
−
2
4
)
Since inverse tangent of
−
2
4
produces an angle in the fourth quadrant, the value of the angle is
−
0.4636476
.
θ
=
−
0.4636476
Substitute the values of
θ
=
−
0.4636476
and
|
z
|
=
2
√
5
.
2
√
5
(
cos
(
−
0.4636476
)
+
i
sin
(
−
0.4636476
)
)
Replace the right side of the equation with the trigonometric form.
z
=
2
√
5
(
cos
(
−
0.4636476
)
+
i
sin
(
−
0.4636476
)
)
A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of division problems to multiplication problems?
Type your answer as a fraction in simplest form
Answer: 2:1
Step-by-step explanation:
hi there! since there are 24 division problems and 12 division problems, you need to divide by the gcf of 24 and 12, which gives you 2:1.
hope it helps!
lovelymoonlight
Answer: 2:1 is the ratio of division problems to multiplication problems.
Step-by-step explanation:
12 is half as small as 24, so the ratio of division problems to multiplication problems is 2:1.
A notary receives $ 3500 for elaborating a title property and $2000 for the constitutive act of an enterprise. In a month did a total of 22 operations, both titles and acts that represented a total wanna go income of $53000. How many title and acts were elaborated?
Answer:
6 titles and 16 acts were elaborated
Step-by-step explanation:
Let the number of titles be t and the number of acts be a
Since the total is 22 operations:
a + t = 22 •••••••(i)
Total amount from titles = 3500 * t = 3500t
Total amount from acts = 2000 * a = 2000a
2000a + 3500t = 53,000 ••••••(ii)
From i, a = 22-t
Insert this in ii
2000(22-t) + 3500t = 53,000
44,000 - 2000t + 3500t = 53,000
1,500t = 53000-44000
1500t = 9000
t = 9000/1500
t = 6
But a = 22 -
= 22-6 = 16
Consider the parent function f(x)=e^x and transformed function g(x)=-f(x)-4. Which features of function F function G are different Y intercept End plz help!
There are no results for Consider the parent function f(x)=e^x and transformed function g(x)=-f(x)-4. Which features of function F function G are different
Answer: y-intercept
Step-by-step explanation:
plato: I got it right. I hope this helps.
Solve the inequality: 9x-4x+4≥36-12
Answer:
x≥4 Brainiest please
Step-by-step explanation:
The solution of the given inequality 9x-4x+4 ≥ 36-12 is x ≥ 4.
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is an inequality 9x-4x+4 ≥ 36-12 is x ≥ 4.
On solving, we get,
9x-4x+4 ≥ 36-12 is x ≥ 4
5x+4 ≥ 24
5x ≥ 20
x ≥ 4
Hence, the solution of the given inequality 9x-4x+4 ≥ 36-12 is x ≥ 4.
For more references on inequality, click;
https://brainly.com/question/28823603
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Mason and Laney ran laps to train for the long-distance running team. The ratio of the number of laps Mason ran to the number of laps Laney ran was 2 to 3. If Laney ran 36 laps, how many laps did Mason run?
I need the fast plz
Enter the first four terms.
Answer:
7, 4, 1, and -2.
Step-by-step explanation:
Our recursive rule is:
[tex]f(1)=7\!, f(n)=f(n-1)-3[/tex]
Where n is the nth term.
So, our first term will be f(1). As defined, this is 7.
Our second term will be f(2). We will use the recursive formula. Substituting 2 for n yields:
[tex]f(2)=f(2-1)-3[/tex]
Subtract:
[tex]f(2)=f(1)-3[/tex]
We know that f(1) is 7. Substitute:
[tex]f(2)=7-3=4[/tex]
Hence, the second term is 4.
We will do the same thing for the third term. Substitute 3 for n:
[tex]f(3)=f(3-1)-3[/tex]
Subtracting yields:
[tex]f(3)=f(2)-3[/tex]
We know that f(2) is 4. So:
[tex]f(3)=4-3=1[/tex]
Hence, the third term is 1.
Finally, we will do the same thing. Substitute 4 for n to find the fourth term:
[tex]\begin{aligned} f(4)&=f(4-1)-3 \\ f(4)&=f(3)-3 \\ f(4)&=1-3 \\ f(4)&=-2\end{aligned}[/tex]
Hence, the fourth term is -2.
