plEASE HELP I WILL GIVE 50 POINTS

The complex number z = (4, 11π / 6) in rectangular form is z = 2√3 - i 2 (z  = 3.464 - i 2). (Correct choice: C)

Herein we find a complex number in polar form, whose definition is shown below:

[tex]z = r\cdot e^{i\,\theta}[/tex]

Likewise,

z = (r, θ)

Where:

This number is equivanlent to the following expression in rectangular form:

z = a + i b

Where:

a = r · cos θ

b = r · sin θ

If we know that r = 4 and θ = 11π / 6, then the complex number in rectangular form is:

a = 4 · cos (11π / 6)

a = 2√3

b = 4 · sin (11π / 6)

b = - 2

The rectangular form of complex number z = (4, 11π / 6) is the number z = 2√3 - i 2.

To learn more on complex numbers: https://brainly.com/question/10251853

#SPJ1

After solving, the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2) is 3x^2 + 4x + 2.

In the question, we have to find the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2).

The polynomial is 3x^3 + 10x^2 + 10x + 4.

We have to divide the given equation by x + 2 to find the quotient.

Four operations, namely divide, multiply, subtract, and bring down, can be used to break down the division process into phases.

1: Find the appropriate integer to use as the divisor for the given number.

2: Multiply the integer (quotient) and divisor to obtain the amount to be deducted from the payout.

3: Deduct the amount from the dividend.

4: Bring down the balance and any additional digits from the dividend in step four.

5: Continue the procedure outlined above until the remainder equals zero or less than the divisor.

x+2 ) 3x^3 + 10x^2 + 10x + 4 ( 3x^2 + 4x + 2

         3x^3 + 6x^2

        -        -

       ___________

                    4x^2 + 10x

                    4x^2 + 8x

                   -       -

               ______________

                                2x + 4

                                2x + 4

                               -      -

                          ____________

                                   0

Hence, the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2) is 3x^2 + 4x + 2.

To learn more about finding the quotient link is here

brainly.com/question/17200398

#SPJ4

The complete question is:

What is the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2)?

Answer:

12x² - 40

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As a square has four sides of equal length, the perimeter of a square is four times the length of one side.

[tex]\begin{aligned}\textsf{Perimeter}&=4(3x^2-10)\\&=4 \cdot 3x^2+4 \cdot (-10)\\&=12x^2-40\end{aligned}[/tex]

Answer:

Perimeter of square = 12x² - 40

Step-by-step explanation:

Perimeter of square formula,

→ P = 4 × Side

→ [ P = 4a ]

Now the perimeter of square is,

→ P = 4 × (3x² - 10)

→ P = 4(3x²) - 4(10)

→ P = (4 × 3)x² - 40

→ [ P = 12x² - 40 ]

Hence, perimeter is 12x² - 40.

We have that the Density of metal X  is mathematically given as

∅ = 5048.33 Kg/[tex]m^{3}[/tex]

Density is a word we use to describe how much space an object or substance takes up (its volume) in relation to the amount of matter in that object or substance (its mass). Another way to put it is that density is the amount of mass per unit of volume. If an object is heavy and compact, it has a high density.

Density of metal,

Generally the equation for the side of fcc  is mathematically given as

fcc = 2 × [tex]\sqrt{2}[/tex] × radius of metal

fcc = 2 × 1.414 × 135

fcc = 381.78 ×  [tex]10^{-12}[/tex] m.

where, volume of 1 unit cell of fcc

fccV = ( 381.78 ×  [tex]10^{-12}[/tex] ) ^3

fccV = 55,646,713.615752 ×  [tex]10^{-36}[/tex] [tex]m^{3}[/tex]

And

weight of 1 atom

Wa = molecular weight / avagadro number

Wa = 42.3/(6.023 × [tex]10^{23}[/tex])

Wa = 7.023 × [tex]10^{-23}[/tex] gm/atom

Therefore, density is

∅ = (28.0923 ×  [tex]10^{-26}[/tex]) / (55,646,713.615752 ×  [tex]10^{-36}[/tex] )

∅ = 5048.33 Kg/[tex]m^{3}[/tex]

Therefore, we have that the Density of metal X  is mathematically given as  ∅ = 5048.33 Kg/[tex]m^{3}[/tex]

To learn more about density visit : brainly.com/question/29775886

#SPJ4

Answer:

Julia parcourt 1200 km par mois en voiture, donc elle parcourt 1200 x 12 = 14400 km par an.

