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The exact value of the cotangent of theta in simplest radical form is -21/20.

What is the simplest radical form?

The simplest radical form is the expression of a radical without any factors inside the radical that can be further simplified.

To find the exact value of cotangent of theta, we need to find the values of cosine and sine of theta first.

Given that the terminal side of the angle passes through the point (21,-20), we can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the angle and the x and y-axes:

[tex]h = \sqrt{(21^2 + (-20)^2)} = \sqrt{(841 + 400)} = \sqrt{(1241)}[/tex]

Then, we can find the values of cosine and sine of theta using the x and y-coordinates of the point:

cos(theta) = adjacent/hypotenuse = 21/sqrt(1241)

sin(theta) = opposite/hypotenuse = -20/sqrt(1241)

Now we can find the value of cotangent of theta:

cot(theta) = cos(theta) / sin(theta) = (21/sqrt(1241)) / (-20/sqrt(1241))

= -21/20

Therefore, the exact value of the cotangent of theta in simplest radical form is -21/20.

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Answer:

x=6

Step-by-step explanation:

(1/3x+2=4)x3

x+6=12

x=12-6

x=6

Answer: 6

Step-by-step explanation:

1/3x + 2 = 4

1/3x = 2 (subtracted 2 from both sides to get rid of the 2)

x = 6 (multiplied both sides by 3 to get rid of the coefficient)

Answer:

D. 22  2/3

Step-by-step explanation:

To find area you multiply length times width.

Here:

L = 5 2/3

and W = 4

So multiply 5 2/3 by 4, you get 22 2/3

Good luck! Please mark brainliest!

Answer:

b=45

Step-by-step explanation:

The two angles form a right angle. This is shown through the box drawn at the angle's vertex; this represents that it is a right angle. A right angle is equal to 90 degrees b can be found by using the other angle. Since 45 and b are complementary angles 45+b=90. This means that b must equal 45 degrees.

Answer:

12-9 i think

Step-by-step explanation:

Because it says the difference if a number y and 9. If y equals 12 then shouldn't it be 12-9?

Answer:

1/100

Step-by-step explanation:

Hope it helps

Please brainliest

Answer:

p≤11

that's all i got from the delta math thing

Answer:

In basicallity if a question such as this pops up, the correct way to go would first be to graph this. y=x-4 would be equivalent to x=4.

My paper work is below:

y = x - 4

0 = x - 4

-x = -4

x = 4

Hope this helped..

Answer:

(x - 8)^2 + (y + 6)^2 = 4.

Step-by-step explanation:

The general equation is:

(x - a)^2 + (y - b)^2 = r^2.

Plugging in the given values:

(x - 8)^2 + (y - (-6))^2 = 2^2

(x - 8)^2 + (y + 6)^2 = 4.

Answer:

2

Step-by-step explanation:

the slope of the given line is 2

parallel lines have the same slope so the answer is 2

Answer/Step-by-step explanation:

1. B = 180 - (90 + 58) (sum of triangles)

B = 32°

Let's find a and b using trigonometric ratios:

Reference angle = 58°

Opposite = a = ?

Hypotenuse = c = 27

Adjacent = b = ?

✔️To find a, apply SOH:

Sin 58 = Opp/Hyp

Sin 58 = a/27

a = 27*Sin 58

a = 22.8972986 ≈ 22.9 (nearest tenth)

✔️To find b, apply CAH:

Cos 58 = Adj/Hyp

Cos 58 = b/27

b = 27*Cos58

b = 14.3 (nearest tenth)

2. B = 180 - (90 + 63) (sum of triangles)

B = 27°

Let's find a and b using trigonometric ratios:

Reference angle = 63°

Opposite = a = 11

Hypotenuse = c = ?

Adjacent = b = ?

✔️To find b, apply TOA:

Tan 63 = Opp/Adj

Tan 63 = 11/b

b = 11/Tan 63

b = 5.6 (nearest tenth)

✔️To find c, apply SOH:

Sin 63 = Opp/Hyp

Sin 63 = 11/c

c = 11/Sin 63

c = 12.3 (nearest tenth)

Answer:

ok

Step-by-step explanation:

Answer:

See Below.

