Answer:
B. cos(pi/2) +i·sin(pi/2)
Step-by-step explanation:
You can convert to rectangular and back, or you can use the trig function relations directly.
w = 4·cis(π/2) = 4i
z = 3·cis(3π/2) = -3i
Then the sum is ...
w +z = 4i -3i = i = cis(π/2) . . . . matches choice B
__
An alternative representation of z is ...
z = -3·cis(π/2)
Then ...
w +z = 4·cis(π/2) -3·cis(π/2) = cis(π/2)
_____
Additional comment
In the above, we have used cis(α) to represent (cos(α) +i·sin(α)).
At the craft store, Ivan bought a bag of orange and purple marbles. The bag contained 48 marbles, and 75% of them were orange. How many orange marbles did Ivan receive?
Answer:
jjjjjjjjjjjjjjjjjjjjjjjj
Write an equation in slope-intercept form of the line shown. (-6, 4) (-2, 2)
Evaluate the expression x=7.x+8
Answer:
15
Step-by-step explanation:
For each time I see x, I replaced it with 7 because I know that x is equal to 7.
I only see one x so I am only replacing that one x so instead of x + 8, I get 7 + 8 and you could split 8 into 5 + 3 and split 7 into 5 + 2.
5 plus 5 is 10. If you are having trouble adding the numbers you could put up 5 fingers first and then add one finger up one by one to still the number 10. Now that just leaves you with 3 + 2.
You could first put up 3 fingers and then add two more to get a total of 5 fingers.
At last, you could just add 10 + 5 to get 15 in total.
Hope this works you!!!
The price of a stock was $24.56 per share. An investor decided to spend $5,000 to buy shares of the stock. To the nearest whole number, what is the maximum number of shares of stock that the investor can buy
Answer:
203 i just did it
Step-by-step explanation:
Answer:
the answer is 203
Step-by-step explanation:
Just got it right on edge 22
one angle of a right triangle measures 80degrees.what is the measure of the other acute angle
Answer:
10°Step-by-step explanation:
the sum of the internal angles of a triangle is 180 °, it is a right triangle so an angle is 90 °, you know another one and it is 80 °, from 180 ° you remove the two known angles and you have the measure of the unknown one.
180 - 90 - 80 =
10°
Danny Whitman, un analista de valores de Your Bottom Dollar, Inc. Siempre ha considerado que es más probable que los bonos convertibles se sobrevaloren más que los bonos de ingresos. De 312 bonos convertibles del año anterior, Danny encontró que 202 estaban sobrevalorados,
mientras que 102 de los 205 bonos de ingreso estaban sobrevalorados. ¿Estos datos confirman la posición de Danny? Sea =., y pruebe la hipótesis
Existe un mayor porcentaje de bonos convertibles sobrevalorados comparado con el porcentaje de bonos de ingresos sobrevalorados, con lo cual la afirmación de Danny es correcta.
Dado que Danny Whitman, un analista de valores de Your Bottom Dollar, Inc. siempre ha considerado que es más probable que los bonos convertibles se sobrevaloren más que los bonos de ingresos, y de 312 bonos convertibles del año anterior, Danny encontró que 202 estaban sobrevalorados, mientras que 102 de los 205 bonos de ingreso estaban sobrevalorados, para determinar si estos datos confirman la posición de Danny se debe realizar el siguiente cálculo:
202/312 = 0.6474102/205 = 0.4975Por lo tanto, existe un mayor porcentaje de bonos convertibles sobrevalorados comparado con el porcentaje de bonos de ingresos sobrevalorados, con lo cual la afirmación de Danny es correcta.
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Find the equation of the line passing through the following : (-1;6) and (-3;0)
Please help...