Sa voiture actuelle consomme 6 L d'essence par 100 km, donc elle consomme 6/100 x 14400 = 864 L d'essence par an.

Si elle remplaçait sa voiture actuelle par une voiture hybride qui consomme moins d'essence, elle économiserait 864 L d'essence par an.

Si le prix d'un litre d'essence est de 1,30 $, alors Julia économiserait 864 x 1,30 = 1129,20 $ par an si elle remplaçait sa voiture actuelle par une voiture hybride.

The equation, Y = - 3x + 7 has infinitely many solutions.

Here we are given the equation y = - 3x + 7.

Now this equation has 2 variables. when an equation has 2 variables, there must be at least 2 equations for the system to have a unique solution, hence the given equation cannot have 1 unique solution.

If we plot this equation on the graph we will see that it makes a never-ending line.

Here for every value of x, we get a different value of y, which can be easily seen in the graph.

Therefore we cannot conclude that this will have no solution. Hence since there can be infinite possible answers to the above equation, this has infinitely many solutions.

To learn more about Equations visit

brainly.com/question/30127282

#SPJ4

Correct Question

How many solutions does Y = - 2x + 3 have?

The amount of each trail mix that should be combined to create the special order trail mix are:

6.25 pounds of the trial that contains 75% nuts.

3.75 pounds of the trial that contains 35% nuts.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Trial mix A = x

= 75% nuts.

Trial mix B = y

= 35% nuts

Now,

Two equations are:

x + y = 10 _____(1)

x = 10 - y _____(2)

0.75x + 0.35y = 10 x 0.60 ______(3)

Substituting (2) in (3)

0.75 (10 - y) + 0.35y = 6

7.5 - 0.75y + 0.35y = 6

7.5 - 6 = 0.75y  - 0.35y

1.5 = 0.40y

y = 1.5/0.40

y = 3.75

Now,

x = 10 - 3.75

x = 6.25

Thus,

6.25 pounds of the trial that contains 75% nuts.

3.75 pounds of the trial that contains 35% nuts.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The value of the upper quartile is 65.

The lower quartile, which is represented by the left border of the box, is the value that the first 25% of the data falls within. 25% of the data are to the right of the upper quartile value, which is indicated by the upper quartile at the right border of the box.

The left whisker represents the bottom 25% of the data, the left half of the box represents the second 25%, the right half of the box represents the third 25%, and the right whisker represents the top 25%.

The value of the upper quartile is 65.          

To learn more about upper quartile refer to:

https://brainly.com/question/10353201

#SPJ1

Answer:

The correct answer is B.

Answer:

19/15

2/3+3/5

Multiply each by 3

10/15+9/15=19/15

[tex] = \frac{2}{3} + \frac{3}{5} \\ [/tex]

[tex] = \frac{2}{3} \times \frac{5}{5} + \frac{3}{5} \times \frac{3}{3} \\ [/tex]

[tex] = \frac{10}{15} + \frac{9}{15 \\ } [/tex]

[tex] = \frac{10 + 9}{15} \\ [/tex]

[tex] = \frac{19}{15} \\ [/tex]

[tex] = 1 \frac{4}{15} \\ [/tex]

Answer:D y=-2x-1

Step-by-step explanation:

