What is the rectangular form of 12(cos(π) + i sin(π))?

12
-12
12 + i
–12 + i

Answer: -11.3875

Step-by-step explanation:

The total segment AE is 46.

"SAS" is when we know two sides and the angle between them.

To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.

The Law of Cosines = a² = b² + c² − 2bc cosA

where

'b' and 'c' are two given sides

'A' is the angle between side 'b' and 'c' and

a' is the unknown side which we have to find.

In ΔABC , b=21, c=20, a= AC

By the Cosine law

a² = 21²+20² - 2*21*20 cos90°

a² =441 + 400 - 0 (∵cos 90° =0)

a² = 841

a=√841

a=29= AC.

Now, in ΔCDE, b=8, c=15 and a = CE

By the Cosine law

a² = 8² + 15²- 2*8*15cos90°

a² = 64 + 225 - 0 (∵cos 90° =0)

a²= 289

a = 17 = CE.

AE = AC + CE

AE = 29+17= 46.

Therefore, the total segment AE is 46.

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The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Given data ,

The angles of the triangle ABC are

∠A = ( 2x + 10 )°

∠B = ( 4x + 2 )°

Let angle ∠C be y

The sum of ∠A + ∠B + ∠C = 180°  

So ,

( 2x + 10 )° + ( 4x + 2 )° + y = 180°   be equation (1)

Now , we can see that AD is a straight line and C is a point on the line AD

The total angle of C on the line AD is 180°

So , ( 5x + 27 )° + y = 180°

y = 180° - ( 5x + 27 )°   be equation (2)

Substituting the value of equation (2) in equation (1) , we get

( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°

On Simplifying , we get

( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0

( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0

x - 15 = 0

Adding 15 on both sides , we get

x = 15°

Substituting the value of x in the ∠A , ∠B and ∠C equation , we get

∠A = ( 2x + 10 )°

     = 40°

∠B = ( 4x + 2 )°

     = 62°

∠C = 180° - ( ∠A + ∠B )

     = 180° - 102°

     = 78°

Therefore , the angles of the triangle ABC are 40° , 62° and 78°

The measure of ( 5x + 27 )° is

= ( 5 x 15 + 27 )°

= 102°

Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

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The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4

Given that,

y forms a circle of radius r

y=2[tex]\pi[/tex]r

r=y/2[tex]\pi[/tex]

(2-y)- forms Square Side x

(2-y) = 4x

x=(2-y)/4

Now Sum of Area's=Area of Square +Area of Circle

Sum = [tex]\pi[/tex]r² + x²

Substitute the r and x values in above equation,

A(y)= y²/4[tex]\pi[/tex]+(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4[tex]\pi[/tex] + 2(y-2)/16 =0

y/2[tex]\pi[/tex] + (y-2)/8 =0

y = 2[tex]\pi[/tex]/[tex]\pi[/tex]+4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/[tex]\pi[/tex]+4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4

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The rearranged form of equation 4(x-3)/a=y will be x=ay+3.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the expression is, 4(x-3)/a=y

First, we open the bracket to make x the variable in the equation.

4x - 12/a = y

4x - 12 = ay

4x = ay + 12

x = ay + 12/4

x = ay + 3

Thus, the rearranged form of equation 4(x-3)/a=y will be x=ay+3.

The question is incomplete,

The complete question is"Rearrange to make x the subject of 4(x-3)/a=y:

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Answer:

y-(-2)= -5(x-4)

= -5x-y+18

Step-by-step explanation:

y-(-2)= -5(x-4)

y+2= -5x +20

y= -5x+18

-5x-y+18= 0

Answer:

23/20

Step-by-step explanation:

110% of 20 is 22/20, so 23/20 is more.

Step-by-step explanation:

23/20 = 1,15

110% = 1,1

1,15 > 1,1

⇒ 23/20 > 110%

The general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]

The given arithmetic sequence is -2, -8, -14, -20

The first term = a = -2,

The common difference = d = -8 -(-2) = -8 +2 = -6

The general term of the arithmetic sequence is given by

[tex]T_{n} = a + (n-1)d[/tex]

Now, putting the values of the first term and common difference in the general term.

[tex]T_{n} = -2 +(n-1) (-6)\\\\T_{n} = -2 -6n +6\\ \\T_{n} = -6n +4[/tex]

Hence, the general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]

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Answer:

26x/7

Step-by-step explanation:

Let's say we have blue and red balls

Blue : Red

3 : 5

Now we can add another ratio for the whole.

