what is the area of the shaded area​

Answer:

Second Option and Fourth Option

Step-by-step explanation:

[tex]cot ^ 2(\theta) cos(2\theta)[/tex]

We know that:

[tex]cot(\theta) = \frac{1}{tan(\theta)}[/tex]

Then:

[tex]cot^2(\theta)cos(2\theta) = cos(2\theta)\frac{1}{tan^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =\frac{cos(2\theta)}{tan^2(\theta)}[/tex]

Also:

For the sum of angles identity:

[tex]cos(2\theta) = cos(\theta + \theta)\\\\cos(\theta + \theta) = cos(\theta)cos(\theta) - sin(\theta)sin(\theta)\\\\cos(2\theta) = cos^2(\theta) - sin^2(\theta)\\\\cos(2\theta) = (1-sin^2(\theta)) - sin^2(\theta)\\\\cos(2\theta) = 1-2sin^2(\theta)[/tex]

Then:

[tex]cot^2(\theta)cos(2\theta) = \frac{cos^2(\theta)}{sin^2(\theta)}[1-2sin^2(\theta)]\\\\cot^2(\theta)cos(2\theta) = \frac{cos^2(\theta)[1-2sin^2(\theta)]}{sin^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =cot^2(\theta) - 2\frac{cos^2(\theta)[sin^2(\theta)]}{sin^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =cot^2(\theta) - 2cos^2(\theta)[/tex]

Answer:

17) Length of arc QPT = 20.9 inches

18) Length of arc QR = 12.6 feet

19) Length of arc PQR = 39.3 meters

20) x = 161°

21) x = 123°

22) x = 24 units

23) EB = 4 units

24) EB = 14 units

Step-by-step explanation:

∵ The length of any arc = Ф/360 × 2πr

   where Ф is the central angle subtended by this arc

17) ∵ m∠RZQ = 60° ⇒ central angle

∵ m∠QZP = 90° ⇒ centeral angle

∵ m∠RZT = 180° ⇒ Z ∈ TR

∴ m∠TZP = 180 - 90 - 60 = 30°

∴ m∠QZT = 90 + 30 = 120° ⇒ central angle

∵ ∠QZT subtended by arc QPT

∵ m∠QZT = 120 , r = 10 inches

∴ Length arc QPT = 120/360 × 2π × 10 = 20.9 inches

18) ∵ m∠QZR = 60° ⇒ central angle subtended by arc QR

∵ r = 12 feet

∴ The length of arc QR = 60/360 × 2π × 12 = 12.6 feet

19) ∵ m∠PZR = 60° + 90° = 150°⇒ central angle subtended

     by arc PQR

∵ r = 15 meters

∴ The length of arc PQR = 150/360 × 2π × 15 = 39.3 meters

20) ∵ SU = ST

∴ Measure of arc SU = measure of arc ST

∵ The measure of the circle is 360°

∵ Measure of arc UT = 38°

∴ x = (360 - 38) ÷ 2 = 161°

21) ∵ AB = AC

∴ Measure of arc AB = measure of arc AC

∵ The measure of the circle is 360°

∵ Measure of arc BC = 114°

∴ x = (360 - 114) ÷ 2 = 123°

22) ∵ The two arcs are equal

∴ Their chords are equal in length

∴ 2x - 12 = 36 ⇒ 2x = 36 + 12 ⇒ 2x = 48

∴ x = 24

23) In circle A

∵ AB is a radius and CD is a chord

∵ AB ⊥ CD

∴ AB bisects CD at point E

∵ AB = 20 , CD = 24

∴ CE = 24/2 = 12

In ΔAEC

∵ m∠ AEC = 90

∵ AC = 20 ⇒ radius

∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem

∴ AE = √(20² - 12²) = 16

∵ AB = 20 ⇒ radius

∴ EB = 20 - 16 = 4

24) In circle A

∵ AB is a radius and CD is a chord

∵ AB ⊥ CD

∴ AB bisects CD at point E

∵ AB = 35 , CD = 56

∴ CE = 56/2 = 28

In ΔAEC

∵ m∠ AEC = 90

∵ AC = 35 ⇒ radius

∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem

∴ AE = √(35² - 28²) = 21

∵ AB = 35 ⇒ radius

∴ EB = 35 - 21 = 14

QUESTION 1a.

We want to add

[tex]( - 2 {x}^{2} - 4x + 13) + (12 {x}^{2} + 2x - 25)[/tex]

We group similar terms to get

[tex]- 2 {x}^{2} + 12 {x}^{2}- 4x + 2x - 25 + 13[/tex]

Simplify:

[tex]- 10{x}^{2} - 2x -12[/tex]

QUESTION 1b.

The given function is:

[tex](7x^2+4x-26)-(-7x^2-3x+15)[/tex]

Expand the parenthesis to obtain,

[tex]7x^2+4x-26 + 7x^2 + 3x - 15[/tex]

Group similar terms,

[tex]7x^2+7 {x}^{2} + 4x + 3x-26 - 15[/tex]

Simplify:

[tex]14{x}^{2} + 7x-41[/tex]

QUESTION 2

The given function is

[tex]f(n)=n^2-6n-16[/tex]

The zeros of this function is given by;

[tex]n^2-6n-16 = 0[/tex]

Split the middle term.

[tex]n^2-8n + 2n-16 = 0[/tex]

Factor;

[tex]n(n - 8) + 2(n - 8) = 0[/tex]

[tex](n - 8)(n + 2) = 0[/tex]

[tex]n - 8 = 0 \: or \: n + 2 = 0[/tex]

[tex]n = 8 \: or \: n = - 2[/tex]

412 pounds for him + 1 pound for his friend = 413 total pounds x $0.80 per pound = $330.40

Sorry, I don’t see this as an answer choice.

Answer:

I am assuming you meant to say '4' instead of '412'. In which case the answer is A.

Step-by-step explanation:

4 + 1 x .80 is 4.00 even. Good luck in your endeavors!

Answer:

The answer I would choose is C

Hope this helped :)

Answer:

B

Step-by-step explanation:

Multiplying f(x) by g(x)

= (2x² + x - 3)(x + 2)

Each term in the first factor is multiplied by each term in the second factor, that is

x(2x² + x - 3) + 2(2x² + x - 3) ← distribute both parenthesis

= 2x³ + x² - 3x + 4x² + 2x - 6 ← collect like terms

= 2x³ + 5x² - x - 6 → B

The total for liking and not liking painting is 51.

28 like painting, so to find the missing number subtract 28 from 51.

The missing number is 23

The missing number in the table is 23, option B is correct.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The given table is below

Like Dance                    28       ?            51

Do Not Like Dance       17         18         35

Total                               45        41         86

We have to find the number of people who like dance when 18 donot like dance and total is 41.

We calculate this by removing 18 from 41 which gives the missing number x

x=41-18

=23

Hence,  the missing number in the table is 23, option B is correct.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ3

Answer:

25.4 units

54.4 units

Step-by-step explanation:

Given that,

length of each side of rhombus = 30 units

interior angle = 25 x 2

                      = 50°

other interior angle = (360-(50x2)) / 2 = 130°

Formula to use

c² = a² + b² - ab cosC

First diagonal

√(30² + 30² - 2*30*30*cos 50)

= 25.35 u

Second diagonal

√(30² +30² - (2*30*30*(cos 130)))

= √(1800-1800cos130)

= 54.37 units

Answer:

909 mm

Step-by-step explanation:

There are 10 mm in a cm

90 x 10 = 900

900 + 9 = 909 mm

(Unless you're asking if this is true/false; if so, it is true)

Answer:

(x - 1)² + (y + 1/2)² = 65/4

Step-by-step explanation:

Given:  the endpoints of the diameter are (3, 3) and (-1, -4).  a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:

      3 - 1

x = -----------

          2

and

         -1

y = ----------

          2

The center is at x = 1 and y = -1/2:  (1, -1/2).

b) The radius is half the diameter.  The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):

diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,

radius = (1/2)√65.

square of the radius = r² = 65/4

The general equation of a circle with center at (h, k) and radius r is

(x - h)² + (y - k)² = r².  In this case, the equation is:

(x - 1)² + (y + 1/2)² = 65/4

Answer:

the correct answer is -9

Step-by-step explanation:

7 because subtract 25 from 250 the divide 225 by 30 to get 7.5 so he can only use 7 square yards

2,3,5,11,13,23,25,31,35,41,43,53,55,61,65,71,73,83,85,91,95

Answer:

Step-by-step explanation:

Prime numbers are neat.

Here they are:

2,3,5,11,13,23,25,31,35,41,43,53,55,61,65,71,73,83,85,91,95

Best,

jrodt

Final answer:

After substituting the x and y values of the point (3,-1) into the circle's equation, it is determined that (3,-1) does not lie on the circle since the equation does not hold true.

Explanation:

To determine if the point (3,-1) lies on the circle given by the equation [tex](x+1)^2 + (y-1)^2[/tex]=16, we must substitute the x and y values of the point into the equation and see if the equation holds true.

Let's plug in x = 3 and y = -1:

[tex](3+1)^2 + (-1-1)^2[/tex]= 16

[tex](4)^2 + (-2)^2[/tex] = 16

16 + 4 = 20

Since 16 + 4 does not equal 16, the point (3, -1) does not lie on the circle