To solve this problem, we first need to look at the direction of the line to determine whether the slope is positive or negative. Since the left portion of the line is Quadrant 2 and the right portion in quadrant 4, the slope will be negative. Anytime the line looks like \ it will be negative, while / is positive. This immediately eliminates answers A and C. Now, our next order of business is to find the slope of the line. To do this, we need to pick two points on the line and use the equation (y2-y1)/(x2-x1). Any points on the line will work, so even if you do not use the same as me, you still should get the same answer (this is a good way to check!)

point 1: (-2,3)

point 2: (0,-1)

(-1 - 3) / (0 - -2) = (-1 - 3) / (0 + 2) = -4/2 = -2

Since the slope is -2, we know the answer is d. Hope this helps

Answer: A). It is 1/6 throughout the line

Step-by-step explanation:

The water that the larger cup can hold more than the smaller cup, given the two cups is 15. 71 cubic inches

To find the amount of water, first find the volume of the cups using the volume of a cone formula. This formula is:

= Pi x r² x height of cone / 3

The amount of water the larger cup can hold is:

= Pi x 2² x 6 / 3

= 25. 13 cubic inches

The water in the smaller cup is:

= Pi x 1.5² x 4 / 3

= 9. 42 cubic inches

The difference is:

= 25. 13 - 9. 42

= 15. 71 cubic inches

Find out more on water at https://brainly.com/question/3386208

#SPJ1

The coordinates of the circumcentre P(x, y) of ΔABC with vertices A (1, 0), B (8, -7), and C(7,-4) is P(6.4, 1.6).

If there is a circle that encompasses all of the vertices of a polygon, it has a circumcenter that is the centre of the circle. The circumcentre and ensuing circumcircle of a triangle are both always distinct.

Let P(x, y) be the circumcentre

Then

PA = PB = PC

⇒PA² =PB² =PC²

Now, PA² = PB²

⇒ (x−1)² +(y−0)² =(x−8)² +(y+(-7))²

⇒  x = 8 − y

And,  PB² = PC²

⇒ (x−8)² +(y+(-7))²= (x−7)² +(y−(-4))²

⇒  x = 24− 11y

Factor out x from both equations

8 − y = 24− 11y

10y = 24 - 8

10y = 16

y = 16/10

y = 1.6

For x

x = 8 − y

x = 8 − 1.6

x = 6.4

Thus, the coordinates of the circumcentre P(x, y) of ΔABC with vertices A (1, 0), B (8, -7), and C(7,-4) is P(6.4, 1.6).

Learn more about circumcentre

https://brainly.com/question/29392149

#SPJ1

When two expressions can be written similarly or when they can be combined into a single, simpler expression, they are said to be equivalent.

Let's evaluate each expression pair separately.

8. (n2+4)-n2 and 4n. (n2+4)-n2 = n2+ 4 - n2 = 4, which is not the same as 4n.

NOT THE SAME

9. The product of 3x + 5 and 2(x + 3) 2(x + 3) equals 2x + 6, not 3x + 5.

NOT THE SAME

10. 15 - 6x and 15(1 - 6x) (1 - 6x)

In other words, 15(1 - 6x) = 15 - 90x, which is not equal to 15 - 6x, is NOT EQUAL.

11. (y + y + 2 + y) + 3y and 6y + 2 (y + y + 2 + y) + 3y equals y+y+y+y +2 + 3y, which equals 3y + 2 + 3y and 6y + 2.

It is equivalent to the other phrase.

EQUIVALENT

12. 8y - 3 + 10y and 3 (6 - 1)

8y - 3 + 10y = 8y + 10y - 3 = 18y - 3 3(6 - 1) = 3(5) = 15

Both of the expressions are incompatible.

NOT THE SAME.

Only the expressions shown in position 11 are equivalent.

To learn more about equivalent expressions refer

https://brainly.com/question/556764

#SPJ1

Answer:

4:5

Step-by-step explanation:

We know that 1 minute is equals to 60 seconds.