Blue : Red : Total

Total is Blue + Red = 3 + 5 = 8

So

Blue : Red : Total

3 : 5 : 8

Then the part : whole ratio for Blue is...

Blue : Total

3 : 8

There are 19/9 ounces in each sprinkle of sundae

From the question, we have the following parameters that can be used in our solution:

Number of sundaes = 4

Ounces of sprinkles = [tex]8\frac49[/tex] ounces

From the above parameter, we can calculate the amount of sprinkles using the constant of proportionality formula

This is represented as

Ounces per sprinkle = Ounces of sprinkles/Number of sprinkles

Substitute the known values in the above equation

So, we have the following equation

Ounces per sprinkle = [tex]8\frac49[/tex]/4

Evaluate the quotient

Ounces per sprinkle = 19/9

Hence, the ounces per sprinkle is 19/9 ounces

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For the given pair of intersecting lines, we find out that the value of x is 1 and the measure of the angle 1 is 169°.

From the figure we see that there are two lines intersecting each other.

We know,

Sum of all the angles formed = 360

We also know that

If there are a pair of two intersecting lines, then the vertically opposite angles are equal.

=> 20x+11 = 25x-14

=> 5x = 5

=> x = 1

Substituting the value of x in 20x+11 , we have

20*1 + 11 = 21°

Substituting the value of x in 25x-14 , we have

25*1 - 14 = 11°

It is also known to us that the sum of the adjacent angles of a pair of intersecting lines is equal to 180°. This implies that

11° + 1 = 180°

=> 1 = 180° - 11°

=> 1 = 169°

Thus, for the given pair of intersecting lines, we find out that the value of x is 1 and the measure of the angle 1 is 169°.

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The number for this equation is 5.

What is equation?

In arithmetic, Associate in Nursing equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

let the number be x.

So , according to question =

3(x+2) = x+16

Now solving this equation , we will get the answer

⇒ 3x +6 = x+16

now moving x to left side and taking the constant to right,

⇒ 3x-x = 16 -6

⇒ 2x = 10

⇒ x=5

Hence the number is 5.

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 y = -3/5x - 123/5 is slope-intercept form .

What is an explanation of the slope-intercept form?

Point = ( 1,24 )

slope = -3/5

the equation in standard form of the line that passes through the point

               y - y₁ = m ( x - x₁)

                y - 24 = -3/5 ( x - 1)

             5 (y - 24) = -3( x - 1 )

                5y -    120 = -3x + 3

                 5y = -3x + 3 + 120

                 5y = -3x + 123

                 y = -3/5x - 123/5

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Check the picture below.

[tex]18m^2~~ + ~~10m^2\implies 28m^2\hspace{5em}(\stackrel{m^2}{28})(\stackrel{\pounds}{10})\implies \text{\LARGE \pounds280}[/tex]

The amount of slushy that was originally in the cup is 225 milliliters and the time it took Mariana to drink all the slushy is 50 seconds.

Total quantity she took

Total quantity = 4.5 × 17

Total quantity = 76.5 milliliters

Original quantity = 148.5 + 76.5

Original quantity = 225 milliliters

b. Time taken to drink all

Time =225 milliliters /2.5

Time = 50 seconds

Therefore original quantity  225 milliliters  and the time is 50 seconds.

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Answer:

10mm = 1cm

Step-by-step explanation:

Milli means 1000th of

Centi means 100th of

1000 / 100 = 10

So,

10mm = 1cm

If Joe spent a total of $23.65 , then the cost of the paints is $5.75  .

In the question ,

it is given that ,

From the hobby shop , Joe bought 2 model sportscars for $8.95 each

the cost for 2 sports car = 8.95*2 = 17.9

the total amount spent by Joe at the shop = $23.65

let the cost of the paint be "$x" .

the above situation can be represented by the equation .

total cost = cost for 2 model cars + cost of paint

substituting the values from above ,

we get ,

23.65 = 17.9 + x

x = 23.65 - 17.9

x = 5.75

Therefore , If Joe spent a total of $23.65 , then the cost of the paints is $5.75  .

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The probability of the next customer paying with a debit or credit card other than cash is =94.82%

We have given,

Genesis owns a small business selling clothing.

