Any complex number [tex]z[/tex] can be written in trigonometric form as
[tex]z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)[/tex]
where [tex]|z|[/tex] is the modulus of [tex]z[/tex] and [tex]\arg(z)[/tex] is its argument, i.e. the angle [tex]z[/tex] makes with the positive real axis in the complex plane.
We have
[tex]|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3[/tex]
and
[tex]\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]
Then
[tex]3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}[/tex]
Rationalize the denominator.
Hello and Good Morning/Afternoon!
Let's take this problem step-by-step:
What the problem asks for:
⇒ to rationalize the denominator
⇒ rationalize means that you multiply the numerator and
demonimator by the denominator
Let's put that into action:
[tex]\frac{\sqrt{a +1}-2 }{\sqrt{a+1}+2 } * \frac{\sqrt{a +1}+2 }{\sqrt{a+1}+2 }\\=\frac{a +1-4 }{a+1+4\sqrt{a+1}+4 } \\=\frac{a-3}{a+4\sqrt{a+1}+5 }[/tex]<== Answer
Hopefully that helps!
Which expression is equivalent to-2x+5?
The equivalent expression of -2x + 5 is 5 - 2x
How to determine the equivalent equation?The expression is given as:
-2x + 5
The symmetry rule of expression states that:
a + b = b + 1
So, we have:
-2x + 5 = 5 - 2x
Hence, the equivalent expression of -2x + 5 is 5 - 2x
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la longitud del jardín
de Carme es 15 m 24 cm. la longitud del jardín de su amigo es 2 m 98 cm más que el de Carmen . ¿cuál es la longitud del jardín de su amigo?
la longitud del jardín del amigo de Carmen es 18 m 22 cm.
¿Qué es una ecuación?Una ecuación se forma cuando dos expresiones algebraicas se igualan usando un signo igual.
Se da que la longitud de Carme
Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.
y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.
Sea La longitud del jardín de Carmen es x m
Entonces la ecuación se convierte en
La longitud del jardín de su amigo = x + 2m 98 cm
ahora ,
x = 15m 24cm
Sustituyendo los valores en la ecuación
La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm
1m = 100cm
La longitud del jardín de su amigo = 17 m 122 cm
as 100 cm = 1m
122 cm = 1 m 22 cm
so ,
La longitud del jardín de su amigo = 18 m 22 cm.
Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.
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ANSWER ASAP, GIVING BRAINLIEST TO FIRST ANSWER!!!
Which linear inequality represents the graph below?
(-3,3)-(0,1)
Answer:
if the red line is included it is a. if the red line is excluded it is C. I believe.
Answer:
A
Step-by-step explanation:
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (0, 1) ← 2 points on the line
m = [tex]\frac{1-3}{0-(-3)}[/tex] = [tex]\frac{-2}{0+3}[/tex] = - [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = - [tex]\frac{2}{3}[/tex] x + 1 ← equation of line
the solutions to the inequality lie above the line, including the line, in the shaded area , then
y ≥ - [tex]\frac{2}{3}[/tex] x + 1 → A
For what value of y does 125 =
(1/25)^y-1
Answer:
[tex] y = -\dfrac{1}{2} [/tex]
Step-by-step explanation:
I assume that y - 1 is an exponent, and the equation is
[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]
[tex] 5^3 = (5^{-2})^{y - 1} [/tex]
[tex] 5^3 = 5^{-2y + 2} [/tex]
[tex] -2y + 2 = 3 [/tex]
[tex] -2y = 1 [/tex]
[tex] y = -\dfrac{1}{2} [/tex]
A cars odometer reads 12,386 if the driver takes the car to and from work for three days and each trip is 32 miles one way what will the odometer read at the end of the third day
At the end of the third day, the new reading on the odometer will be 12,578 mi
What will the odometer reading at the end of the third day?
The initial odometer reading is 12,386 miles.
Then, the driver takes drives to and from work, such that each trip is 32 miles. Then each day he drives 2*2mi = 64 miles.
And he does this for 3 days, then the total distance driven is:
3*64mi = 192 miles.
