What is the argument of -5\sqrt{3}+ 5i?
Answers
Answer:
150 degrees
Step-by-step explanation:
Graphing the complex number we see the angle terminates in the second quadrant. This means the argument, the angle, will be between 90 degrees and 180 degrees.
So if we create a right triangle with that point after graphing it. We see the height of that triangle is 5 because that is the imaginary part. The base of that triangle has length [tex]5\sqrt{3}[/tex]. The problem is this doesn't give us any part of the angle we want, but it does give us the complementary of the part of the angle that is in second quadrant.
Let's find the complementary angle.
So the opposite side of the complementary angle is 5.
The adjacent side of the complementary angle is [tex]5\sqrt{3}[/tex].
[tex]\tan(\theta)=\frac{5}{5\sqrt{3}}[/tex]
[tex]\tan(\theta)=\frac{1}{\sqrt{3}}[/tex]
[tex]\theta=\tan^{-1}(\frac{1}{\sqrt{3}})[/tex]
[tex]\theta=30[/tex]
So 90-30=60.
The answer therefore 60+90=150.
Answer:
D 150 degrees
Step-by-step explanation:
got it right on edge
Related Questions
A grocery store sells 6 bottles of water for $4 and 18 bottles of water for $10. Which is the better deal and why?
Answers
Answer:
18 bottles of water for $10 because each bottle costs 56c compared to 6 bottles of water for $4 at 67c
Step-by-step explanation:
All values rounded to the hundredth
6 bottles of water for $4
4/6=0.67
Each bottle costs 67c
18 bottles of water for $10
10/18=0.56
Each bottle costs 56c
the sides of a triangle are 3 whole 1 by 6 cm 4 whole 2 by 3 cm and 5 whole 2 by 3 cm. Find the total length of the three sides of the triangle
Answers
Answer:
[tex]16\frac{2}{3}[/tex]cm
Step-by-step explanation:
Given dimensions:
[tex]3\frac{1}{6}[/tex] cm by [tex]4\frac{2}{3}[/tex]cm by [tex]5\frac{2}{3}[/tex] cm
The total length:
it is the sum of all the sides;
[tex]\frac{19}{6} + \frac{14}{3} + \frac{17}{3}[/tex]
LCM of the denominators = 6 ;
[tex]\frac{38 + 28 + 34}{6}[/tex] = [tex]\frac{100}{6}[/tex]
= [tex]\frac{50}{3}[/tex]
= [tex]16\frac{2}{3}[/tex]cm
Help me now!!!!! This is due at 12
Answers
i know this because
2 x 9 = 18
4 x 9 = 36
and 14 x 9 = 126
so, the constant of this proportional ratio table is 9
144 divided by 9 is 16
Answer:
umm what grade are you in???
144/9= 16!!!!!
Step-by-step explanation:
anyways wont act exactly like you and the answer is 16
A pair of headphones are on sale for 15% off. The sale price is marked at $51.00, what is the original cost of the headphones?
Answers
Answer:
awh i cant help u
Step-by-step explanation:
1. What is the domain of the relation
represented by the ordered pairs (-12, 2),
(-6,4), (0, 6), (3, 7), and (9, 9)?
A. {-12, -6,0,3, 9}
B. {2, 4, 6, 7, 9)
C. {3,9}
D. {-12, -6,0, 2, 3, 4, 6, 7,9}
Answers
Answer:
A
Step-by-step explanation:
Domain is the x values only
Rewrite the rational exponent as a radical
Answers
Answer:
C OR D
Step-by-step explanation:
Daca adun sfertul lui a cu jumatatea lui b si cu treimea lui c, obtin 120. Stiind ca jumatatea lui b este cu 24 mai mare decat sfertul lui a si de 4 ori mai mare decat treimea lui c, afla cele 3 numere si suma acestora. Ajutor, va rog!
Answers
Answer:
Step-by-step explanation:
Dacă adaug un sfert de la jumătate de b și o treime de c, obțin 120.
Aceasta se exprimă ca:
1 / 4a + 1/2 b + 1 / 3c = 120 ..... Ecuația 1
Știind că jumătate din b este de 24 de ori mai mare decât un sfert de a
1 / 2b = (1/4 × a) 24
b / 2 = (a / 4) 24
b / 2 = 6a
Cross Multiply
b = 6a × 2
b = 12a
a = b / 12
Jumătate din b este de 4 ori mai mare decât o treime din c
1/2 × b = 4 × (1/3 × c)
b / 2 = 4 (c / 3)
b / 2 = 4c / 3
Cross Multiply
b = 2 × 4c / 3
b = 8c / 3
8c = 3b
c = 3b/8
1 / 4a + 1/2 b + 1 / 3c = 120 ..... Ecuația 1
Înlocuim
1/4 × b / 12 + 1 / 2b + 1/3 × 3b / 8= 120
b / 48 + b / 2 + b/8 = 120
Înmulțiți cu 48
b/48 × 48 + b/2 × 48 + b/8× 48 = 120 × 48
b + 24b + 6b = 5760
31b = 5760
What are the equations of the lines with the given slope and y-intercept
1. Slope:2, y-intercept: -3
2. Slope: 4, y-intercept: -2
Answers
Answer:
1. y=2x-3
2. y=4x-2
Step-by-step explanation:
1) y = 2x-3
2) y = 4x-2
Hope you have a wonderful day!
