In the diagram a || b, if m∠6 = 21°, what is m∠4?

A) 21°

B) 10.5°

C) 159°

D) 339°

Answer:

C, [tex]4e^{i(7\pi/4)}[/tex]

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

[tex]e^{ix}=\cos{x}+i\sin{x}[/tex]

Given the complex number [tex]2\sqrt{2}-2i\sqrt{2}[/tex], we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression [tex]2(\sqrt{2}-i\sqrt{2})[/tex]

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression [tex]4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right)[/tex] , and now we have something to work with.

Looking back at Euler's formula [tex]e^{ix}=\cos{x}+i\sin{x}[/tex], we can map our expression inside the parentheses to the one on the right side of the formula, giving us [tex]\cos{x}=\frac{\sqrt2}{2}[/tex] and [tex]\sin{x}=-\frac{\sqrt2}{2}[/tex], or equivalently:

[tex]\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x[/tex]

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so [tex]x=\frac{7\pi}{4}[/tex], and we can finally replace our expression in parentheses with its exponential equivalent:

[tex]4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}[/tex]

Which is c on the multiple choice section.

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

the parameter tells you something about the whole population

Answer:

Step-by-step explanation:đáp án a

∆=b²-4ac= 1² - 4*3*(-11)=133

=>√∆=√133

X=(-b±√∆)/2a

X=(-(-1)±√133)/2*6

X=(1±√133)/6

Answer:

a) P(a)= 0.0001

b) P(b)= 0.0024

Step-by-step explanation:

Given:

Chosen number = 3079

Possible numbers that have chance of winning from 0000 to 9999= 10,000

Winning condition=  if made choice matches the winning digits

Now

a)What is the probability that the winning number matches your number exactly?

From 0000 to 9999, only one time can the number 3079 can be the winning number, so

P(a)= 1/10000

     = 0.0001

b)What is the probability that the winning number has the same digits as your number in any order?

Winning numbers from 0000 to 10000 that have same digits as 3079 are

4 x 3 x 2 x 1 = 24 ways

Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:

0379

0397

0973

0937

0793

0739

3079

3097

3970

3907

3790

3709

7039

7093

7930

7903

7390

7309

9073

9037

9370

9307

9730

9703

P(b)= 24/10000

     =0.0024 !

Answer: v = [tex]-\frac{1}{6}[/tex]

6v + 2 - 4 = -3                         Combine like terms

6v - 2 = -3                               Add 2 to both sides

6v = -1                                     Divide both sides by 6

v = [tex]-\frac{1}{6}[/tex]          Answer!

Step-by-step explanation:

You need to remember that

[tex] log( \frac{a}{b} ) = log(a) - log(b) [/tex]

and

[tex] log(ab) = log(a) + log(b) [/tex]

then the solution is

[tex] log( \frac{r}{st} ) = log(r) - log(st) \\ = log(r) - ( log(s) + log(t) ) \\ = log(r) - log(s) - log(t) [/tex]

Answer:

The equation of the hyperbola is x²/16 - y²/1 = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

# The length of the transverse axis is 2a

# The coordinates of the vertices are (±a , 0)

# The length of the conjugate axis is 2b

# The coordinates of the co-vertices are (0 , ±b)

# The coordinates of the foci are (± c , 0),  

# The distance between the foci is 2c where c² = a² + b²

* Now lets solve the problem

∵ The center of the hyperbola is (0 , 0)

∵ It is opening horizontally

∴ x²/a² - y²/b² = 1

∵ a = 4 , b = 1

∴ a² = (4)² = 16

∴ b² = (1)² = 1

∴ x²/16 - y²/1 = 1

∴ The equation of the hyperbola is x²/16 - y²/1 = 1

x²/16 - y²/1 = 1

Step-by-step explanation:

To subtract the given expressions, first, simplify each expression separately by combining like terms. Then subtract the second expression from the first expression by distributing a negative sign and adding it to the first expression.