At the end of the third day, the new reading on the odometer will be:
R = 12,386 mi + 192mi = 12,578 mi
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Which of the set of ordered pairs contains the line 1/3x+y=15
Answer:
{(-3, 16),(0, 15),(3, 14)}
Step-by-step explanation:
just plug in the points for x and y and solve to see if 15 is the answer you get for all of them which would give you B as your answer
numbers like 0 and 1 and 3 (because it would cancel 1/3x) are good numbers to do quick math with
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Please help me!
For a certain company, the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0.5x^2.
The profit that the company makes is how much it takes in (revenue) minus how much it spend (cost). In economic models, one typically assumes that a company wants to maximize its profit or at least wants to make a profit:
Set up an expression for the profit from producing and selling x items
Find two values of x that will create a profit of $300
Using the profit concept, we have that:
The expression is: P(x) = -0.5x² + 40x - 300.A profit of $300 is found with x = 20 and x = 60.What is the profit concept?Profit is given by revenue subtracted by costs.
In this problem, we have that:
The revenue is: R(x) = 90x - 0.5x².The costs are: C(x) = 50x + 300.Hence the expression for the profit is given as follows:
P(x) = R(x) - C(x)
P(x) = 90x - 0.5x² - 50x - 300
P(x) = -0.5x² + 40x - 300.
A profit of $300 is found when P(x) = 300, hence:
300 = -0.5x² + 40x - 300
0.5x² - 40x + 600 = 0.
x² - 80x + 1200 = 0.
(x - 60)(x - 20) = 0.
Hence the values are:
x - 60 = 0 -> x = 60.x - 20 = 0 -> x = 20.More can be learned about the profit concept at https://brainly.com/question/4001746
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PLS HELP ME Solve the following equation: two fifths plus one fifth equals
one fifth,
three tenths,
two fifths,
or three fifths.
it is three fifths,
and it is the answer.
Write an equation for the nth term of the arithmetic sequence 8, 3, -2, -7,... Find the 9th term of the sequence.
if 3²× = 27 what is x
Answer:
3
Step-by-step explanation:
whenever solving for x, you have to work backwards…like so:
3 squared is 9
27 divided by nine is 3
x=3
To double check the answer, substitute the value that we just found into x
(3x3)x3=27
Answer:
[tex]x=\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]3^{2x}=27[/tex]
Rewrite 27 in exponential form with base 3:
[tex]\implies 3^{2x}=3^3[/tex]
As both exponents have the same base,
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies 2x=3[/tex]
Divide both sides by 2:
[tex]\implies x=\dfrac{3}{2}[/tex]
Factor by Grouping.
The ac product of 35x² + 41x + 12 is
The factors of the ac product that add to 41 are
35x² + 41x + 12 =
Submit Question
x +
)(
and
x +
000
Answer:
The ac product of [tex]35x^2+41x+12[/tex] is 420.
The factors of the ac product that add to 41 are 20 and 21.
[tex]35x^2+41x+12 =[/tex] [tex](7x+4)(5x+3)[/tex]
Step-by-step explanation:
1) The general form of a quadratic is [tex]ax^2 + bx + c[/tex]. Hence, multiplying 35 by 12 gives you the product of ac, which is 420.
2) We need to find two numbers that multiply to 420 and add up to 41 simultaneously. If we pull out the factors of 420, two of them will be 20 and 21, which multiply to 420 as well as add up to 41.
3) Write [tex]41x[/tex] as a sum.
[tex]35x^2+20x+21x+12[/tex]
Now, we can factor them out by grouping.
[tex]35x^2+20x+21x+12\\5x(7x+4)+3(7x+4)[/tex]
Since, [tex]7x +4[/tex] is common in both of the factors, we only take one of the [tex]7x+4[/tex] along with [tex]5x[/tex] and [tex]3[/tex].
[tex](7x+4)(5x+3)[/tex]
Answer:
[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]
[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]
[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]
Step-by-step explanation:
Given quadratic:
[tex]35x^2+41x+12[/tex]
Factoring quadratics by grouping
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=35 \cdot 12 = 420[/tex]
[tex]\implies b = 41[/tex]
Therefore, the two numbers that multiply to 420 and sum to 41 are:
20 and 21
Rewrite b as the sum of these two numbers:
[tex]\implies 35x^2+20x+21x+12[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 5x(7x+4)+3(7x+4)[/tex]
Factor out the common term [tex](7x+4)[/tex] :
[tex]\implies (5x+3)(7x+4)[/tex]
Conclusion
[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]
[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]
[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]
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en un proyecto de innovacion, se deben determinar montos para varios gastos, Se gasta un 25% en equipamiento, un quinto en salarios, un 35% en publicidad, qudando un remanente de $1.500.000 para gastos varios
The amount that's was attributed to the project from the start based on the percentage is $7,500,000.
How to calculate the percentage?From the information given, the remaining percentage will be:
= 100% - (25% + 20% + 35%)
= 100% - 80%
= 20%
Let the total amount be x.
Therefore, 20% of x = 1,500,000
0.2x = 1,500,000
x = 1500000/0.2
x = 7500000
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How did I do? for one of the questions I assumed you didnt take in count for the base so I just did lateral area
The area of the exposed surface is 442 square feet
What is a right square pyramid?A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.
Analysis:
The exposed surface is the area of the four triangles.
The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft
Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.
In conclusion, area of exposed surface is 442 square feet.
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Sam ran 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday. How many total miles did Sam run ?
Answer:
6 1/12 miles total
Step-by-step explanation:
3 1/4 = 13/4
2 5/6 = 17/6 to ADD fractions, you must have a common denominator
I will use 12 for these
13/4 = 39/12
17/6 = 34 /12
now you can add and simplify 39/12 + 34/12 = 73/12 = 6 1/12 miles
Solve for x: -5(-3x+1)=-45
Answer:
x = -8/3
Step-by-step explanation:
-5(-3x+1)=-45
⇔ 15x - 5 = -45 (left side of the equation expanded)
⇔ 15x = -45 + 5 (add 5 to both sides)
⇔ 15x = -40
⇔ x = -40/15 (Divide both sides by 15)
⇔ x = -8/3 (simplify)
77 is the product of 7 and diego's height use the variable d to represent diego';s height
Diego's height is 7 units
How to determine Diego's height?The statement is given as:
77 is the product of 7 and Diego's height
This means that:
77 = 7 * d
Divide both sides by 7
d = 11
Hence, Diego's height is 7 units
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What is the simple interest that is missing from the table?
I
?
p
$375
r
2.2%
t
3 years
Answer:
SI =PXRXT/100
Step-by-step explanation:
THIS WOULD HELP YOU
Question 18
Which formula is used to find the y-coordinate of the vertex of the quadratic function?
Answer:
[tex]\frac{-D}{4a}[/tex]
Step-by-step explanation:
y-coordinate is [tex]\frac{-D}{4a}[/tex] where a is coefficient of quadratic polynomial (ax^2+bx+c) and D is discriminant of the quadratic equation when you equate it to zero.
need help with this question.
We have this equation:
[tex]\log(x) + \log(x + 99) = 2[/tex]
First, combine both logarithms using the multiplication property and simplify the expression.
[tex]\log[x(x + 99)] = 2[/tex]
[tex]\log[ {x}^{2} + 99x ] = 2[/tex]
Now, use the definition of logarithm to transform the equation.
[tex] {10}^{2} = {x}^{2} + 99x[/tex]
[tex] {x}^{2} + 99x - 100 = 0[/tex]
Finally, use the quadratic formula to solve the equation.
[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]
With this, we can say that the solution set is:
x = 1x = -100We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
What is the domain and range of this graph?
Find the unit rate.
594 chairs in 9 rows
Submit
||
chairs per row
Answer:
66 chairs
Step-by-step explanation:
Total number of chairs = 594
Total number of rows = 9
Number of chairs per row
= 594/9
= 66 chairs
__________
Hope it helps ⚜
What is the least possible value of (x+1)(x+2)(x+3)(x+4)+2019 where x is a real number?
