Find the arc length of the circle with a central angle of 30 degrees and a radius 12. Leave the answer in terms of π.

Answer:

7 x 12

Step-by-step explanation:

[tex]a=l *w[/tex]

[tex]84=l*w\\w=l+5\\[/tex]

these equations we know, so we can use them like this

[tex]84=l*(l+5)\\84=l^2 +5l\\[/tex]

I then plugged this equation into the desmos calculator to get the answer

[tex]l=7[/tex]

we then plug this into a previous equation

[tex]w=l+5\\w=7+5\\w=12[/tex]

to get our answer l=7, w=12

Answer:

See below for answers and explanations

Step-by-step explanation:

If we check x=5:

[tex]f(5)=-(5)^3+7(5)^2-7(5)-15\\f(5)=-125+7(25)-35-15\\f(5)=-125+175-50\\f(5)=50-50\\f(5)=0[/tex]

So [tex]x=5[/tex] is indeed a zero

If we check x=3:

[tex]f(3)=-(3)^3+7(3)^2-7(3)-15\\f(3)=-27+7(9)-21-15\\f(3)=-27+63-36\\f(3)=36-36\\f(3)=0[/tex]

So [tex]x=3[/tex] is also indeed a zero

If we check x=-1:

[tex]f(-1)=-(-1)^3+7(-1)^2-7(-1)-15\\f(-1)=1+7+7-15\\f(-1)=8+7-15\\f(-1)=15-15\\f(-1)=0[/tex]

So [tex]x=-1[/tex] is also indeed a zero

End Behavior

Since the degree of [tex]-x^3[/tex] is odd [tex](3)[/tex] and the leading coefficient is negative [tex](-1)[/tex], the end behavior of function [tex]f[/tex] is as follows:

Answer:

See below ~

Step-by-step explanation:

Blue inequality

Red Inequality

Answer:

See below

Step-by-step explanation:

Find the equation of the blue line....the blue shaded area is LESS than or EQUAL to this SOLID line

Blue line =    y = -x+4        so   y <= -x+4

Red line  =    y = 1/4 x              y > 1/4x     (dotted line says line is not included so the inequality is >   NOT ≥   )

Answer:

A = 12

Step-by-step explanation:

We can define ratio a to b as 12:3. If we are finding the value of A when B is 3, we go to the ratio. The ratio says that when B is 3, A is 12. Therefore, A is 12.

Answer:

A = 12

Explanation:

Given:

A ∝ B

set "k" constant

A = k(B)

Find "k"

12 = k(3)

k = 4

Then find A when B = 3

A = k(B)

insert values found

A = 4(3)

A = 12

Answer:

t = 3

Step-by-step explanation:

Given: 9t - (2t - 4) = 25

Distributive property: a(b + c) = ab + ac

1. Distribute '-' or '-1'

9t + -1(2t) + -1(-4) = 25

9t - 2t + 4 = 25

2. Combine like terms

7t + 4 = 25

3. Subtract 4 from both sides

7t + 4 - 4 = 25 - 4

7t = 21

4. Divide both sides by 7 to isolate the variable

7t ÷ 7 = 21 ÷ 7

t = 3

Learn more about the distributive property and equations here:

Answer:

<6 and <16 are alternate exterior angles.

Hey there!

12w = 102

DIVIDE 12 to BOTH SIDES

12w/12 = 102/12

SIMPLIFY IT!

w = 102/12

w = 102 ÷ 6 / 12 ÷ 6

w = 17 / 2

w = 8 1/2

Therefore, your answer should be:

w = 17/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

D

Step-by-step explanation:

The logical step is to factorize the left side of the equation, which becomes:

Then, you can take the square root on both sides.

Not asked, but good to understand the procedure regardless.

Step-by-step explanation:

number 2)

3√2/3√4=

=3√2/3×2

=3√2/6

=3√2/6 ×3/3

=1√2/2

=√2/2

Answer:

degrees like in angles. from 0 to 180

nwcggov

Answer:

x(1,2) = -5 ± √61) / (-2)

Step-by-step explanation:

The ABC formula of quadratic equation states

x(1,2) = (-b ± √b^2 - 4ac) / 2a

-x^2 + 5x + 9 = 0

a = -1

b = 5

c = 9

Thus x(1,2) = (-b ± √b^2 - 4ac) / 2a

= (-5 ± √(-5)^2 - 4*(-1)*9) / 2*(-1)

= (-5 ± √25+36) / (-2)

= (-5 ± √61) / (-2)

Answer:

There are 9 geese and 18 horses.

Step-by-step explanation:

Step 1: Make equations.

g ... number of geese

h ... number of horses

First equation: There are 27 animals in the barn.

g + h = 27

Second equation: There are 90 legs in all.

We know geese have two legs and horses 4.

2g + 4h = 90

Step 2: Solve the system of equations.

g + h = 27 (first equation)

2g + 4h = 90 (second equation)

Let's express g in terms of h in first equation.

g + h = 27

g = 27 - h

Now let's substitute g in second equation with g in first equation.

2g + 4h = 90

2(27 - h) + 4h = 90

And solve for h.