So the ratio is now:

48 seconds : 60 seconds

We need to simplify the ratio in its simplest form. 12 goes into both 48 and 60 so:

48/12 = 4 seconds

60/12 = 5 seconds

So the ratio 48 seconds: 1 minute in its simplest form is:

4 seconds : 5 seconds

Answer:

F

Step-by-step explanation:

(x + 2)² + (y - 3)² = 37

intersection points with the x-axis means that their y-values are 0 !

that is the whole trick, as I am sure you experienced already with lines and y-intersects (x = 0) and x-intersects (y =0).

so, we need to solve for x, when y = 0 :

(x + 2)² + (-3)² = 37

x² + 4x + 4 + 9 = 37

x² + 4x - 24 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-4 ± sqrt(4² - 4×1×-24))/(2×1) =

= (-4 ± sqrt(16 + 96))/2 = (-4 ± sqrt(112))/2 =

= (-4 ± sqrt(16×7))/2 = (-4 ± 4×sqrt(7))/2 =

= -2 ± 2×sqrt(7)

x1 = -2 + 2×sqrt(7)

x2 = -2 - 2×sqrt(7)

so, F is the right answer.

In point-slope form, the equation of the line through the indicated points is y - 2 = -4/3. ( x - 4 ).

Y - Y1 = m is the line's equation in point slope form (x – x1).As a result, the equation for a line passing through the origin and having a slope of m is given by y - 0 = m(x = 0), which equals y = mx. Given the information in the query;

A Point (4, 2)

x₁ = 4

y₁ = 2

B Point (1, 6)

x₂ = 1

y₂ = 6

We start by figuring out the line's slope.

Slope m is equal to (y2 - y1)/(x2 - x1)

Slope: m = (6 - 2) ( 1 - 4 )

(4)/ Slope m ( -3)

Slope m=-4/3

Then, simplify the point slope formula y - y1 = m(x - x1) using the slope -4/3 and point (4,2).

y - y₁ = m(x - x₁)

y - 2 = -4/3( x - 4 ) ( x - 4 )

As a result, y - 2 is the equation of the line in point-slope form that passes through the indicated places.

To learn more about Slope refer

https://brainly.com/question/18989413

#SPJ1

Answer:

6 apples and 5 bananas

Step-by-step explanation:

x + y = 11

x = 11 - y

1.75x + 0.70y = 14

1.75(11 - y) + 0.7y = 14

19.25 - 1.75y + 0.7y = 14

5.25 = 1.05y

y = 5

x = 11 - 5 = 6

Answer: 4 apples and 10 bananas

Step-by-step explanation:

Consider: a=apple, b=bananas

1) a + b = 14 // 14 total of apples and bananas

   a = 14 - b

2) 1.75a + 0.70b = $14 // $14 worth of apple and bananas

3) Substituting 1) in 2):

  1.75(14 - b) + 0.70b = 14

  24.5 - 1.75b + 0.70b = 14

   b = 10.5 / 1.05

    b = 10

4) Substituting 3) in 1):

   a = 14 - 10

   a = 4

For the line y = -2-4x, the slope of a line parallel to this line is -4 and the slope of a line perpendicular to this line is 1/4.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The equation for the line is - y = -2 - 4x.

The slope of a line is represented by the coefficient of the x term. In this case, the slope of the line y = -2 - 4x is -4.

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. The negative reciprocal of -4 is 1/4.

So, the slope of a line perpendicular to y = -2 - 4x is 1/4.

The slope of a line parallel to a given line is the same as the slope of the given line.

So the slope of a line parallel to y = -2 - 4x is -4.

Therefore, the parallel and perpendicular slope is -4 and 1/4 respectively.

To learn more about slope from the given link

https://brainly.com/question/16949303

#SPJ1

The value of side x for the right-angle triangle is 8.6 cm.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the sides are Hypotenuse H = 15 cm, perpendicular = x, and the base is y.

The value will be calculated as,

x = [ sin(35) x 15 ]

x = 8.6 cm

To know more about trigonometry follow

https://brainly.com/question/13729598

#SPJ1

The distance between given pair of points ( 2, 3 ) and ( 4, 1) is equal to

2√2.

