use de moivres theorem to write the complex number in trigonometric form.
[sqrt(2)(cos(10)+isin(10)]^6

Answer:

  B.  The sum of the squares of the two smaller sides is equal to the square of the third side.

Step-by-step explanation:

It can be helpful to recognize that the given side lengths, 12, 16, 20 are in the ratio 3:4:5, a recognizable Pythagorean triple. That is, you may know already that the triangle is a right triangle and the sum of squares of the short sides is equal to the square of the longest side (choice B).

In case you aren't aware of common Pythagorean triples, or didn't recognize these numbers, you can try the options to see which fits.

A. The sum of the two smaller sides is 12 +16 = 28. It is NOT equal to the third side, 20.

__

B. The sum of the squares of the two smaller sides is 12^2 + 16^2 = 144 + 256 = 400. This IS equal to the square of the third side: 20^2 = 400.

__

C. The absolute value of the difference between the squares of the two smaller sides is |256 -144| = 112. This is NOT equal to the square of the third side, 20^2 = 400.

__

D. The sum of the squares of the two smaller sides is 400 (as above). It is NOT equal to the third side, 20.

___

The only answer choice that fits is choice B.

It’s a 33% chance rolling a one or a three

Dilation since one image is bigger than the other

A dilation transformation must be included to result in quadrilateral T.

To result in quadrilateral T, a dilation transformation must be included. A dilation is a transformation that changes the size of the figure without changing its shape. In this case, the side lengths of quadrilateral T are twice as long as those of quadrilateral S, indicating a scaling factor of 2. Therefore, a dilation is needed to scale up the size of quadrilateral S by a factor of 2 to obtain quadrilateral T.

Answer:

You should order 66 short sleeve mediums.

hope this helps

Answer:

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium

Step-by-step explanation:

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium

There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).

Torque is the expression of a rotational or twisting force. The engines in vehicles rotate about an axis, thus creating torque.

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero.

When a body or a system is in equilibrium, there is no net tendency to change.

In mechanics, equilibrium has to do with the forces acting on a body. When no force is acting to make a body move in a line, the body is in translational equilibrium; when no force is acting to make the body turn, the body is in rotational equilibrium.

There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).

These two conditions must be simultaneously satisfied in equilibrium.

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Answer:

$7500

Step-by-step explanation:

$5000 was deposited

5% annual interest of the $5000 is $250

so in ten years the interest will be 10 ×$250 =$2500

so the total sum that will be in the account is $5000 + $2500 =$7500

Answer:

(x + 1) (3x - 1)

Step-by-step explanation:

Using the AC method, here a = 3, b = 2, and c = -1.

ac = 3 * -1 = -3

Factors of -3 that add up to +2 are +3 and -1.

Divide by a: +3/3, -1/3

Reduce: +1/1, -1/3

So the factors are x + 1 and 3x - 1.

3x² + 2x - 1 = (x + 1) (3x - 1)

Answer:

x = 1/3 or x = -1

Step-by-step explanation:

    3x^2 + 2x - 1

=>  3x^2 + 3x - 1x - 1                                         product = -3     sum = 2

=>   3x( x + 1 ) - 1(x + 1 )

=>    (3x - 1) (x + 1)

       3x = 1  

    =>x=1/3  or x = -1  

HOPE THIS HELPS YOU ~                                                          

Answer:

10.125 feet

Step-by-step explanation:

h(t) = -2t² + 3t + 9

The maximum height is at the vertex of the parabola.  For a parabola ax² + bx + c, the vertex is at x = -b/(2a).

t = -3 / (2×-2)

t = 3/4

h(3/4) = -2(3/4)² + 3(3/4) + 9

h(3/4) = -9/8 + 9/4 + 9

h(3/4) = 81/8

h(3/4) = 10.125 feet

Answer:

Carpenter = 12 hours

Blacksmith = 18 hours

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Giselle works as a carpenter and as a blacksmith. She earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 30 hours and earned a total of $690.