54 - 2h + 4h = 90

54 + 2h = 90

2h = 90 - 54

2h = 36

h = 18

Let's substitute the value of h back to first equation to get g.

g = 27 - h

g = 27 - 18

g = 9

Answer:

Step-by-step explanation:

left to right

63 33 28 88 55 120 24 24 2 90

48 28 40 50 72 30 60 99 12 20

18 16 81 9 42 32 62 40 22 66

18 8 60 6 49 108 110 27 121 80

36 35 20 24 44 36 54 96 132 12

56 144 77 30 72 36 70 16 15 14

45 21 25 84 10 100 40 12 120 54

64 30 27 60 24 36 121 10 18 18

The equation that can be determined by the coordinates for point B will be 25 = (x - 6)² + (y - 5)².

The study of geometry using points in space is known as coordinate geometry. This may be used to discover the length between the endpoints, the dividing line's m:n ratio, the line's mid-point, and so on.

Segment AB has point A located at (6, 5). If the distance from A to B is 5 units.

Then the equation that can be determined by the coordinates for point B will be

[tex]\rm 5 = \sqrt{(x-6)^2 +(y-5)^2}[/tex]

This can be written as

25 = (x - 6)² + (y - 5)²

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

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Answer:

C=12

Step-by-step explanation:

The interior angle of a polygon is 360.

So just add them all up.

(3c-29)+(127)+(c+43)+(c+43)+(2c+36)+(c+44)=360

Combine like terms

8c+264=360

Simplify

8c=96 .  Divide both sides by 8

C=12

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

      Find the slope of the line that passes through (10, 7) and (3, 15).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

We can find the slope using the following formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with numbers:-

[tex]\boxed{\frac{15-7}{3-10}}[/tex]

[tex]\bigstar[/tex] On simplification,

[tex]\boxed{\frac{8}{-7}}[/tex]

[tex]\bigstar[/tex] The slope is

[tex]\boxed{-\frac{8}{7}}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

Step-by-step explanation:

The equation is solved by starting with the given equation, then performing inverse operations to undo what is done to the variable.

__

The equation shown is the same as the given equation.

  reason: given

The equation shown has the "-5" term missing. That happens when +5 is added to both sides of the equation. -5 +5 = 0, and 0 added to anything leaves the value unchanged.

  reason: addition property of equality

The equation shown has the "-6" coefficient of 'a' missing. That happens when the equation is multiplied by the multiplicative inverse of -6. That is, it is divided by -6.

  reason: division property of equality

_____

Additional comment

As we have noted in Step 3, division is the same as multiplication by the multiplicative inverse. The definition of multiplicative inverse tells you that the product of a number and its inverse is 1. The identity element property for multiplication tells you that multiplying by 1 leaves the value unchanged.

  (1/(-6))(-6a) = 1a = a

So, the reason for Step 3 could also be "multiplication property of equality."

Answer:

400 centimeters

Step-by-step explanation:

hope this helps. have a nice day

Answer:

[tex]-2\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\textsf{Given expression}: \quad(\sqrt{3}+1)(\sqrt{3}-3)[/tex]

[tex]\textsf{Use the FOIL method to expand}\quad(a+b)(c-d)=ac-ad+bc-bd:[/tex]

[tex]=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}+1(-3)[/tex]

[tex]=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}-3[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{a}=a:[/tex]

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

[tex]\textsf{Collect like terms}:[/tex]

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

[tex]\textsf{Combine like terms}:[/tex]

[tex]=0-2\sqrt{3}[/tex]

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

Answer:

X = 10.09

Step-by-step explanation:

Answer:

(-1 , -5)

Hope this helped you! I would appreciate a Brainliest, if you wouldnt mind!

The percent of change in the number of points she scored between the first and second tests  = 4.878 %

If the data is decreasing,

Decrease = Original Number - New Number.

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100.

Given that:

The score of first Math test = 82

The score of second Math test = 78

Changes occurs in marks by=78-82

                                               =-4

So, there is decrease in marks.

We have to find the decrease percentage:

Decrease%= [tex]\frac{change \;in \;value}{Original\; value} *100[/tex]

                   = [tex]\frac{4}{82} *100[/tex]

                   = 0.04878 * 100

                  = 4.878 %

There is 4.88% decrease in Olivia's score.

Learn more about percentage decrease here:

https://brainly.com/question/10168902

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Answer:

Step-by-step explanation:

i hope these help

Answer:

498

Step-by-step explanation:

dI'd the math

The equation that represents the value of collection after 6 years is $420 + 54.6(6).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given data provided by the question,

The worth of the vintage collection = is $420

The price of the collection appreciates per year = by 13%

The price appreciates per year = 420 × 13/100 = $54.6.

So, the equation for n years is,

$420 + $54.6(n)

Where n is the number of years.

$420 + $54.6(6) = $747.6

To know more about the expression:

https://brainly.com/question/14083225

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its true

they are both already right triangles so if both have acute angles that are congruent then the right triangles are similar

if one of the acute angles of a right triangle is congruent to an acute angle of another right triangle then by angle angle Similarity the triangles are similar

Answer:

Exterior angle = sum of opposite interior angles

Step-by-step explanation:

Answer:

Step-by-step explanation:

= -40 + 56i -30i +42i

= 68i - 40