Step-by-step explanation:

We are given that:

[tex]EL\cong KP[/tex]

And we want to prove that:

[tex]KE\cong LP[/tex]

Congruent chords have congruent arcs. Therefore:

[tex]\stackrel{\frown}{EL}\, \cong \, \stackrel{\frown}{KP}[/tex]

Arc EL is the sum of Arcs LP and PE:

[tex]\stackrel{\frown}{EL}\,=\, \stackrel{\frown}{LP}+\stackrel{\frown}{PE}[/tex]

Likewise, Arc KP is the sum of Arcs KE and PE:

[tex]\stackrel{\frown}{KP}\, =\, \stackrel{\frown}{KE}+\stackrel{\frown}{PE}[/tex]

Since Arcs EL and KP are congruent:

[tex]\stackrel{\frown}{LP}+\stackrel{\frown}{PE}\, =\, \stackrel{\frown}{KE}+\stackrel{\frown}{PE}[/tex]

Subtraction Property of Equality:

[tex]\stackrel{\frown}{LP} \, \cong\, \stackrel{\frown}{KE}[/tex]

Congruent arcs have congruent chords. Therefore:

[tex]LP\cong KE[/tex]

Answer:

2004

Step-by-step explanation:

if it was 2005 theyd be 15

Answer:

30-25%=22.5

Step-by-step explanation:

Answer:

22.5

Step-by-step explanation:

25% of 30=7.5

30-7.5=22.5

Answer:

6. a

------

7. b

------

8. d

------

9. d

------

Answer:

x = 9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + x² = (9[tex]\sqrt{2}[/tex] )²

2x² = 162 ( divide both sides by 2 )

x² = 81 ( take the square root of both sides )

x = [tex]\sqrt{81}[/tex] = 9

Answer:

94.20 yds

Step-by-step explanation:

C = 2 pi r

     2 pi (15) = 94.20 yds

Answer:

The left side

−

16

does not equal to the right side

−

7

, which means that the given statement is false.

False

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

9+6-31=-7 -16=-7

Answer: 4

Step-by-step explanation:

First we need to find the difference of the balance.

it was -80 then it became -44. The difference is 36.

Next we divide 36 by 9 from the 9 parents.

The answer is 4

Answer:

It would be an equal chance

Step-by-step explanation:

Answer:

[tex]5x \: + \: 13x \: = 180[/tex]

Answer:

4 & 8

Step-by-step explanation: hope this helps :)

Answer: the distance from x axis is 4

Step-by-step explanation:

the y coordinate is 2 the x axis is on the bottom and 2 units for each number so 4 units

Answer:

Since e on the y-axis is 2, e on the x-axis would be 2 if you look at its distance from the x-axis because you have to look at the intersect

Step-by-step explanation:

Answer:

0.08333333333

hope this answer helps you!

Answer:

1/12

Step-by-step explanation:

Using a calculator and rounding the result (quotient) off, we get:

64/768 = 0.083333...  (approximately) or 1/12 (exact quotient)

Answer:

Events A and B are dependent

Step-by-step explanation:

If A and B are two events such as A and B are dependent then

P(A∩B)  P(A) P(B)

An event A will occur with probability 0.4 that is  

An event B will occur with probability 0.6 that is  

The probability that both A and B will occur is 0.20 that is P(A∩B) = 0.20

Therefore,

P(A∩B)  P(A) P(B)

So,

events A and B are dependent

Answer:

D

Step-by-step explanation:

Option A:

(3)¹ × (3)⁻¹⁰   =  (3)⁽¹⁻¹⁰⁾   = 3⁹

=

=

Option B :

(3)⁻¹ × (3) ¹⁰   = 3⁽¹⁰⁻¹⁾

= 3⁹

= 19683

Option C :

(3⁻⁴) × (3)⁷   = 3⁽⁷⁻⁴⁾

              = 3³

Option D :

3⁴ × 3⁻⁷ = 3⁴⁻⁷

= 3⁻³

=  

=

Therefore, option D is the answer.