Let 'x' be the number of hours of a blacksmith and 'y' be the number of hours of a carpenter. Then the equations are given as,

x + y = 30                         ...1

20x + 25y = 690             ...2

From equations 1 and 2, then we have

20(30 - y) + 25y = 690

600 - 20y + 25y = 690

5y = 90

y = 18

Then the value of 'x' is given as,

x + 18 = 30

x = 30 - 18

x = 12

Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.

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Answer:

D. 1,344 in^2

Step-by-step explanation:

The area of the standard placemats is 84 in^2. To make 6 we need to multiply that by 6. 84 in^2*6 is 1,344 in^2. Please rate brainliest. It would really help!

Answer:

Option D

Step-by-step explanation:

The standard size of the rectangular placemat is 14 inches by 16 inches.

So fabric needed to make a placemat = Length × Width

                                                               = 14 × 16

                                                               = 224 inch²

Now for 6 placemats fabric required = 6 × 224

                                                             = 1344 inch²

Option D is the answer.

Step-by-step explanation:

you don't give us information about the runner

Answer:

question 8: 30975

question 9:

I don't know if it wants me to find the interest from the bond or the quote price of the bond.

If it is the bond it would be $1400 interest.

If it is the quote price of the bond, it would be $1,239 interest.

Answer:

Yes, no, no, no

Step-by-step explanation:

The first method is random.  There's no bias in selecting fans spaced out evenly as they enter.

The second method is not random.  It is biased towards those who hear the announcement and wish to participate.

The third method is not random.  It is biased towards those in the biggest rush to leave.

The fourth method is not random.  It is biased towards those with the best seats.

if the rectangular coordiante is (x,y) and the polar coordinate is (R,t), then they are related as follows:

R^2=x^2+y^2

tant=y/x

1.(pi,pi/4)

here, R=

[tex] \sqrt{ {\pi}^{2} + { (\frac{\pi}{4} })^{2} } = \sqrt{ \frac{17 {\pi}^{2} }{16} } = \frac{\pi}{4} \sqrt{17} \\tant = \frac{ \frac{\pi}{4} }{4} \\ t = {tan}^{ - 1} \pi = 89.682[/tex]

therefore the polar form of Q.1 is

(pi sq. root 17/4,89.682°)

you can do 2 in similar way.

B.y i think I’m not smart

Answer:

[tex]x-2 => f(x)=x^{3}-2x^{2}-x+2\\x+3=>f(x)=x^{3}-3x^{2} -13x+15\\x+4=>f(x)=-x^{3}+13x-12\\x+5=>f(x)=x^{4}+3x^{3}-8x^{2}+5x-25[/tex]

Step-by-step explanation:

The value of a function will be zero if the factor is put in it. In order to check whether a factor is of a function or not we will put the value of x from that factor in the function:

So

x-2 = 0 => x=2

Putting in first function

[tex]x^{3}-3x^{2} -13x+15\\=(2)^{3}-3(2)^{2} -13(2)+15\\=8-3(4)-26+15\\=8-12-26+15\\=23-38\\=-15 \neq 0\\[/tex]

So x-2 is not a factor of first function.

Putting in second function

[tex]f(x)=x^{4}+3x^{3}-8x^{2}+5x-25\\ =(2)^{4}+3(2)^{3}-8(2)^{2}+5(2)-25\\=16+3(8)-8(4)+10-25\\=16+24-32+10-25\\=-7\neq 0[/tex]

So x-2 is also not a factor of second function.

Putting in third function:

[tex]f(x)=x^{3}-2x^{2}-x+2\\ =(2)^{3}-2(2)^{2}-2+2\\=8-2(4)-2+2\\=8-8-2+2\\=0[/tex]

So x-2 is factor of third function.

...........................

For x+3

x+3=0

x=-3

First function:

[tex]f(x)=x^{3}-3x^{2} -13x+15\\=(-3)^{3}-3(-3)^{2} -13(-3)+15\\=-27-3(9)+39+15\\=-27-27+39+15\\=-54+54\\=0\\[/tex]

So x+3 is a factor of first function.

.............................

For x+4

x+4=0

x=-4

As we have already found the factors of first and third function, we will now only check second and fourth function.