To subtract the given expressions, (2x^3+7x^2-4) - (2x^2+4x-10), we need to simplify each expression separately and then subtract them. First, combine like terms within each expression. Then, subtract the terms of the second expression from the first expression. This can be done by distributing a negative sign to each term in the second expression and then adding it to the first expression.

So, (2x^3+7x^2-4) - (2x^2+4x-10) = 2x^3+7x^2-4 - 2x^2-4x+10.

Combining like terms, we get 2x^3+(7x^2-2x^2)+(-4-4x)+(10). Simplifying further, we have 2x^3 + 5x^2 - 4x + 6. Therefore, the result of the subtraction is 2x^3 + 5x^2 - 4x + 6.

https://brainly.com/question/17538351

#SPJ2

ANSWER

Option D

EXPLANATION

The given function is

[tex]y = \sqrt{16x - 32} - 3[/tex]

We factor 16 under the radical.

[tex]y = \sqrt{16(x - 2)} - 3[/tex]

[tex]y = \sqrt{16} \times \sqrt{(x - 2)} - 3[/tex]

[tex]y = 4 \sqrt{x - 2} - 3[/tex]

This is the graph of

[tex]y = 4\sqrt{x } [/tex]

translated 2 units right and 3 units down.

The last option is the correct choice.

Answer: End behaviour is,

f(x) => -∞ as x => -∞;

f(x) => +∞ as x => +∞

The graph touches, but does not cross, the x–axis at x = 4

The graph of the function crosses the x–axis at x = 0

Step-by-step explanation:

Given function is,

[tex]f(x)=x^5-8x^4+16x^3----(1)[/tex]

The degree of f(x) is 5 ( odd ) with positive leading coefficient,

Hence, the end behaviour of f(x) is,

f(x) => -∞ as x => -∞;

f(x) => +∞ as x => +∞

Now, from equation (1),

[tex]f(x)=x^3(x^2-8x+16)[/tex]

If f(x) = 0,

[tex]x^3(x^2-8x+16)=0[/tex]

[tex]\implies x^3=0\text{ or }x^2-8x+16=0[/tex]

[tex]x^3=0\text{ or }(x-4)^2=0[/tex]

[tex]x^3=0\text{ or }x-4=0[/tex]

[tex]\implies x=0\text{ or }x=4[/tex]

Now, the multiplicity of 4 is 2 ( even )

Thus, the graph touches, but does not cross, the x–axis at x = 4

Also, the multiplicity of 0 is 3 ( odd )

Hence, the graph of the function crosses the x–axis at x = 0

By using the concept of end behavior of a function, the result is

f(x) [tex]\rightarrow[/tex] [tex]-\infty[/tex] as x [tex]\rightarrow -\infty[/tex] and f(x) [tex]\rightarrow[/tex] [tex]\infty[/tex] as [tex]x \rightarrow[/tex] [tex]\infty[/tex]

The graph touches, but does not cross the x - axis at x = 4 as the multiplicity of 4 is even

The graph of the function crosses the x - axis at x = 0 as the multiplicity of 0 is odd.

What is end behavior of a function?

Let the function be f(x). End behavior of a function f(x) indicates how will the function behaves as x tends to +[tex]\infty[/tex] and [tex]-\infty[/tex]

Here,

f(x) = [tex]x^5 - 8x^4 + 16x^3[/tex]

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} x^5 - 8x^4 + 16x^3\\\\= -\infty[/tex]

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} x^5 - 8x^4 + 16x^3\\\\= \infty[/tex]

So f(x) [tex]\rightarrow[/tex] [tex]-\infty[/tex] as x [tex]\rightarrow -\infty[/tex] and f(x) [tex]\rightarrow[/tex] [tex]\infty[/tex] as [tex]x \rightarrow[/tex] [tex]\infty[/tex]

f(x) = [tex]x^5 - 8x^4 +16x^3[/tex]  

     = [tex]x^3(x^2 - 8x +16)\\[/tex]

     = [tex]x^3(x - 4)^2[/tex]

[tex]x^3 = 0[/tex] or [tex](x - 4)^2 = 0[/tex]

[tex]x = 0[/tex] (Multiplicity 3 which is odd)

[tex]x = 4[/tex] (Multiplicity 2 which is even)

So The graph touches, but does not cross the x - axis at x = 4 as the multiplicity of 4 is even

The graph of the function crosses the x - axis at x = 0 as the multiplicity of 0 is odd.