Answer:
Step-by-step explanation:
[tex](x_{1} , y_{1}) = (-1,6)\\\\(x_{2},y_{2}) = ( -3, 0)\\\\Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_1}}\\\\\\=\dfrac{0-6}{-3+1}\\\\\\=\dfrac{-6}{-2}\\\\=3[/tex]
Equation of the line: y= mx +b
y = 3x + b
Substitute ((-1 , 6) in the above equation
6 = 3*(-1) + b
6 = -3+b
6 +3 = b
b = 9
y = 3x + 9
A certificate of deposit with principal $150 earns 4% annual interest for 2 years. Select all the options that would earn the same amount of interest.
$300 at 2% for 2 years
$150 at 6% for 18 months
$400 at 3% for 1 year
$100 at 1% for 8 years
$50 at 48% for 6 months
Answer:
a,c
Step-by-step explanation:
You would get $12 in the certificate of deposit, and
a. 12
b. 13.5
c. 12
d. 8
e. 24
so, a and c
Hope this helps!
Let me know if it does and if the answer is right
Interest earned in options $400 at 3% for 1 year, $400 at 3% for 1 year
and $50 at 48% for 6 months has the same interest earned by, as $150 earn 4% annual interest for 2 years.
As mentioned in the question, A certificate of deposit with a principal of $150 earns 4% annual interest for 2 years.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
here,
1. $300 at 2% for 2 years
Simple Interest = principal × rate × time / 100
Simple interest = 300 × 2 /100 × 2
Simple interest = $12
Similarly, interest earned by other options is given as,
2. $13.5
3. $12
4. $8
5. $12
Thus, Options A, C, and E are correct.
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Complete the table using the equation y = 8x + 8 ( helppp plsss)
Answer:
0, 8, 16, 24, 32
Step-by-step explanation:
plug in the values given for x into the 8x+8 equation
Example:
8(-1)+8
8(0)+8
Answer:
(-1, 0), (0, 8), (1, 16), (2, 24), (3, 32)
Step-by-step explanation:
To find answers to problems like these, take the x-value, which in this case is -1, and replace it with the variable,
y = 8*-1 + 8. Then do the rest, y = -8 + 8, y = 0. You already have the x, -1, and now you got y, 0. Then pit in ordered pairs, x first, then y, (-1, 0)
Jacob has a headache. He can't stand long lists. "Can you repeat that again?" he asks. "It's easy. Name a number that is greater than 10, less than 20, is a multiple of 7, and FINALLY is a factor of 42," Replies Eric.
Answer:
Well here are the constraints given to us here
Lets make this number “x”
x > 10
x< 20
7x
X = 1, 2, 6, 7, 21, 42
So with all this we can come up with this
10 < 7x < 20 = 1, 2, 3, 6, 7, 14, 21, 42
So lets cut this down a bit
It’s gotta be a multiple of 7 so we can get rid of 3 of the solutions
It can be 7, 14, 21, 42
Now it has to be more then 10 but less then 20
So that gets rid of everything except 14
14 is your answer
it costs $20 per day to board a dog and $16 per day to board a cat. The kennel needs to make at least $800 per day to cover expenses, but can hold no more than 80 total animals. Write a systems of inequalities, graph , and give two possible solutions to the number of dogs and cats they can board each day
Answer:
Step-by-step explanation:
the anwer is r=dog y=cat 20r+16y>800-->y>-5/4 r+50 20r-16y<r+80 40 dogs+20 cats 15+55 cats
9y?+21yz -8y?
hey, cansomebody help me? we've to factorize.
The factor of the expression 9y² + 21yz⁴ - 8y² will be y and (y + 21z⁴).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 9y² + 21yz⁴ - 8y²
Simplify the expression, then we have
⇒ 9y² + 21yz⁴ - 8y²
⇒ y² + 21yz⁴
Factorize the expression, then we have
⇒ y² + 21yz⁴
⇒ y(y + 21z⁴)
The factor of the expression 9y² + 21yz⁴ - 8y² will be y and (y + 21z⁴).
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At a certain theater 4 adult tickets and 2 children's tickets cost
$36.50. Three adult tickets and 5 children's tickets cost $38.75. Which
system of equations could be used to determine the cost of one adult
ticket, a, and one child's ticket, c?
