Answer:
C. 27iStep-by-step explanation:
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))^3
= {3(cosπ/6 + isinπ/6)}^3
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
The right answer is 27i
Which are the roots of the quadratic function f(q) = 02 - 125? Select two options.
O q = 5/5
O q = -5/5
q=3/5
q = -3/5
q=25/5
Write this algebraic expression in words 5(n-4)+7
Answer:
Five times the difference of n and four plus seven
Step-by-step explanation:
Five times the difference of n and four plus seven
Answer:
five multiplied by the difference of N and four plus seven
what is the distance between the points (-4,0) and (-7, -14) ?
Answer:
Step-by-step explanation:
(-4,0) ; (-7, -14)
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(-7-[-4])^{2}+(-14-0)^{2}}\\\\ =\sqrt{(-7+4)^{2}+(-14)^{2}}\\\\=\sqrt{(-3)^{2}+(-14)^{2}}\\\\=\sqrt{9+196} \\\\=\sqrt{205} \\\\=14.3178[/tex]
If you take out a loan that costs $561 60 over eight years at an interest rate of 9% how much was the loan for?
Answer:
The loan was $28184.81
Step-by-step explanation:
Let the loan amount be x
Rate of interest on Loan = 9%
Time = 8 years
Amount of loan over 8 years = $56160
Formula : [tex]A=P(1+r)^t[/tex]
Where A = Amount =56160
P = Principal = x
r = rate of interest = 9% = 0.09
t = time = 8 years
Substitute the values in the formula :
So,[tex]56160=x(1+0.09)^8[/tex]
[tex]\frac{56160}{(1+0.09)^8}=x[/tex]
$28184.81=x
Hence The loan was $28184.81
One batch of walnut muffins uses 1 1/3 cup of walnuts.How many cups of walnuts are needed to make 3 3/4 batches of muffins?
A. 5 1/12cups
B.3 3/12cups
C. 5 cups
D. 4 cups
PLS HELP !! ILL GIVE BRAINIEST
Answer: first one is a the second one is b
Step-by-step explanation:
the bottom is the total amount and the top should relate to the bottom
What is the distance between (6, 2) and (-3,-2)?
09
03
O V97
05
Answer:
√ 97
Decimal Form:
9.84885780 …
At a particular restaurant, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories and twice as many onion rings as there are sliders. Write a system of equations that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal. Define the variables that you use to write the system.
Step-by-step explanation:
r = onion rings amount
s = sliders amount
system of equations
2s = r
r(70) + s(200) = 1020
(for deltamath)
This question is based on the system of equations. Therefore, the system of equations 2s = r and r(70) + s(200) = 1020 are that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal.
Given:
At a particular restaurant, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories and twice as many onion rings as there are sliders.
According to the question,
Let the amount of onion rings be r and the amount of sliders be s.
Now, it is provided in question that, amount of sliders is twice as the onion rings. In mathematically expressed as,
⇒ 2s = r is the first system of equation.
Then, it is also give that, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories. This representing as,
⇒ r(70) + s(200) = 1020 is the second system of equation.
Therefore, the system of equations 2s = r and r(70) + s(200) = 1020 are that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal.
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What is the measure of AngleJHN? 25° 45° 50° 95°
Answer:
95 is the answer!
The measure of the angle ∠JHN will be 45°. Then the correct option is B.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Angle ∠MHL and angle ∠JHK are equal because the angles are opposite angles.
∠MHL = ∠JHK
3x + 20 = x + 20 + x + 25
x = 25
Then the measure of the angle ∠JHN is calculated as,
∠JHN = x + 20
∠JHN = 25 + 20
∠JHN = 45°
The measure of the angle ∠JHN will be 45°. Then the correct option is B.
More about the angled link is given below.
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The missing diagram is given below.
Can i get some help ♂️
Answer:
[tex]AC=13.5[/tex]
Step-by-step explanation:
Use the Law of Sines as follows:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
Insert the values (use the steps from the last problem):
[tex]\frac{sin25}{14} =\frac{sin24}{b}[/tex]
Isolate b. Multiply both sides by b:
[tex]b*(\frac{sin25}{14} )=b*(\frac{sin24}{b})\\\\b*\frac{sin25}{14}=sin24[/tex]
Multiply both sides by 14:
[tex]14*(b*\frac{sin25}{14})=14*(sin24)\\\\b*sin25=14*sin24[/tex]
Isolate b. Divide both sides by sin 25:
[tex]\frac{b*sin25}{sin25} =\frac{14*sin24}{ysin25} \\\\b=\frac{14*sin24}{sin25}[/tex]
Insert the equation into a calculator and round to the nearest tenth:
[tex]b=13.5[/tex]
The length of AC is 13.5 units.