To learn more about end behavior of a function, refer to the link-

https://brainly.com/question/1365136

#SPJ2

Answer:

a,b,d,f

Step-by-step explanation:

Answer:

(q-9) (5+c)

Step-by-step explanation:

Factor out the common factor.  In this case, q-9.

5(q-9) + c(q-9)

(q-9) (5+c)

Step-by-step explanation:

2 * (x + 1) = 8   | :2

x + 1 = 4   | -1

x = 3

Answer:

x = 3

Step-by-step explanation:

2 ( x + 1 ) = 8

⇒ Expand brackets

2 x + 2 = 8

⇒ Minus 2 from both sides

2 x = 6

⇒ Divide by 2 from both sides to isolate x

x = 3

Answer:

Step-by-step explanation:

10 contain both chocolate and caramel

There are 18 candies.

3 don't contain either chocolate or caramel

12 contain chocolate.

There are 18 - 12 - 3 that are not accounted for. So we have 3 that are not mentioned. Those 3 must contain just caramel.

So it should be filled out like this

contain caramel      Do not contain Caramel

         10                          2

          3                           3

Answer:

0.3(8.2 x 10^-3) = 2.46 X 10 ^ -3

Step-by-step explanation:

We need to solve the equation 0.3(8.2 x 10^-3) and write answer in scientific notation.

Solving,

= 0.3(8.2 x 10^-3)

= 0.3 * 0.0082

= 0.00246

Writing in scientific notation

= 2.46 X 10 ^ -3

So, after solving the expression 0.3(8.2 x 10^-3) the result is 2.46 X 10 ^ -3.

ANSWER

D. x=55

EXPLANATION

The given radical equation is

[tex] \sqrt{x - 6} + 3 = 10[/tex]

Add -3 to both sides

[tex] \sqrt{x - 6} = 10 - 3[/tex]

[tex] \sqrt{x - 6} =7[/tex]

Square both sides.

[tex] { (\sqrt{x - 6})}^{2} = {7}^{2} [/tex]

[tex]x - 6 = 49[/tex]

Solve for x to get:

[tex]x = 49 + 6 = 55[/tex]

[tex]\frac{3}{5}(x - 5) \leq 27[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Option D

The inequality that represents the  situation is:

[tex]\frac{3}{5}(x-5)\leq 27[/tex]

following situation

Step-by-step explanation:

Suppose an unknown number X.

That number minus 5 is:

[tex]x-5[/tex]

Now, [tex]\frac{3}{5}[/tex] times the unknown number minus 5 is:

[tex]\frac{3}{5}(x-5)[/tex]

We know that all this expression is not greater than 27.

Then we use the symbol "less or equal than" ([tex]\leq[/tex]) to represent the situation

[tex]\frac{3}{5}(x-5)\leq 27[/tex]

At aphelion, the distance between Pluto and the sun is approximately 8,000,000,000 km.

The distance between Pluto and the sun at aphelion can be calculated using the formula:

Distance at aphelion = length of the minor axis / (1 + eccentricity).

Plugging in the given values, we get:

Distance at aphelion = 10,000,000,000 km / (1 + 0.25).

Calculating the result gives us a distance of approximately 8,000,000,000 km.

https://brainly.com/question/32379878

#SPJ12

Answer:

4x-10y thingi 3

Step-by-step explanation:

Answer:

2(1/2)(5)(12) + 11(5) + 11(12) + 11(13) =

60 + 55 + 132 + 143 = 390 m²

Answer: Number 4.

Since Pedro deposited $35, the line would start at 0 and go up to positive 35. However, Pedro then withdrew $50- which is more than he has in his account, so he would have $-15, which means he'd owe a fee.

Good luck,

LaciaMelodii :)

Answer:

d). or the 4th choice

Step-by-step explanation:

hope this helped!!