A. 4a +2c= 36.50
3a + 5c = 38.75
B. 7a+ 7 = 14
a+b= 75.2
C. 7a = 36.50
5a + 7c = 38.75
D. 4a + 2c = 38.75
За + 5c = 36.50
And how much is an adult ticket?how much is an child ticket?
Answer:
A
Step-by-step explanation:
if a = amount of adult tickets and c = amount of children's tickets
4 adult tickets plus 2 children's tickets equals $36.50
4a + 2c = 36.50
Also, 3 adult tickets and 5 children's tickets equals $38.75
3a + 5c = 38.75
Benny has a baseball card collection he has 13,789 cards he wants to put the card in a scrapbook that holds 15 cars on a page how many pages does Denny need in his scrapBook.
Answer:
920 pages
Step-by-step explanation:
Divide 13,789 by 15, you should get 919.27 so just round up so you can hold all the cards.
Pleaseee help me A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function (x) -0.8x? - 256x+29,444. What is the minimum unit cost?
Do not round your answer.
Answer: 8,964
Step-by-step explanation: x= -b/2a. So, -(-256)/2(0.8)= 160. Plug in 160 to the whole equation.
0.8(160)^2 -256(160)+29444
=8,964
find the measure of the indicated angle that makes lines u and v parallel
Answer:
55 degrees
Step-by-step explanation:
if u and v are parallel and cut by the transversal in the middle the two angles would be congruent or equal to each other , therefore the angle in question is also 55
Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28.
(correct the error below!)
first term =4
common difference =8
tenth term =4 +10(8) = 84
Answer: The tenth term is 76
=======================================================
Explanation:
We use this arithmetic sequence formula to get the nth term
[tex]a_n = a_1 + d(n-1)[/tex]
Plug in [tex]a_1 = 4, \ d = 8, \ n = 10[/tex] and you should get the following:
[tex]a_n = a_1 + d(n-1)\\\\a_{10} = 4 + 8(10-1)\\\\a_{10} = 4 + 8(9)\\\\a_{10} = \textbf{76}\\\\[/tex]
The tenth term is 76
---------
We can verify this by listing out the terms one by one. Start at 4, add on 8 each time, until you generate the 10th term. A table like the one shown below is a good way to keep track of all the terms.
[tex]\begin{array}{c|c}\boldsymbol{n} & \boldsymbol{a_n}\\1 & 4\\2 & 12\\3 & 20\\4 & 28\\5 & 36\\6 & 44\\7 & 52\\8 & 60\\9 & 68\\10 & \textbf{76}\\\end{array}[/tex]
---------
In short, the error is with the "10" in the expression 4+10(8). The student should have used 9 instead. This is because of the n-1 term in [tex]a_n = a_1 + d(n-1)[/tex] which shifts everything one spot to the left.
Assuming lines m and n are parallel, what is the value of x?
Solve the system of linear equations below.
6x + 3y = 33
4x + y = 15
A x = 2, y = 7
B. X = -13, y = 7
C x = -2/3, y = 12*2/3
D. x = 5, y = 1
Answer:
A
Step-by-step explanation:
6x+3y=33 <=> 2x+y=11<=>4x+2y=22 (1)
4x+y=15 (2)
(1)-(2) <=> y=7
Answer:
A x = 2, y = 7
Step-by-step explanation:
6(2)+3(7)= 33
4(2)+(7)=15
ANSWER ASAP WILL AWARD BRAINLIEST
Answer:
18/5 + −8/5√3 (as a decimal: 0.828719)
Which of the following decimals is equal to 3 1/40 ? Select TWO that apply
A 3.0025
B 3.025
С 3. overline 0025
D 3.overline 025
E 3.0025 overline0
F. 3.025overline0
=======================================================
Explanation:
Use long division or your calculator to find that 1/40 = 0.025
Add on 3 to get 3 & 1/40 = 3 + 1/40 = 3 + 0.025 = 3.025 which is choice B
For some reason, your teacher has decided to add on a string of 0's onto this to form [tex]3.025\overline{0}[/tex] that horizontal line over the '0' means the 0's go on forever. So, [tex]3.025 = 3.025\overline{0} = 3.025000000...[/tex], but we can always chop off the trailing zeros to make life simpler. I'm not sure why your teacher has decided to use this fairly strange format.