:Done
A volcano Irruption blasts a boulder upward with an initial velocity of 240 ft./s This modeled by the equation h(t)=-16t^2+240t. How heigh will the boulder be after 5 seconds?
Answer:
1600 ft
Step-by-step explanation:
Larry, Barry, Terry are saving their money for a trampoline that costs $340.
• The amount of money Larry has saved can be represented by x.
• The amount of money Barry has saved is 1
1
2
times the amount Larry has saved.
• The amount of money Terry has saved is 1
1
3
times the amount Larry has saved.
• The total amount of money saved by Larry, Barry, and Terry is $322.
What is x, the amount of money saved by Larry?
Answer:
Larry=X
Barry=112x
Terry=113x
L+B+T=322
x+112x++113x=322
226×=322
Larry saved $1.42
Answer:
$84
Step-by-step explanation:
I did it before.
What are the solutions to the equation 0 = x2 - X-6? Select two options
X=-3
X=-2
Ex=0
x=2
X = 3
Step-by-step explanation:
x2 - x - 6 = 0
x2 - 3x + 2x - 6 = 0
x(x - 3) + 2(x - 3) = 0
x - 3 = 0. x + 2 = 0
x = 3 x = - 2
Option no 2 and 5 are the correct answer
Simplify the Expression:
-5/8 (-3/8-1/4)
Answer:
25/64
Step-by-step explanation:
please help!!!!!!!!!!!!!!!!!
Answer:
x= 112
Step-by-step explanation:
(n-2)180
n is the number of sides
(7-2)180
(5)180
900
900-130-132-130-130-128-138=x
rules of pemdas
x=112
1 gal 3 c= _fl oz
Convert the unit of capacity
Answer:
152 fluid ounces
Step-by-step explanation:
there are 128 fluid ounces in 1 gallon. there are 24 fluid ounces in 3 cups. 128+24 is 152. :)
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 26 feet and a height of 14 feet. Container B has a diameter of 18 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full. After the pumping is complete, what is the volume of the empty space inside Container A
Answer:
First, let's work out the V of container A and B
V_A = pi x (diameter/2)^2 x height = pi x (26/2)^2 x 14 = 2366 pi (ft3)
V_B = pi x (diameter/2)^2 x height = pi x (18/2)^2 x 15 = 1215 pi (ft3)
After pumping water from container A to container B until B is full:
The empty space inside container A would be:
V_empty = V_A - V_B = 2366 pi (ft3) - 1215 pi (ft3) = 1151 pi (ft3) = ~3615.97 (ft3)
Answer:
3,815.1 feet³
Step-by-step explanation:
Volume filled in B = Volume emptied from A
pi × r² × h
3.14 × (18/2)² × 15
3815.1 feet³
Which could be the area of the base of the triangular prism?
[Not drawn to scale]
A) 6 ft2
B) 10 ft2
C) 12 ft2
D) 20 ft2
Answer:
It's 20 because 5ft times 4ft gives you 20ft
help me plz asap!!!!!!!!!!
Answer:
125
Step-by-step explanation:
8x-41+9x+17=180
17x-24=180
17x=204
x=12
9(12)+17
125
Are my answers correct?
Answer:
I would have got the same answers so probably yea
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
According to my understanding I believe you are correct!
help please, what is the the perimeter of the figure to the nearest hundredth.
Answer:
100
Step-by-step explanation:
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answer:
Step-by-step explanation:
y4−
(y2−9)(y2+9)
9
Distribute:
=y4+
−1
9
y4+9
Combine Like Terms:
=y4+
−1
9
y4+9
=(y4+
−1
9
y4)+(9)
=
8
9
y4+9
Answer:
=
8
9
y4+9
The polynomial expression is divisible by 9
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial be represented as A
Now , A = y⁴ - (y² - 9)(y² + 9)
To prove that the expression y⁴ - (y² - 9)(y² + 9) is divisible by 9 for any value of y, we can use algebraic manipulation and factorization.
First, we can simplify the expression inside the parentheses:
y² - 9 = (y - 3)(y + 3)
y² + 9 = (y + 3i)(y - 3i)
where i is the imaginary unit, i.e., i² = -1.