By completing the square, we have
[tex](x+1)(x+4) = x^2 + 5x + 4 = \left(x+\dfrac52\right)^2 - \dfrac94[/tex]
[tex](x+2)(x+3) = x^2 + 5x + 6 = \left(x + \dfrac52\right)^2 - \dfrac14[/tex]
Then
[tex](x+1)(x+2)(x+3)(x+4) = \left(x+\dfrac52\right)^4 - \dfrac52 \underbrace{\left(x + \dfrac52\right)^2}_{=y} + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = y^2 - \dfrac52 y + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(y - \dfrac54\right)^2 - 1 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(\left(x + \dfrac52\right)^2 - \dfrac54\right)^2 - 1[/tex]
This product has a minimum of -1 when
[tex]\left(x + \dfrac52\right)^2 - \dfrac54 = 0[/tex]
which has two real solutions; then the minimum of the overall expression is -1 + 2019 = 2018.
Question 11 (5 points)
Select the expression that is equivalent to x+x+yxyxy.
O 2x+y³
Ox² + y²
O² + 3y
2x+3y
Answer:
I don't know if you have any questions or need any further information please contact me your Telugu movie review poster
A block is a rectangle that measures 100yards by 76yards. How many times around the block do you have to drive in order to drive one mile?
If block has length 100 yards and breadth 76 yards then we have to drive 5 times to drive one mile.
Given The length of block is 100 yards, the breadth of block is 76 yards.
We have to find number of times we need to drive one mile.
The perimeter of a rectangle= 2(length +breadth)
length is 100 yards
Breadth is 76 yards
perimeter=2(100+76)
=2*176
=352 yards.
We know that 1 mile is equal to 1760 yards.
We have to find number of times to drive 1 mile=1760/352
=5 times.
Hence we have to drive 5 times around the block which have length 100 yards and breadth 76 yards.
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Suppose U = The set of one digit numbers and A = {x: x is an even natural number less than or equal to 9} Describe each of the sets by complete listing method: A'
The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}
How to list the set elements?The sets are given as:
U = The set of one-digit numbers
A = {x: x is an even natural number less than or equal to 9}
One-digit numbers are numbers 0 - 9.
So, we have
U = {0, 1, 2, 3.....,9}
Natural numbers are numbers from 1.
Even natural numbers can be divided by 2 without remainder'
So, we have
A = {2, 4, 6, 8}
Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}
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Answer:
Step-by-step explanation:
22POINTS PLEAS ANsewer
Answer:
2y>-y+5
Step-by-step explanation:
because it has a eligible number at the right hand side
7) Which statement about perpendicular lines is true?
A. Perpendicular lines form 90° angles.
B. Perpendicular lines share no points.
C. Perpendicular lines have the same slope.
D. Perpendicular lines are equidistant along their lengths.
Answer:
is the a. Perpendicular lines form 90° angles.
Dilate ∆ABC about the origin using the scale factor n. Measure and compare the lengths of the sides of the dilated triangle, ∆A'B'C', with those of ∆DEF. Take a screenshot of your dilation, save it, and insert the image below the table.
The attached graph represents the image of the triangles
How to dilate the triangle?To do this, we make use of the following coordinates
A = (1, 0)
B = (5, 0)
C = (1, 6)
The lengths of the triangle are calculated using
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(1-5)^2 + (0 -0)^2} = 4[/tex]
[tex]BC = \sqrt{(1-5)^2 + (6 -0)^2} = 7.2[/tex]
[tex]AC = \sqrt{(1-1)^2 + (6 -0)^2} = 5[/tex]
Using the scale factor of 2, we have the image of the dilation to be:
D = (2, 0)
E = (10, 0)
F = (2, 12)
The lengths of these sides are
DE = 8
EF = 14.4
DF = 10
See attachment for the image of the triangles ABC and DEF
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The lsrl after an exponential transformation is log yhat=.4785 + 1.468x. What is the exponential form of the regression?
Answer:
[tex]10^{0.4785+1.468x}=y[/tex]
Step-by-step explanation:
So I'm assuming when you typed "log yhat=.4785 + 1.468x", you meant to write: [tex]log(y)=0.4785+1.468x[/tex]. And generally a logarithm can be written in the form [tex]log_ba=c[/tex] which can then be rewritten as [tex]b^c=a[/tex], but since the log has no base, it's assumed to be 10. So in this case you have the equation:
[tex]log_{10}y=0.4785+1.468x[/tex], which can then be written in exponential form as:
[tex]10^{0.4785+1.468x}=y[/tex]