The decimal value is equivalent to 3.025.
What are decimal numbers?A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.We have the following fraction -
3 [tex]\frac{1}{40\\}[/tex]
We can write the mixed fraction as -
3 [tex]\frac{1}{40\\}[/tex]
(40 x 3 + 1)/40
121/40
3.025
Therefore, the decimal value is equivalent to 3.025.
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solve for the wavelength frequency and energy then identify the type of electromagnetic wave to complete the table
Answer:
See attachment
Step-by-step explanation:
λν = c [Wavelength, λ (lambda), times frequency, ν (nu), equals the speed of light.]
c = 3.0 x 108 m/s.
E = hν
h = Plank's constant = 6.626x10-34 J-s
I put the data in a spreadsheet and calculated the values as per the equations above. The table showing the types of energy was not attached, so I left that column blank. I assume it is looking for labels such as UV, Visible, IR, Radio, etc.
Here is the problem: (Picture)
Answer:
c
Step-by-step explanation:
If you can get poland spring water, 3 for $11.00 how much would be 2 cases of water?
explain
3 cases /3= $11 /3
1 case x 2= 11/3 x2
2 case = 22/3 = (round to the hundreth) $7.33
1 Solve for the unknown variable:
Answer:
Approximately 6.4
Step-by-step explanation:
We can use the pythagorean thereom here, that tells us (a^2)+(b^2)=c^2. C is the hypotenuse, the side opposite from the right angle, while a and b are the other sides. We can insert 5 and 4 as a and b, and solve for c
:(5^2)+(4^2)=c^2
:25+16=c^2
:41=c^2
:sqrt(41)=6.4=c (We square rooted both sides. 6.4 is only rounded to the nearest hundredths place.) Hope this helps!
Answer:
c = 6.4
Step-by-step explanation:
To find c, we need to use Pythagoras theorem which is:
[tex]a^2 + b^2 = c^2[/tex]
Plug known variables in:
[tex]5^2 + 4^2 = c^2\\25 + 16 = c^2\\\sqrt{25 + 16} = c\\\sqrt{41} = c \\c = 6.403\\c = 6.4[/tex]
Hope this helps!
Given that
2
x
−
9
y
=
11
Find
y
when
x
=
7
Answer:
y = 1/3
Step-by-step explanation:
[tex]2x-9y=11\\\\2(7)-9y=11\\\\14-9y=11\\\\-9y=-3\\\\y=\frac{1}{3}[/tex]
2 1/5
Step-by-step explanation:
Any where u see x u write 7;2(7)-9y=11
14-9y=11
Divide both sides by the difference of 14 and 9y
11/5y ; y=2 1/5
simplify by combining like terms 3k-2k
Answer:
k
Step-by-step explanation:
3k-2k=1k
1k=k so this is the answer
PLEASSSSSSE HELP, WILL GIVE BRAINLIEST
How many chromosomes would a diploid offspring have when the haploid sex cells contain 46 chromosomes?
23
46
58
92
Answer:
I think its 46 since the 2 speices need the same amount of chromosomes to make an offspring
Step-by-step explanation:
4x – 5y = 15
m=
b=
(I need to graph the linner equation)
Answer:
yea I agree that this is correct and it's 15 and it's 4x
can someone please tell me what is 12 x 8 +5?
Use BODMAS
first solving 12×8
which is = 12×8=96
than add +5
so, 96+5= 101
Hope This HelpsAnswer: 12x8=26+5= 31
Step-by-step explanation: