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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Lets do this step by step.
This is the trigonometric form of a complex number where [tex]|z|[/tex] is the modulus and [tex]0[/tex] is the angle created on the complex plane.
[tex]z = a + bi = |z| (cos ( 0 ) + I sin (0))[/tex]
The modulus of a complex number is the distance from the origin on the complex plane.
[tex]|z| = \sqrt{a^2 + b^2}[/tex] where [tex]z = a + bi[/tex]
Substitute the actual values of a = -5 and b = -5.
[tex]|z| = \sqrt{(-5) ^2 + (-5) ^2}[/tex]
Now Find [tex]|z|[/tex] .
Raise - 5 to the power of 2.
[tex]|z| = \sqrt{25 + (-5) ^2}[/tex]
Raise - 5 to the power of 2.
[tex]|z| = \sqrt{25 + 25}[/tex]
Add 25 and 25.
[tex]|z| = \sqrt{50}[/tex]
Rewrite 50 as 5^2 . 2 .
[tex]|z| = 5\sqrt{2}[/tex]
Pull terms out from under the radical.
[tex]|z| = 5\sqrt{2}[/tex]
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
[tex]0 = arctan (\frac{-5}{-5} )[/tex]
Since inverse tangent of [tex]\frac{-5}{-5}[/tex] produces an angle in the third quadrant, the value of the angle is [tex]\frac{5\pi }{4}[/tex] .
[tex]0 = \frac{5\pi }{4}[/tex]
Substitute the values of [tex]0 = \frac{5\pi }{4}[/tex] and [tex]|z| = 5\sqrt{2}[/tex] .
[tex]5\sqrt{2} ( cos( \frac{5\pi}{4}) + i sin (\frac{5\pi}{4}))[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
The complex number (5 - 5i) in trigonometric form is
5√2 [cos(-π/4) + i sin(-π/4)]
What is an imaginary number?An imaginary number is denoted by i.
The value of i is √-1.
We have,
To express the complex number (5 - 5i) in trigonometric form,
We first need to find its modulus (r) and argument (θ).
The complex number (a - bi) in trigonometric form is
|r| [cosФ + i sinФ]
Now,
Modulus (r).
|r| = √(5² + (-5)²)
= √(50)
= 5√(2)
And,
Argument (θ).
θ = [tex]tan^{-1}[/tex](-5/5)
= -π/4
(since the complex number is in the fourth quadrant)
Therefore,
The complex number (5 - 5i) in trigonometric form is
5√2 [cos(-π/4) + i sin(-π/4)]
Learn more about imaginary numbers here:
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What is the simplified expression for 3 y squared minus 6 y z minus 7 + 4 y squared minus 4 y z + 2 minus y squared z? y squared minus y squared z minus 10 y z minus 5 y squared minus y squared z minus 5 y z minus 5 7 y squared minus y squared z minus 10 y z minus 5 7 y squared minus y squared z minus 2 y z minus 5
Answer:
7y^2 - y^2z - 10yz-5
C. 7 y squared minus y squared z minus 10 y z minus 5
Step-by-step explanation:
A. y squared minus y squared z minus 10 y z minus 5
B. y squared minus y squared z minus 5 y z minus 5
C. 7 y squared minus y squared z minus 10 y z minus 5
D. 7 y squared minus y squared z minus 2 y z minus 5
Given:
3y^2 - 6yz - 7 + 4y^2 - 4yz + 2 - y^2z
Collect like terms in the expression
3y^2 + 4y^2 - 6yz - 4yz - y^2z - 7 + 2
Simplify
7y^2 - 10yz - y^2z - 5
Rewritten as
7y^2 - y^2z - 10yz-5
Option C. 7 y squared minus y squared z minus 10 y z minus 5
Is the answer
Answer:
C. 7 y squared minus y squared z minus 10 y z minus 5
Step-by-step explanation:
I took the cumulative exam...
Also I want the person above me to get brainliest... :)
Please answer it now in two minutes
Answer:
[tex] C = 28.9 [/tex]
Step-by-step explanation:
Given the right angled triangle, ∆BCD, you are required to find the measure of angle C.
Apply the trigonometric ratio formula to find m < C.
Adjacent side = 7
Hypotenuse = 8
Trigonometric ratio formula to apply would be:
[tex] cos(C) = \frac{7}{8} [/tex]
[tex] cos(C) = 0.875 [/tex]
[tex] C = cos^{-1}(0.875) [/tex]
[tex] C = 28.9 [/tex]
(To nearest tenth)
Find the product of additive inverse and multiplicative inverse of 3/2
Answer:
Additive inverse = -3/2
Multiplicative inverse = 2/3
Step-by-step explanation:
To find Additive inverse, just change the sign.