She knows that in the last week 6 customers paid cash, 66 customers used a debit card, and 44 customers used a credit card.

we are asked to determine  the probability that the next customer will pay with something other than cash as a percent to the nearest whole number

P(A)= number of favorable outcome in event A divided by the total outcome in a sample space

customers will pay through debit or credit card other than cash.

last week of customers paid cash: 6

last week of customers paid w/ a debit card: 66

last week of customers paid w/ a credit card: 44

Therefore, 6+66+44= 116

=110/116

=0.9482

= 94.82% is the probability that the next customer will pay with

something other than cash as a percent to the nearest whole number.

Hence we get the required answer.
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The value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

From the figure:

MZ is a perpendicular bisector of ∆GHJ.

GM = MJ

GM = 14.5

KZ is a perpendicular bisector of ∆GHJ.

GK = KH

GK = 18.6

Z is the circumcenter of ∆GHJ.

JZ = GZ

JZ = 19.9

Therefore the value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

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The transformations to function f(x) that results in function g(x) are described as follows:

5. Reflection over the x-axis, vertical stretch by a factor of 2.

6. Shift right of 6 units, shift up of 4 units.

7. The rule for g(x) after the transformation is given as follows:

[tex]g(x) = \sqrt[3]{-x + 7}[/tex]

For item 5, the functions are given as follows:

The transformation is a multiplication by -2, which means that the function was:

For item 6, the functions are given as follows:

Then the transformations are explained as follows:

For item 7, the parent function is:

[tex]f(x) = \sqrt[3]{x}[/tex]

Then the transformations and their effects are given as follows:

Hence the function is:

[tex]g(x) = \sqrt[3]{-x + 7}[/tex]

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Using the fraction concept, we can say that The number of beads each friend will get is 4.

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

Number of bead = 32 bead;

Total number of friends = 8;

So,

we need to find how many beads will one friend get:

So,

The number of beads each friend will get : [tex]\frac{32}{8}[/tex]

The number of beads each friend will get is 4.

Hence,

using the fraction concept, we can say that The number of beads each friend will get is 4.

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Answer:

a= im not sure sorry

h= horizontal shift

k= vertical shift

Step-by-step explanation:

a = the vertical stretch or compression factor

h = is the x-translation, that is it moves the graph right or left

k = The 'k' is the "vertical shift".

If positive, moves graph up k units.

If negative, moves graph down k units.

The equation of line with slope is -1/3 and y intercept 5/3 is : x + 3y = 5.

In the form of a slope intercept, the line's equation looks like this:

y = mx + b

where

slope = m

y-intercept = b

Here given slope = -1/3

y-intercept at 5/3

As a result, the line's equation has a slope of -1 / 3.

Let's use the locations to determine the y-intercept 5/3.

y = mx + b

Here b = 5/3

By substituting ,

y = -1/3x + 5/3

Multiplying both sides by 3,

3y = -x + 5

3y + x = 5

= x + 3y = 5.

Therefore the equation of line is x + 3y = 5.

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Explanation:

Let x = depth of the gutter

then

14-2x = width of the gutter

:

Cross section area:

A = depth * width

A = x(14-2x)

A = 14x - 2x^2

:

Axis of symmetry will give x value for max area: x = -b/(2a)

x = -14/2 * -2

x = -14/-4

x = +3.5 inches is the depth for max area

:

:

Max area: 3.5 * 9 = 31.5 sq/in

Answer:

y = 2x + 3

Step-by-step explanation:

The slope

As the y changes by 2, the x changes by 1.  2/1 is 2

The y intercpet is 3.  This what y is when x is 0.

Answer:

12

Step-by-step explanation:

12*12=144

Answer: 12 is the correct answer

Step-by-step explanation:

144 = a × a = 122

Then a = √144 = √(12 × 12)

12 × 12 = 144 or -12 × -12 = 144

The square root of 144 is +12 or -12

This shows that 144 is a perfect square.

Answer:

======================

(a) f(-7)

(b) f(0)

(c) f(4)

Answer:

Step-by-step explanation:

a) f(-7) = ?

→ f(x) = 8 - 4x

→ f(-7) = 8 - 4(-7)

→ f(-7) = 8 + 28

→ f(-7) = 36

Hence, f(-7) = 36.

b) f(0) = ?

→ f(x) = 8 - 4x

→ f(0) = 8 - 4(0)

→ f(0) = 8 - 0

→ f(0) = 8

Hence, f(0) = 8.

c) f(4) = ?

→ f(x) = 8 - 4x

→ f(4) = 8 - 4(4)

→ f(4) = 8 - 16

→ f(4) = -8

Hence, f(4) = -8.