Therefore, our first four terms are 7, 4, 1, and -2.
How many solutions does the following equation have?
2(3x+5)=5(2x-4)-4x
Answer: None
Step-by-step explanation:
!!HELP ME PLEASE!!
Which describes the graph of y = (x + 6)2 + 1?
A. Vertex at (−6, 1)
B. Vertex at (6, −1)
C. Vertex at (−6, −1)
D. Vertex at (6, 1)
Answer:
answers
Step-by-step explanation:
A. Vertex at (−6, 1)
What is the slip of the line shown in the graph A) -2 B) -1 C) 1/-2 or D) 1/2
Answer:
m = -1/2
Step-by-step explanation:
[tex]m=\frac{rise}{run}=\frac{1-2}{0+2}=\frac{-1}{2}=\boxed{-\frac{1}{2}}[/tex]
Hope this helps.
What is 3.4 x10written in standard notation?
Answer:
34
Step-by-step explanation:
Standard notation is the common answer for a problem. Instead of an expanded problem or a scientific notation, you would simply solve the problem without answering with another problem.
3.4 x 10
Move the decimal 1 place to the right.
34.00 x 1 = 34
If tan x = m, what is sin x in terms of m?
Answer: m/sqrt(m^2)+1
Step-by-step explanation: if tan x = m, then the opposite angle is m and the adjacent angle is 1 so 1 squared plus m squared equals c squared. c = sqrt (1 + m^2)
sin x = opposite/hypotenuse = m/sqrt(m^2)+1
The value of sin x in terms of m is [tex]\frac{m}{\sqrt {m^2+1}}[/tex]
Trigonometry are identities used to express the sides and angles of a triangle.
According to SOH CAH TOA,
Tan θ = Opposite/Adjacent
Given that tan x = m
Opposite = m
Adjacent = 1
Get the hypotenuse using the pythagoras theorem
Hyp² = Opp² + Adj²
Hyp² = m²+1²
Hyp² = m²+1
Take the square root of both sides
√Hyp² =√m²+1
Hypotenuse = √m²+1
Next is to get sin x:
Sin x = Opposite/Hypotenuse
Sin x = [tex]\frac{m}{\sqrt {m^2+1}}[/tex]
Hence the value of sin x in terms of m is
[tex]\frac{m}{\sqrt {m^2+1}}[/tex]
Learn more on trigonometry ratio here: https://brainly.com/question/13729598
Stephan has a dog that weighs 5 times as much as Ian's dog. The total weight of both dogs is 72 pounds. how much does Stephans dog weigh??
Answer:
Stephan's dog weighs 60 pounds.
Step-by-step explanation:
Judah's mother gave him a certain amount of money for doing his chores last week. This week she gave him two times the amount because he did a few more chores. After counting the money his mother gave him for the two weeks of chores and the $15 that was already in his wallet, Judah had $52.50. How much did he earn for one week of chores?
Answer:
He earned $37.50
Step-by-step explanation:
Just subtract the $15 that he already had and you’ll get the answer
3/5 = x/6 that = 10 rightt??
Answer:
yeah ur correct i know u posted this long time... so yeah
I need help with this question? Anyone understand?
Answer:
A. y = 2x + 4
Step-by-step explanation:
y = mx + b
Slope (m) = 2/1 (up 2, right 1)
Y-intercept (b) = 4
There are 48 students in a school play. The ratio of boys to girls is 5:7. How many more girls than boys are in the play? Explain how you found your answer
Answer:
48 students total in the school play
Ratio of boys to girls is 5:7
How many more girls are there than boys in the play?
Let's let "5x" represent the number of boys in the school play and "7x" represent the number of girls in the school play.
5x = boys
7x = girls
If we know that the total number of students in the play equals 48, then that must me that both the number of boys and girls combined must equal 48:
5x + 7x = 48
12x = 48
x = 4
Now, take your x-value and plug it into both the boys' and girls' values to figure out how many boys and girls there are in the play:
5x = 5 (4) = 20 boys
7x = 7 (4) = 28 girls
To find out how many more girls there are than boys in the play, just subtract the number of girls minus the number of boys:
# girls - # boys = 28 - 20 = 8
This means that there are 8 more girls than boys in the school play.