how many solutions does 6x - 18 = 4(2x - 3) - (2x +6)
Answers
Answer:
x=0
Step-by-step explanation:
6x-18=4(2x-3)-(2x+6)
We move all terms to the left:
6x-18-(4(2x-3)-(2x+6))=0
We calculate terms in parentheses: -(4(2x-3)-(2x+6)), so:
4(2x-3)-(2x+6)
We multiply parentheses
8x-(2x+6)-12
We get rid of parentheses
8x-2x-6-12
We add all the numbers together, and all the variables
6x-18
Back to the equation:
-(6x-18)
We get rid of parentheses
6x-6x+18-18=0
We add all the numbers together, and all the variables
=0
x=0/1
x=0
Jimmy and Lauren are
organizing transportation for
a field trip from ACIT. Jimmy
found out that his group has
841 students, and he needs 9
vans and 16 buses to
accommodate. While Lauren’s
group has 351 students, and
she needs 8 vans and 5 buses
for them. How many students
fit in a van and a bus for this
field trip? (please include steps)
Answers
Step-by-step explanation:
Jimmy's group : has 841 students
Lauren's group: has 351 students
9 vans 16 buses
8 vans 5 buses
Vans: V
Buses: B
9v + 16b = 841
9v + 16b = 841
-16b -16b
9v/ 9 = 841 /9 - 16b/9
8( 841/9 - 16b/9) +5b = 351
v - (841/ 9 - 16b / 9 )
8 (841 / 9 - 16b/9) +5b = 351
6728/9 - 128b / 9 +5b = 351
-128b/9 + 45b/9 = -83/9b
6728/9 -83/9
- 6728/9 +83/9 = 3159/9 - 6728/9
(9)83b / 9 = -3569 (9)/9
-83b = -3564
-83 -83
B = 43 students
8v + 5b = 351
8v + 5 (43) = 351
8v + 215 = 315
-215 -215
8v = 136
8 8
V = 17 students
43 students can fit on a bus and 17 students can fit in a van.
ANSWER PLEASE? I NEED HELP!
Answers
Answer:
5x+2=17
x=3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
17-2=15
15/5=3
Find the slope of the line that passes through the given two points:
(1.4) and (3,7)
m =
Please help me don’t use this for Free answers
Answers
Answer: 3/2
Step-by-step explanation: slope is 3/2, I calculated it with the slope formula
the price of a item yesterday was $160. today, the price fell to $104. find the percentage decrease
Answers
Answer:
-35% decrease in price.
Step-by-step explanation:
Type in "percentage decrease calculator" onto google and click on first result
Here's the equation
Please help me i will really appreciate it!!!
Answers
Answer:
[tex]\displaystyle x=\sqrt{\frac{2U}{k}}[/tex]
The third option is the correct answer.
Step-by-step explanation:
Equation Solving
We have the following equation:
[tex]\displaystyle U=\frac{1}{2}kx^2[/tex]
And it's required to solve it for x.
To solve this equation we need to perform some operations to have the x isolated from any other variables, constants, or operations.
This will be done by conveniently operating on both sides as follows:
Eliminate the denominator by multiplying by 2:
[tex]\displaystyle 2U=kx^2[/tex]
Move k to the other side by dividing by k:
[tex]\displaystyle \frac{2U}{k}=x^2[/tex]
Swapping sides to have x at the left side:
[tex]\displaystyle x^2=\frac{2U}{k}[/tex]
Taking the square root:
[tex]\mathbf{\displaystyle x=\sqrt{\frac{2U}{k}}}[/tex]
The third option is the correct answer.
⚠️Tell if the following systems of equations have zero, one, or infinite solutions: -6x + 3y=18 and y=2x - 2⚠️
Answers
Answer:
0 solutions
Step-by-step explanation:
-6x+3y=18
y=2x-2. so substitute y in the first equation
-6x+3(2x-2)=18 distribute and combine like terms
-6x +6x-6=18 and we end up with
-6=18 witch is never true so the system of equation has 0 solutions
Answer this question please.
Answers
Answer:
x = 11
Step-by-step explanation:
We know that vertical angles (opposite angles when two lines cross), are equal.
2x - 6 = 6x - 50
4x = 44
x = 11
can somone tell me the interior angle of a polygon with 20 sides
Answers
Answer:
162
Step-by-step explanation:
Sum of all the angles of any polygon = (n - 2) * 180
= (20 - 2) *180
= 18 * 180
= 3240
Interior of a polygon with 20 sides = 3240 /20
= 162
The price of a smart watch is $109.99 and the sales tax is 6.5%. What is the total cost of the smart watch? Enter your answer in the box.
Answers
Answer:
$117.14
Step-by-step explanation:
A "sales tax" refers to a specific amount of money (according to its percentage) that you need to pay other than the price of the good stated.
So, if the price of the smart watch is $109.99 and the sales tax is 6.5%, you have to know much is 6.5% of $109.99. This can be computed by using the multiplication operation.