Additive inverse of 3/2 = -3/2
If we add a number and its additive inverse, we will obtain 0.
Multiplicative inverse of number a is 1/a and multiplicative inverse of a fraction a/b is b/a.
When we multiply a number & its inverse, we will get 1
Multiplicative inverse of 3/2 = 2/3
What is the value of r? What is the length of EB?
Answer:
r=9
EF = 55
Step-by-step explanation:
CF = ED
9r - 6 = 8r+3
Subtract 8r from each side
9r-8r - 6 = 8r-8r+3
r-6 =3
Add 6 to each side
r-6+6 = 3+6
r = 9
EF= CD = 4r+19
= 4*9+19
=36+ 19
=55
What is the function rule for the line
Which table represents a function?
Answer:
Table 4 represents a function.
Step-by-step explanation:
Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.
determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use the pi key on your calculator.
a) the volume is _____
b) the surface area is ____
Step-by-step explanation:
The figure above is a cube since all it's sides are equal
Volume of a cube = l³
where l is the length of one side
From the question
l = 3yd
So the volume of the cube is
Volume = 3³
Volume = 3yd³
Surface area of a cube = l²
Surface area = 3²
= 9yd²
Hope this helps you
What is the discriminant of 9x^2+2=10x
Answer:
28.
Step-by-step explanation:
9x^2 + 2 = 10x
9x^2 - 10x + 2 = 0
The discriminant is b^2 - 4ac.
In this case, a = 9, b = -10, and c = 2.
(-10)^2 - 4 * 9 * 2
= 100 - 36 * 2
= 100 - 72
= 28.
Since the discriminant is positive, there are two real solutions to the function.
Hope this helps!
2) The senior classes at High School A and High School B planned separate trips to the local
amusement park. The senior class at High School A rented and filled 2 vans and 14 buses with
294 students. High School B rented and filled 3 vans and 7 buses with 161 students. Each van
and each bus carried the same number of students. Find the number of students in each van and
in each bus.
A) Van: 9, Bus: 28 B) Van: 11, Bus: 27
C) Van: 20, Bus: 7 D) Van: 7, Bus: 20
Answer:
D) Van: 7, Bus: 20
Step-by-step explanation:
Add the amount of students together (455 students in total)
Then I added the amount of buses and vans together (5 Vans and 21 Buses)
Then I plugged in each answer
5 x 7 = 35
455 - 35 = 420
420 / 21 = 20
4. If and β are zeroes of the polynomial x²+4x+3, find the polynomial whose zeroes are 1+/ and 1+/ β
Answer:
(1+β)/α = 2
(1+α)/β = 0
Step-by-step explanation:
We need to determine the zeros of the polynomial. This would be done by equating the polynomial to zero and using factorization method to find the variables
x²+4x+3 = 0
x²+x+3x+3=0
x(x+1) +3 (x+1) = 0
(x+1)(x+3) = 0
(x+1)= 0 or (x+3) = 0
x= -1 or -3
If α = -1, and β=-3
(1+β)/α = (1-3)/-1 = -2/-1
(1+β)/α = 2
(1+α)/β = (1-1)/-3 =0/-3
(1+α)/β = 0
Find the values ofx and y for the triange.
x
60°
30°
у
Answer:
X=36.4 or 36.37306696.... and Y=42
Step-by-step explanation:
So you have a 30-60-90 triangle!
Do Not Worry this is a hard subject to understand, but I will try to do my best with helping you. Right now you need to find x and y. All you have is 21. Under your 60 angle, which is pointing downward, is the 21. And 21 is initially in the spot of x or 1. so 21 is the x(But not the x on the side of 90). I am sorry if this is a bit confusing.
You are then going to take your side which is x, the side that is directly in the path of 90, and it is going to be 21[tex]\sqrt{3[/tex]. Then on the side of your y, which is in the path of your 60, it will be 2 times your x.
The general layout of this is:
x is underneath the side of 90 degrees.
then on the side where 60 degrees and 30 degrees is, is going to be x[tex]\sqrt{3[/tex].
Then the last side, where 30 degrees and 90 degrees lay, will be 2(x).
So all you have to do is plug everything in.
x=36.4 in decimal
y=42(because all you had to do was plug 21 where the x is, because that is where x is in the general layout.)
The value of x = 42 units
The value of y = 21√3 units
What is Trigonometry?The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.
As per the given diagram:
The triangle is a right angle triangle.
Using trigonometric ratios to find x and y:
tan30° = (P/B)
tan30° = (21/y)
(1/√3) = (21/y)
y = 21√3 units
sin30° = (P/H)
(1/2) = (21/x)
x = 2 × 21
x = 42 units
The value of x and y is 42 units and 21√3 units, respectively.
To learn more on Trigonometry, click:
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Pleas answer it now in two minutes
Answer:
30
Step-by-step explanation:
cos^-1(square root of 3 divided by 2)
The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Select three options. On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 0.5, 6.75), and goes through (1, 0). The vertex is the maximum value. The axis of symmetry is x = negative one-half. The domain is all real numbers. The range is all real numbers. The function is decreasing from (−∞, 6.75).
Answer:
On a coordinate plane, a parabola opens down
has a vertex at (negative 0.5, 6.75)
The vertex is the maximum value. The axis of symmetry is x = negative one-half.
The domain is all real numbers
Step-by-step explanation:
Answer:
The vertex is the maximum value.
The axis of symmetry is x = negative one-half.
The domain is all real numbers.
Step-by-step explanation:
The answer above is correct.
Meryl needs to cut down 10.5 trees for every 5 cabins she builds. How many trees will she need to cut down if she builds 7 cabins?
Answer:
14.7 TreesStep-by-step explanation:
[tex]10.5 \:trees = 5 \:cabins\\x \: trees\:\:\:\:\:\:=7\:cabins\\\\5x = 73.5\\\frac{5x}{5} = \frac{73.5}{5}\\ x = 14.7 \: trees[/tex]
Given the following formula, solve for t.
v=u+at
Answer: t= v-u/a
Step-by-step explanation: V=u-at
V-u=at
Subtract u from both sides
V-u=at
Divide both sides by a
v-u/a=at/a
v-u/a=t
Help me with these 2 questions please
Answer:
1st one= B 25 cents
2nd one= D 2 miles
Step-by-step explanation:
1.
8x3=24
6/24=25
= 25 cents
2.
1.6 km= 1 mile
so 1/2 of a mile =
0.8 km
1/4 of an hour = 15 minutes
0.8km= 15 minutes
15x3= 45 minutes
0.8km x 3= 2.4km
2.4km = 2 miles
hope it helps hunney xx
A pair of dice is rolled. What is the probability that the sum is 11? Please show your work!
Answer:
2/36 or 1/18
Step-by-step explanation:
There are 36 possible outcomes (6x6).
Only 2 possibilities equal 11. (5+6 and 6+5).
So the probability is 2/36, or 1/18.
If it rains, I do not go sailing. It rains 10 % 10\% 10% of days; I go sailing 3 % 3\% 3% of days. If it does not rain, what is the (conditional) probability that I go sailing? Written "p(I go sailing | it does not rain)''
Answer:
0.03333 or 1/30
Step-by-step explanation:
Let A =" I go sailing" and B = "it does not rain"
P(A) = 0.03
P(B) =0.90
Since I never go sailing when it rains, P(A and B) =0.03.
Therefore, the (conditional) probability that I go sailing, given that it does not rain is:
[tex]P(A|B)=\frac{P(A\ and\ B)}{P(B)} \\P(A|B)=\frac{0.03}{0.90}=0.033333[/tex]
The probability is 0.03333 or 1/30.
Which of these r-values represents the strongest correlation?
A. -0.7
B. -0.8
C. -0.6
D. -0.5
I guess the answer is D because it is the most far from -1 rather than the other
Answer: The answer should be D.-0.5
How to find and solve this ?
Shape A = ______ units
Shape B = _______ units
Answer:
A = 12
B = 14
Step-by-step explanation:
You essentially have to count the number of squares that are filled in.
Shape A has 12 units filled in.
Shape B has 14 units filled in.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
B.
Step-by-step explanation:
First, it must be in descending order (i.e. largest to smallest). Thus, we can eliminate C and D since they go from smallest to largest.
Next, we need to find the degree of A and B. The degree of a polynomial is simply the highest exponent value of all the variables in a single term. If this is confusing, let's use A as an example.
In A, we have four terms: x^3y^3, xy^2, 5xy, and -4. This is a sixth degree polynomial. This is because for the first and largest term, x^3 and y^3, the total value of their exponents is 6. Because of this, A is not our answer.
For B, the biggest term is xy^2, and the degree is 1+2=3. Therefore, our answer is B since it is a third degree polynomial and it's in descending order.
Note that C is also a third-degree polynomial, but it's not written in descending order.
Compare the functions shown below: f(x) x y −3 −27 −2 −8 −1 −1 0 0 1 1 2 8 3 27 4 64 g(x) linear graph with y intercept of negative 1 and x intercept of negative 2 h(x) = (x + 4)2 + 2 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4? f(x), g(x), h(x) g(x), f(x), h(x) h(x), g(x), f(x) g(x), h(x), f(x)
Hey There!!