Step-by-step explanation:
Hope this helped
can you solve what is 5 x 1 2/3
Answer:
8.33333333
Step-by-step explanation:
Which graph represents the equation y=−12x+1?
Answer:
Graph the equation of the line for the equation , y = 3x-12.
Step-by-step explanation:
hope this helps
Help will give a crown!!
Answer:
okay
Step-by-step explanation:
1) Each side length is 12
2) Each side length is 2
Bentano spends $170 to order 30 pounds of nuts from an online company. The company charges $3.50 per pound for peanuts and $7.50 per pound for almonds. It also charges a flat fee of $13 for shipping and handling.
Which equation can be used to find p, the number of pounds of peanuts Bentano buys?
3.5p+7.5(p−30)−13=1703 point 5 p plus 7 point 5 times open paren p minus 30 close paren minus 13 is equal to 170
3.5p+7.5(30−p)−13=1703 point 5 p plus 7 point 5 times open paren 30 minus p close paren minus 13 is equal to 170
3.5p+7.5(p−30)+13=1703 point 5 p plus 7 point 5 times open paren p minus 30 close paren plus 13 is equal to 170
3.5p+7.5(30−p)+13=170
Given :
Bentano spends $170 to order 30 pounds of nuts from an online company.
The company charges $3.50 per pound for peanuts and $7.50 per pound for almonds. It also charges a flat fee of $13 for shipping and handling.
To Find :
Which equation can be used to find p, the number of pounds of peanuts Bentano buys.
Solution :
Price of peanuts + Price of almonds + Delivery charge = Total amount
3.5p + 7.5( 30 - p ) + 13 = 170
Comparing the answers with given options, the matching answer is option D).
Hence, this is the required solution.
A boat travels 19 miles per hour. At this rate, how long will it take for the boat to travel 114 miles?
Answer:
Step-by-step explanation:
Answer:
6 hours
Step-by-step explanation:
114 divided by 19 equals 6
Classifying Polynomials
Answer:
Remember that a monomial has one term, a binomial has two, and a trinomial has three. Also, a constant expression will not have any exponents, a quadratic will have an x², a cubic will have an x³, a fourth degree will have a x⁴, and a fifth degree will have an x^5.
Vinh bought 412 gallons of ice-cream to serve. If a pint is 18 gallons, how many pint-sized servings can be made?
Answer:
The answer would be 22.8 it would have to be rounded down so 412 could make 22 pint sized servings.
Step-by-step explanation:
Help plz Brainliest if I can gave u cuz sometime I can’t
Answer:
3 1/2 * 4 = 14
Step-by-step explanation:
To find your answer, which is 14, one side is 3 1/2, and to find cm you need to multiply. 3 1/2 times 4 (Prisms have 4 sides) which is 14!
hiii so my parents just finally agreed to let me get a puppy so could you list some boy and girl name ideas? tyyyy
pls say at least 3
Answer:
abby
frisk
mimi
Step-by-step explanation:
Answer:
Mochi, Athena, and Oreo ^^
Step-by-step explanation:
Congrats! :D
Need help with these types of questions
Answer:
this answer is going to a 20 out of 100 percent
the answer is C or D
Answer:
A. Angle C = Angle C'
Step-by-step explanation:
It cannot be B because that would make them congruent by ASA, so it has to be A because C and D are both sides.
someone please help
Answer:
I would say either the 7/16 or the if the 7/16 is still to small
Step-by-step explanation:
I dont understand this
Answer:
x=66
Step-by-step explanation:
180-114=66
Interior angles on the same side of transversal are supplementary (180°).
So,
x + 114° = 180°
=> x = 180° - 114°
=> x = 66°
Triangle P'Q'R is the image of PQR under a transformation
Answer:
what is your question
Step-by-step explanation:
Answer:
Step-by-step explanation:
there is no picture....
Just need the answers
Answer:
Answers are below
Step-by-step explanation:
1) Area is approx. 268.8
2) Area is approx. 490.87
3) Area is approx. 539.13
4) Radius is approx. 18.99; Area is approx. 1132.92