109.99 x 6.5% (0.065) = $7.15 (this is the sales tax)
In order to know the total cost of the smart watch, you have to add the sales tax to the price of the smart watch.
$109.99 + $7.15 = $117.14
The total cost of the smart watch is $117.14
Answer:
$117.14
Step-by-step explanation:
I toke the quiz and a k12 student.
Write a slope-intercept form equation for a line that passes through (0,4) and (2,-2).
Show the step by step process please.
Answers
Answer:
-3
Step-by-step explanation:
Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:
m =
y2 - y1
x2 - x1
12. For QR one endpoint is Q(3,2) and the other is R(5,10). Using the Midpoint Formula, find the coordinates of the midpoint of Q and R.
Answers
Answer:
[tex](4,6)[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDASMidpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define points
Q (3, 2)
R (5, 10)
Step 2: Find Midpoint
Substitute: [tex](\frac{3+5}{2},\frac{2+10}{2})[/tex]Add: [tex](\frac{8}{2},\frac{12}{2})[/tex]Divide: [tex](4,6)[/tex]A right triangle with leg lengths of 4 and 3 units has to be positioned in the
coordinate plane to write a coordinate proof. Which set of coordinates
would make the proof easier to complete?
Answers
Answer:(0,4),(0,0),(3,0)
Step-by-step explanation:
It is easy to find lengths of horizontal and vertical segments and distances from (0,0) so always place one vertex at the origin and one or more sides on an axis.
As in this answer has y intercept, and x intercept, and (0,0)
A generator can run for 11 hours on 3 gallons of gasoline. How many hours can the generator run on 9 gallons of gasoline?
Answers
Answer:
11 / 3 hours
Step-by-step explanation:
Can you determine the solution of the |4x−2|≥−6 without solving?
Answers
Answer:
|4x-2|">"-6
add 2 to both sides
4x">"-4
divide both sides by 4
x">"-1
the ">" means greater than or equal to, I just don't have that character on my keyboard
Step-by-step explanation:
so the answer is x is greater than or equal to -1
IN: (-∞,-1]
for number line: You would write the number line from -1-10
then, you would put a closed dot on negative one, with an arrow going to the right!
Hope this helped! <3
Helpp hurry plzzz!!
Which is an equation of the line parallel to 4y - 7x = 8 and passes through (-4, 0)?
A. y = 7/4x + 7
B. y = - 7x - 28
C. y = - 7/4x - 7
D. y = 7x + 28
Answers
Answer:
A. y = 7/4x + 7
Step-by-step explanation:
y = mx +c
4y -7x = 8
(make y the subject of formulae)
4y = 8 + 7x
divide through by the coefficient of y (4)
y = 2 + 7/4x
7/4 = m1
since the line is parallel m1 = m2
let see : {y -y¹}÷ {x-x1} = 7/4
x¹= -4 , y¹ = 0
{y - 0} ÷ {x- (-4) } = 7/4
cross multiply
4(y - 0) = 7(x+4)
4y - 0 = 7x + 28
4y = 7x +28 +0
4y = 7x + 28
(divide both sides by the coefficient of y)
y = 7/4x +28/4
y = 7/4x + 7
Which of the following will decrease your monthly mortgage payment?
A. Points
B. Bad Credit Score
C. High interest Rate
D. $0 Down Payment
Answers
Answer: A. Points
Step-by-step explanation:
I got the answer wrong with the first answer. So it’s A. Points
Answer:
Step-by-step explanation:
(3.6 X 102)(1.9 x 10-4)
Multiply write the answer in scientific notation
Question 2
(4.7. x 10)(2.0 x 10
Answers
Answer:
1.)5508 2.)5600 x^2
Step-by-step explanation:
please help, we have 0 brain cells left
Answers
Answer:
no solution
Step-by-step explanation:
7/15 simplified I’ve tried everything!!PLEASE ANSWER ASAP
Answers
Answer:
You cannot simplify 7/15 to a smaller fraction. But you could divide 7 by 15 to get a decimal.
Step-by-step explanation:
Answer:
you can't simplify the number 7
Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work is shown below. What mistake did she make?
Answers
Answer:
Equivalent fraction: 45/100
Reduced fraction: 9/20
Decimal equivalent: 0.45
Step-by-step explanation:
Equivalent fraction: percentage is just out of 100. 45% is 45 out of 100, aka 45/100.
Reduced fraction is just simplifying both sides by the GCF. In this case, 5.
Decimal equivalent of a percentage is just dividing the numerator by the denominator, or taking the numerator or the percentage and placing the decimal point forward two digits.
Answer:
45|1000
Step-by-step explanation:
urjrbrbruw9qi1i818
find the slope of the line if it exists
a. the slope is ___
b. the slope is undefined
Answers
Answer:
The slope is -4/3.
Step-by-step explanation:
Slope = rise/run. Starting at (3, -1), you go up 4 units and over to the left 3 units to (0,3). Since it's a line of decay, the slope is negative.
Answer:
the slope should be -4/3
Step-by-step explanation:
you go down 4 and to the right 3 so I am pretty sure it is -4/3