Answer:

Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Step-by-step explanation:

We are given that we deal with three cards from a regular deck of 52 cards.

We are to find the probability of getting all three Jacks.

There are a total of 4 jacks in a regular deck of 52 cards.

Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Answer:

no i don't sry

Step-by-step explanation:

Fulton Virtual provides competency based, personalized middle and high school learning options for FCS students throughout the district. This page is where students request and access Fulton Virtual courses. Parents can access the Fulton Virtual parent portal here too.

2x

so...

2x (4t - 2 - 9)

2x (4t -  11)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

It's 2x.

Step-by-step explanation:

The GCF of 8, 4 and 18 is 2.

The GCF of xt x and x  is x.

y = 218.2. The lenght of side y by  trigonometry is 218.2.

In order to solve this problem we are going to use the angles and sides of a right triangle and its relation by expressions that we call trigonometric ratios.

In the image we can see that the lenght of the opposite leg is 141 , we do not know the lenght of the adjacent leg y and the hypotenuse x. The key to solve this problem is to use trigonometric ratios and the equation tan θ = sin θ/cos θ = opposite leg/adyacent leg = 141/y

Clear for y for the equation tan θ = sin θ/cos θ = 141/y, we obtain:

y = arctan θ (141)

y = arctan (43°)(141) = 218.2

Answer:

50,24cm

Step-by-step explanation:

For circumference, you can use C = πd OR 2πr = C:

3,14[16] = 50,24

2[3,14][8] = 50,24

The diameter is double the radius.

I am joyous to assist you anytime.

Answer:

P = (4.8, 11)

Step-by-step explanation:

P = 3R + 2W

RP + PW

= 3(4,5) + 2(6,20)

2 + 3

= (12,15) + (12,40)

5

= (24,55) = (4.8, 11)

5

Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is

on RW such that RP: PW is 2:3. the coordinates of point P would be (0, 11).

Suppose that there is a line segment {AB} such that a point P(x,y) lying on that line segment{AB} divides the line segment {AB} in m:n, then, the coordinates of the point P is given by:

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

where we have:

the coordinate of A is (x_1, y_1)

and the coordinate of B is (x_2, y_2)

Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is

on RW such that RP: PW is 2:3.

[tex](x,y) = \left( \dfrac{2(6) + 3(-4)}{2+3} , \dfrac{2(20) + 3(5)}{2+3} \right)\\\\(x,y) = \left( \dfrac{12- 12}{5} , \dfrac{40+15}{5} \right)\\\\(x,y) = \left( \dfrac{0}{5} , \dfrac{55}{5} \right)\\\\(x,y) = (0, 11)[/tex]

Learn more about a point dividing a line segment in a ratio here:

https://brainly.com/question/14186383

#SPJ2

Square root x=13

x=169

Hope you get it!

To solve the equation x^2√x-8+2=7, follow these steps: combine like terms, square both sides, simplify, take the cube root, and simplify again to find x = 3.

To solve the equation x2√x-8+2=7, we need to isolate the variable x. Here are the steps:

Therefore, the solution to the equation is x = 3.

https://brainly.com/question/17870110

#SPJ11

Answer:

Step-by-step explanation:

[tex]4y^2-37=27\qquad\text{add 37 to both sides}\\\\4y^2=64\qquad\text{divide both sides by 4}\\\\y^2=16\to y=\pm\sqrt{16}\\\\y=-4\ or\ y=4[/tex]

To solve for 'y' in the equation 4y^2 - 37 = 27, you isolate y^2, take the positive square root, and find that the positive value of y is y = 4.

To find the positive value of 'y' from the equation 4y^2 - 37 = 27, we first need to isolate y. Starting with 4y^2 - 37 = 27, add 37 to both sides to get 4y^2 = 64. Divide both sides by 4 to isolate y^2, leading to y^2 = 16. Finally, take the square root of both sides. Remember that the square root of a number gives both positive and negative solutions. However, because the question asks for the positive value, we ignore the negative root. Thus, the positive value of y is y = 4.

https://brainly.com/question/32436021

#SPJ2

Answer: The jacket cost $34.79