[tex]f(x)=x^{4}+3x^{3}-8x^{2}+5x-25\\ =(-4)^{4}+3(-4)^{3}-8(-4)^{2}+5(-4)-25\\=256+3(-64)-8(16)-20-25\\=256-192-128-20-25\\-109\neq 0[/tex]

So x+4 is not a factor of second function.

Putting in fourth function:

[tex]f(x)=-x^{3}+13x-12\\ =-(-4)^{3}+13(-4)-12\\=64-52-12\\=64-64\\=0\\[/tex]

So x+4 is a factor of fourth function

..........................

For x+5=0

x=-5

Since only one function is remaining we'll only check for that.

[tex]f(x)=x^{4}+3x^{3}-8x^{2}+5x-25\\ =(-5)^{4}+3(-5)^{3}-8(-5)^{2}+5(-5)-25\\=625+3(-125)-8(25)-25-25\\=625-375-200-25-25\\=0\\[/tex]

Answer:

  BC = 52

Step-by-step explanation:

The point of the question is to have you recognize and use the fact that the tangent segments from the same point are of equal length. That lets you write the equation ...

  4x +8 = 2(3x -7) . . . BC = BA

  2x +4 = 3x -7 . . . . . divide by 2

  11 = x . . . . . . . . . . . . add 7-2x

The length of segment BC is computed using this value of x:

  BC = 4x +8 = 4·11 +8

  BC = 52

Answer:

0.125

Step-by-step explanation:

This is a standard calculus question. If you search out L'Hopital's Rule you will find that there are only Calculus examples present. If you use calculus, the answer comes to 1/8. The only way I can think of doing this without the use of Calculus is to let x = something very small -- say x = 0.0001 That approaches 0, but it is not quite = to 0.

So let's try it.

16 + 0.00001  = 16.00001

sqrt(16.0001) = 4.00000125

Now subtract 4

4.00000125 - 4

0.00000125

Now divide by 0.00001

0.12499998

which is close to 0.125.

If someone else can give you an answer that is "purer" than this one, take it.

Answer:

actually ASA and SAA is the same ASA stands for angle side angle while SAA stands for side angle angle .lets prove

Step-by-step explanation:

first name the triangle as i told earlier like ABC and PQR then

first side:AB=PQ,angleA=angleP,angleB=angleQ

Answer:

4

Step-by-step explanation:

The table clearly shows that if x = 0, y = 4.

The required output for the input of 0 in the function is 4.

Given that,
A table is shown the input and output value of the function, we have to determine the output value of the function for the corresponding input value 0.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the table,
f(x) shows the output for the corresponding input x,
In the given question for x = 0 {input} there is f(0) = 4 in the table,

Thus, the required output for the input of 0 in the function is 4.

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Answer:

29

Step-by-step explanation:

50 - 20 = 30

7 - 8 = -1

30 - 1 = 29

Answer:

C

Step-by-step explanation:

A function is even if:

f(x) = f(-x)

In other words, the function is symmetrical about the y-axis.

Function f is symmetrical, but it's not centered on the y-axis.

Function g is both symmetrical and centered on the y-axis.

So only g is an even function.  Answer C.

Answer:

The coordinates of point s are (-3 , 3)

Step-by-step explanation:

* Lets revise some transformation

- If the point (x , y) translated horizontally to the right by h units

 then the new point  = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point  = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point  = (x  , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point  = (x  , y - k)

* Now lets solve the problem

∵ The vertices of triangle cde are c (-3 , 1) , d (-1 , 4) , e (-6 , 4)

∵ The new coordinates of two vertices are q (-1 , 6) , r (-6 , 6)

- The image of point d is q and the image of point e is r

∵ Point d = (-1 , 4) and point q = (-1 , 6)

∵ Point e = (-6 , 4) and point r = (-6 , 6)

- The x-coordinate has no change but the y-coordinate added by 2

∴ The triangle cde translated vertically up by 2 units to create the

  congruent triangle sqr

- Lets translate point c two units up to find the coordinates of point s

∵ Point c = (-3 , 1)

∴ Poin s = (-3 , 1 + 2) = -3 , 3)

* The coordinates of point s are (-3 , 3)

Answer:

Step-by-step explanation:

Answer:

125 grams.

Step-by-step explanation:

We have been given an equation , which models the mass of a mammal’s brain, in grams, where x is the mass of the mammal, in kilograms.

To find the approximate mass of a mammal's brain with a body that has a mass of 60 kg, we will substitute  in our given equation.

Therefore, the mass of the mammal's brain is approximately 125 grams.

Answer:

.A.The volume of a gas varies directly with its temperature at constant pressure.

Step-by-step explanation:

This law is expressed mathematically as;

V₁ /T₁ =V₂/T₂ where

V₁=initial volume

T₁=initial absolute temperature

V₂=final volume

T₂=final absolute temperature

The temperature is converted to Kelvin when doing calculations where;

0°c = 273 K

An application of this law in real world examples could be  when a ball is left outside overnight it the cold, the ball shrinks a little in its volume due to decreased temperatures.

Answer:

A is the answer for sure i got it right after working it out.

The magnitude of the net force on the box is 100 Newtons to the left.

A force is the result of the interaction between two things and can be either a push or a pull. Due to the fact that it is a vector quantity, it possesses both magnitude and direction. The object's state of motion, direction, size, and form might all change as a result.

Given, the box is being pushed to the right with a force of 300 newtons, and to the left with a force of 400 newtons.

Here,

400 newtons > 300 newtons

400 newtons is much more than 300 newtons,

The net force on the box will be the sum of F₁ and F₂.

Let the forces F₁ and F₂ act on the table in opposite direction,

F₁ is the greater than F₂,

the F net = F₁-F₂

And the magnitude of the net force on the box,

400 -300 = 100 newtons.

Therefore, net force on the box is 100 Newtons to the left.

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The complete question is:

A box is being pushed to the right with a force of 300 Newtons', and to the left with a force of 400 Newtons'. What is the magnitude of the net force on the box?

Answer:

Option D) 64

Step-by-step explanation:  

see the attached figure with letters to better understand the problem

In the right triangle BCD find BC

Applying the Pythagoras Theorem

[tex]BC^{2}=48^{2}+36^{2}\\BC^{2}=3,600\\BC=60\ units[/tex]

In the right triangle ABC

[tex]cos(C)=BC/AC[/tex]

substitute the values  

[tex]cos(C)=60/(x+36)[/tex] -------> equation A

In the right triangle BDC

[tex]cos(C)=CD/BC[/tex]

substitute the values

[tex]cos(C)=36/60[/tex] -------> equation B

equate equation A and equation B

[tex]60/(x+36)=36/60\\ \\(x+36)*36=60*60\\ \\36x+1,296=3,600\\ \\36x=3,600-1,296\\ \\36x=2,304\\ \\x=64\ units[/tex]

To find the missing length, use the Pythagorean theorem by setting up an equation with the given lengths in a right triangle. Solve for the missing length using the equation and determine the correct answer.

To find the missing length, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let's assume the missing length is represented by 'x'. Using the theorem, we can set up the equation as follows:

We can solve for 'x' by substituting the given lengths into the equation and solving for 'x'.

x2 = a2 + b2

x2 = 162 + 302

x2 = 256 + 900

x2 = 1156

x = √1156

x = 34

Therefore, the missing length indicated is 34. Option B) 36 is not the correct answer.

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Answer:

C

Step-by-step explanation:

C:  7 spaces to the right and 5 spaces up

this point is in Quadrant I.

Answer:

7  spaces to the right and 5 spaces up

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

we know that

Applying the law of sines

24/sin(92°)=7/sin(Z°)

sin(Z)=7*sin(92°)/24

sin(Z)=0.291489

Z=arcsin(0.291489)=16.9°

Answer:

12%

Step-by-step explanation:

60000 people are unemployed, out of 500000 people.

That means that 60000/500000 of the population is unemployed.

Simplify: 60000/500000 = 6/50 = 0.12 = 12%

The overall unemployment rate is will be 12% based on the given data.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

Total people = 5000000

40000 are employed and 60000 are unemployed out of 300000 people are in the labor force.

The % unemployment rate = (60000)/500000 x 100 = 12%

Hence "The overall unemployment rate is will be 12% based on the given data".

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