As given in the question,

Given pair of points is represented by the coordinates

( x₁ , y₁ ) = ( 2, 3 )

( x₂ , y₂ ) = ( 4, 1 )

Standard formula to find the distance between two pair of points is :

= √( y₂ - y₁ )² + (x₂ - x₁ )²

Substitute the values to get the distance between two pair of points we have,

= √ ( 1 - 3 )² + ( 4 - 2 )²

= √ 2² + 2²

= √4 + 4

= √8

= 2√2 units.

Therefore, the distance between the given pair of points is equal to 2√2.

The above question is incomplete , the complete question is:

What is the distance between the pair of points (2, 3) and (4, 1) ?

Learn more about distance here

brainly.com/question/15172156

#SPJ4

Answer:

[tex] \sf \: -4z - 5 [/tex]

Step-by-step explanation:

Given expression,

→ (-7z - 4) - (-3z + 1)

Let's simplify the expression,

→ (-7z - 4) - (-3z + 1)

→ -7z - 4 + 3z - 1

→ (-7z + 3z) + (-4 - 1)

→ (-4z) + (-5)

→ -4z - 5

Hence, the answer is -4z - 5.

The vertices of the feasible region are  (0,100) (0,700) (400,500)

The minimum profit is (0,100)  and the maximum profit is (400,500)

Given that, P=14x+22y-900  where p is the profit

y > x +100    y must exceed the production of x by at least 100 units

x+2y<1400

x>0

y>0

We cannot produce negative quantities

Substitute y = x+100 into x+2y <1400

x+2(x+100) < 1400

x+2x+200 <1400

3x+200<1400

Subtract 200 from each side

3x<1200

Divide by 3

x<400

y = x+100

y = 400+100

y = 500

(400,500)

y > x +100

when x=0  y > 100  

x+2y <1400

0+2y <1400

2y <1400

y <700

When x=0  y = 700

a)  The vertices of the feasible region are  (0,100) (0,700) (400,500)

b)  Maximum and minimum profit occur at the vertices.

P=14x+22y-900

P(0,100) = 14(0) +22(100)-900 =2200-900=1300

P(0,700) = 14(0) +22(700)-900 =15400-900=14500

P(400,500) = 14(400) +22(500)-900 =5600+11000-900=15700

Thus, The vertices of the feasible region are  (0,100) (0,700) (400,500)

The minimum profit is (0,100)  and the maximum profit is (400,500)

Complete question: A factory can produce two products, x and y, with a profit approximated by P=14x+22y-900. The production of y must exceed the production of x by at least 100 units. Moreover, production levels are limited by the formula x+2y<1400.

a) Identify the vertices of the feasible region.

b) What production levels yield the maximum profit, and what is the maximum profit?

To know more about profits visit: brainly.com/question/22802773

#SPJ4

Option B does not represent a polynomial identity.

Polynomial identities are equations that are true for all possible values of the variable. The polynomial identities are -

Given are the equations as shown in the image.

The equation that is not a polynomial identity is option B.

Therefore, Option B does not represent a polynomial identity.

To solve more questions on algebraic functions, visit the link below -

brainly.com/question/1041084

#SPJ1

Answer : -4

explained:

you would have to sub 2 from -2x and -30(-30 - 2 = -32) to get x by it self then divide 8 by 8(equals) x then divide -32 with 8 = -4

your welcome!

The y-intercept is (0, 8).

The equation, y = mx + b, is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

The y-intercept is what you get when you plug in x = 0

Similarly, the x-intercepts are what you get when you plug in y = 0

So, because we're finding the y-intercept, plug in 0 for x and solve for y.

Therefore, the y-intercept is (0, 8).

To know more about slope-intercept form visit: brainly.com/question/29146348

#SPJ4

The length of the base of the rectangle is B = 11 yards  

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

To learn more about area of rectangle click :

https://brainly.com/question/15225905

#SPJ1