To get the average rate of change, we simply have to use this formula:
ARC = (y2 -y1) / (x2 - x1)
For the first function:
ARC = (64 - 0) / (4 - 0) = 16
For the second function, since it's a line, the ARC would just be equal to the slope
m = ARC = (-1 - 0) / (0 - (-2)) = -0.5
For the third function:
h(0) = 18
h(4) = 66
ARC = (66 - 18) / (4 - 0) = 12 Therefore, the order of the functions from lest to greatest according to the average rate of change on the interval from x= 0 to x = 4 is:
g(x)
h(x)
f(x)
Hope This Helps!!
By ☆Itsbrazts☆
Answer:
slope of f(x) is 16 slope of g(x) is -1/2 and tho slope of h(x) 12.5
Step-by-step explanation:
Decide whether the data table represents a linear function or an exponential function
Answer:
A
Step-by-step explanation:
Answer is a because the common difference is -9
Answer:
the data represent a linear function because there is a common difference of -9
Step-by-step explanation:
Brock wants to compete for the featherweight boxing title, but the upper limit for that weight class is 126 pounds. He currently weighs 134 pounds. Brock can lose 3 pounds per day if he does vigorous workouts. The number of days, d, that Brock will need to work out to compete at the featherweight level is represented by the inequality 134 – 3d < 126. Select the fewest number of days he would have to work out to compete at the featherweight level. A. 1 B. 2 C. 3 D. 4 E. 5
Answer:
C. 3
Step-by-step explanation:
Brock weighs 134 pounds, he will lose 3 pounds a day until he is 126 pounds
D will represent the number of days he will work out.
134 - 3d < 126
134 - 3(3) < 126
134 - 9 = 125
125 < 126
3 days
We can say that Brock needs to workout for minimum 3 days to compete at feather weight level.
HELLLPPPP I need a explication on whether or not these angle relationships are possible
Answer:
Step-by-step explanation:
5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180
Answer:
no, the values would be above 180º
Step-by-step explanation:
if...
(4x - 9) + (2x + 3) + y = 180
(5x + 30) + y = 180
then...
(4x - 9) + (2x + 3) = 5x + 30
so...
6x - 6 = 5x + 30
x = 36
plug it in.
4(36) - 9 = 135
2(36) + 3 = 75
already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.
Select the correct answer.
This table defines a function.
Х
13
16
7
21
10
30
y
39
48
Which table represents the inverse of the function defined above?
Answer:
B.
Step-by-step explanation:
To get the inverse of the function defined by the table given, all you need to do is to interchange the coordinate pairs.
That is, the coordinates pair on a table that defines a function is usually given as (x, y). The inverse of the function would be (y, x).
The following are the coordinate pairs given and the inverse of the function represented:
(x, y) => inverse = (y, x)
(7, 21) => inverse = (21, 7)
(10, 30) => inverse = (30, 10)
(13, 39) => inverse = (39, 13)
(16, 48) => inverse = (48, 16)
The table that represents the inverse of the function given in the question is option B
winthrop has $4.40 worth of nickles and dimes. If winthrop has 3.5 times as many nickles as he has dimes, how many dimes does he have?
Answer:
16
Step-by-step explanation:
If n is number of nickles and d is number of dimes:
5n + 10d = 440
n = 3.5d
Substitute:
5(3.5)d + 10d = 440
17.5d + 10d = 440
27.5d = 440
d = 16
Mrs.joshi bought a saree for Rs 1750.she sold it at a profit of 4%.what would be her profit or loss percent ?
Answer: Rs 1820
Step-by-step explanation:
This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750. Thus, simply do 1.04*1750 to get 1820.
Hope it helps <3
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
f(x) = 2(x –3)²
Step-by-step explanation:
f(x) = 2x² – 12x + 18
The vertex form of the above expression can be obtained as follow:
f(x) = 2x² – 12x + 18
Factorise
f(x) = 2(x² – 6x + 9)
Next, we shall simplify x² – 6x + 9 by factorisation method.
This is illustrated below:
x² – 6x + 9
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.
The factors are –3x and –3x
Next, replace –6x with –3x and –3x in the equation above as shown below:
x² – 6x + 9
x² – 3x –3x + 9
Factorise
x(x – 3) –3(x –3)
(x –3)(x –3)
(x –3)²
f(x) = 2x² – 12x + 18
f(x) = 2(x² – 6x + 9)
f(x) = 2(x –3)²
Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is
f(x) = 2(x –3)²
given that 2d=5b^3+c express b in terms of c and d
Answer:
b = [tex]\sqrt[3]{\frac{2d-c}{5} }[/tex]
Step-by-step explanation:
Given
2d = 5b³ + c ( subtract c from both sides )
2d - c = 5b³ ( divide both sides by 5 )
[tex]\frac{2d-c}{5}[/tex] = b³ ( take the cube root of both sides )
[tex]\sqrt[3]{\frac{2d-c}{5} }[/tex] = b