Substituting these expressions back into the original equation, we get:
y⁴ - (y² - 9)(y² + 9) = y⁴ - (y - 3)(y + 3)(y + 3i)(y - 3i)
Now, we can factor out (y − 3)(y + 3) from the second term:
y⁴ - (y² - 9)(y^2 + 9) = y⁴ - (y² - 9)(y² + 9) + 9(y - 3)(y + 3)
= y⁴ - (y² - 3^2)(y² + 3²)
= (y²)² - (3²)²
= (y² + 3²)(y² - 3²)
= (y² + 9)(y² - 9)
= (y + 3i)(y - 3i)(y + 3)(y - 3)
Now, we can see that the expression is equal to the product of four factors: (y + 3i), (y - 3i), (y + 3), and (y - 3). Note that either (y + 3i) and (y - 3i) or (y + 3) and (y - 3) must have the same residue modulo 3, since there are only three residues modulo 3 (0, 1, and 2) and four factors. In either case, the product of the two factors that have the same residue modulo 3 is divisible by 3, and therefore the entire expression is divisible by 3.
Moreover, since (y + 3) and (y - 3) are both odd or both even, the product of (y + 3) and (y - 3) is divisible by 8, which implies that the entire expression is also divisible by 8.
Hence , the expression y⁴ - (y² - 9)(y² + 9) is divisible by both 3 and 8 for any value of y, and therefore it is also divisible by their least common multiple, which is 9
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What is the area of the trapezoid?
Answer:
The answer is 36 squared centimeters
What is the answer please help me
Answer:
Step-by-step explanation:
the first one is D
Answer:
first one is 180
Step-by-step explanation:
3x and -2x are they like terms or unlike terms
Answer:
Yes they are like terms.
Step-by-step explanation:
As like terms are those who has same variables or powers.Here,we have same variables for both the terms and both have the power 1.
hope it helps!
What value of x is in the solution set of 8x - 6 > 12 + 2x?
ܟ
ܢܐ ܘ ܚ ܗ
Answer:
x > 3
Step-by-step explanation:
8x - 6 > 12 + 2x
1. add 6 to both sides.
8x > 12 + 2x + 6
2. Simplify 12 +2x + 6 to 2x + 18.
8x > 2x + 18
3. Subtract 2x from both sides.
8x - 2x > 18
4. Simplify 8x - 2x to 6x.
6x > 18
5. Divide both sides by 6.
x > 18/6
6. Simplify 18/6 to 3.
x > 3
What is the volume of the composite figure?
Answer:
Make headway with these volume of a composite 3D figure worksheet pdfs featuring figures made up of 2 or 3 solid shapes. Add the volume of each geometric ...
Step-by-step explanation:
Help me please I really need help
Answer: Find the area of all figures and then add it together
Step-by-step explanation:
A family has 4 children: Ariel, Bob, Chris, and Diana. Assuming that all birth orders are equally likely.
Find the probability that Ariel is older than Diana.
Find the probability that Ariel is older than Diana, if it is given that Ariel is older than Bob.
Find the probability that Ariel is older than Diana, if it is given that Chris is older than Diana.
Find the probability that Ariel is older than Diana, if it is given that Diana is older than Bob.
Answer:
A) 0.5
B) 0.375
C) 0.375
D) 0.167
Step-by-step explanation:
Let's call
a: Ariel
b: Bob
c: Chris
d: Diana
There are 4*3*2*1 = 24 total combinations to order the 4 children
A) Ariel is older than Diana in the following 12 cases:
a b c d
a b d c
a c b d
a c d b
a d b c
a d c b
b a c d
b a d c
b c a d
c a b d
c a d b
c b a d
Then, the probability is 12/24 = 0.5
B) The condition "Ariel is older than Diana, if it is given that Ariel is older than Bob" is satisfied in the six first cases and last three cases of before.
Then, the probability is 9/24 = 0.375
C) Ariel is older than Diana, if it is given that Chris is older than Diana, in the following cases:
a b c d
a c b d
a c d b
a d c b
b a c d
b c a d
c a b d
c a d b
c b a d
Then, the probability is 9/24 = 0.375
D) Ariel is older than Diana, if it is given that Diana is older than Bob, in the following cases:
a c d b
a d b c
a d c b
c a d b
Then, the probability is 4/24 = 0.167
Answer:
jesus
Step-by-step explanation:
plz help
(2x/0.25)−0.525=7.475
what's x?
Answer:
i used calculator and got 1
Step-by-step explanation:
