Elizabeth bought a cheese pizza. It was served on a metal tray with a diameter of 22 centimeters. What is the tray's area?

[tex]2tan^2(\theta )+tan(\theta )=0\implies tan(\theta )[2tan(\theta )+1)]=0 \\\\[-0.35em] ~\dotfill\\\\ tan(\theta)=0\implies \theta=tan^{-1}(0)\implies \theta= \begin{cases} 0\\ 360^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 2tan(\theta)+1=0\implies 2tan(\theta)=-1\implies tan(\theta)=-\cfrac{1}{2} \\\\\\ \theta=tan^{-1}\left( -\cfrac{1}{2} \right)\implies \theta \approx \begin{cases} \stackrel{180^o~~ - ~~26.57}{153.43^o}\\ \stackrel{360~~ - ~~26.57}{333.43^o} \end{cases}[/tex]

for the second pair of angles, the angle of reference is really about 26.57°.  Now, the tangent is only negative in two quadrants, the II and IV Quadrants, using the angle of reference, it'd give us those angles.

Make sure your calculator is in Degree mode.

The seattle great wheel is an illustration of sectors, arcs, circumference and area of circles

The diameter is given as:

d = 175 feet

The circumference (C) is calculated as:

C = πd

This gives

C = 3.14 * 175

C = 549.5 feet

Hence, the circumference of the wheel is 549.5 feet

This is calculated as:

A = π(d/2)^2

This gives

A = 3.14 * (175/2)^2

A = 24040.625

Hence, the area of the wheel is 24040.625 square feet

This is calculated as:

θ = 360/n

Where n is the number of capsules

So, we have:

θ = 360/42

This gives

θ = 8.57 degrees

Hence, the central angle of the wheel in degrees is 8.57

This is calculated as:

Radians = Degrees × π/180

So, we have:

θ = 360/42 * π/180

This gives

θ = π/21 rad

Hence, the central angle of the wheel in radians is π/21 rad

This is calculated as:

L = θ * d/2

So, we have:

L = π/21 * 175/2

This gives

L = 175π/42

Hence, the arc length between two capsules is 175π/42

This is calculated as:

A = 0.5 * (d/2)^2 * θ

So, we have:

A = 0.5 * (175/2)^2 * π/21

This gives

A = 168π

Hence, the area of sector between two capsules is 168π

Read more about sector areas and arc lengths at:

https://brainly.com/question/4115882

Answer:

[tex]y=x^3-12x^2+48x-58[/tex]

Step-by-step explanation:

Transformation Rules

[tex]f(x+a)=f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a)=f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

Given equation: [tex]y=x^3+6[/tex]

If the graph of the equation is translated 4 units to the right, then we replace [tex]x[/tex] with [tex](x-4)[/tex]:

[tex]\implies y=(x-4)^3+6[/tex]

[tex]\implies y=(x-4)(x-4)(x-4)+6[/tex]

[tex]\implies y=(x-4)(x^2-8x+16)+6[/tex]

[tex]\implies y=x^3-8x^2+16x-4x^2+32x-64+6[/tex]

[tex]\implies y=x^3-12x^2+48x-58[/tex]

Answer:

Step-by-step explanation:

Given

Translating 4 units right

Answer:

(x-3,y+4) is the rule

a. -6, 0 input. This would equal (-6)-3 for x and (0)+4 for y. Answer: -9, 4

b. 3, -4 input. This would equal (3)-4 for x and (-4)+4 for y. Answer: -1, 0

c. The rule is a function because each input only has one output

Answer:

Alicia is writing the program for a video game.  For one part of the game she uses the rule (x, y) → (x - 3,y + 4) to move points on the screen.

(a)  What output does the rule give when the input is (-6, 0)?
Show your work.

(b)  What output does the rule give when the input is (3, -4)?
Show your work.

(c)  Is the rule a function? Explain why it is or why it is not.

(a)  Input (-6, 0) → Output (-6 - 3, 0 + 4) = (-9, 4)

(b)  Input (3, -4) → Output (3 - 3, -4 + 4) = (0, 0)

(c)  The rule is a one-to-one function as each value in the range (y-values) corresponds to exactly one value in the domain (x-values).

Answer:

1

Step-by-step explanation:

have you smiled today? its very important:)

Answer:

“I think wolves are scary, too. You’ll have to do more to convince me that they’re not!”

Step-by-step explanation:

Answer:

y = -x + 7

Step-by-step explanation:

Hi there!

We are given the following points:
(5,2) and (10,-3)

We want to find the equation of the line that passes through these 2 points

There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b (m is the slope and b is the y intercept).

First, let's find the slope of the line.

The slope can be calculated from 2 points using the equation [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes.

[tex]x_1=5\\y_1=2\\x_2=10\\y_2=-3[/tex]

Now substitute these values into the formula to find the slope

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

m=[tex]\frac{-3-2}{10-5}[/tex]

Simplify

m=[tex]\frac{-5}{5}[/tex]

Divide

m=-1

The slope of the line is -1

We can substitute this value as m in y=mx+b.

Here's the equation of our line so far:

y=-x+b

Now we need to find b

As the equation passes through the points (5,2) and (10,-3), we can use either point to find the value of b

Taking (5,2) for example:

Substitute 5 as x and 2 as y

2=-5+b

Add 5 to both sides

7=b

Substitute 7 as b in the equation

y = -x + 7

Hope this helps!

See more on this topic here: https://brainly.com/question/27166723

Answer:

1/3 of twelve is 4 so four must be the answer

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

We need the square root of H to equal 7, so we can just square 7 to get the answer. So 7x7 = 49.

Answer:

The stick hits the ground 2.37 seconds after it is dropped.

Step-by-step explanation:

Your function is incorrect.

I will assume that the correct function is

h = -16t² + 90

When the stick hits the ground, its height is 0.

We are looking for the value of t, time, when h = 0.

Set h = 0, and solve for t.

h = -16t² + 90

-16t² + 90 = 0

-16t² = -90

t² = 5.625

t = 2.37

The stick hits the ground 2.37 seconds after it is dropped.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

Cost price for each Orange :

[tex]\qquad \tt \dashrightarrow \: \dfrac{60}{200} [/tex]

[tex]\qquad \tt \dashrightarrow \:0.3 \: \: kobo[/tex]

Now, Cost price for 8 oranges :

[tex]\qquad \tt \dashrightarrow \:0.3 \times 8[/tex]

[tex]\qquad \tt \dashrightarrow \:2.4 \: \: kobo[/tex]

And we have been given that selling price for 8 oranges is 12 kobo.

Therefore, the gain is :

[tex]\qquad \tt \dashrightarrow \:12 - 2.4[/tex]

[tex]\qquad \tt \dashrightarrow \:9.6 \: \: kobo[/tex]

Percentage gain is ~

[tex]\qquad \tt \dashrightarrow \: \dfrac{9.6}{2.4} \times 100[/tex]

[tex]\qquad \tt \dashrightarrow \:4 \times 100[/tex]

[tex]\qquad \tt \dashrightarrow \:400 \: \%[/tex]

Answer:

70

Step-by-step explanation:

Same side interior angles of parallel lines cut by a transversal are supplementary, so their measures have a sum of 180°.

2x - 5 + 45 = 180

2x + 40 = 180

2x = 140

x = 70

Answer:

$308

Step-by-step explanation:

Hope this helped! :)

If this is wrong please comment below! :)

Thx!

Answer:

[tex]\sf \boxed{\bold{x = 3}}[/tex]

Explanation:

subtract both sides by 4x

group similar terms

simplify

divide both sides by -1 or cancel out the negatives

Check:

L.H.S = R.H.S  Thus x = 3 confirmed

Answer:

x = 3

Step-by-step explanation:

We are trying to move all terms that have x on one side of the equal sign and terms that  do not have an x on the other side of equal sign.

terms with x = terms without x

            4x -3 = 3x , subtract 3x from both side of the equation

      4x -3x -3 = 3x -3x

      4x -3x -3 = 0 , add 3 to both sides of the equation

4x -3x -3 + 3 = 0 + 3

          4x -3x = 3 , combine like terms

                 x = 3

Or

We can think we move each term where we want it, yet keep in mind that once we cross the equal sign we change the sign of the term if addition or subtraction are the only operations involved.

4x -3 = 3x , 3x is positive so will become negative on the other side of the equal sign and -3 is negative so will become positive on the other side.

4x -3x = 3

        x = 3

Answer:

D. (1, 1), (2, 2), (3, 3), (4,4), (5,5)

Hope this helps!

Answer:

B

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .

Answer:

B. [tex]-\frac{1}{5} x+\frac{4}{5}[/tex]

Step-by-step explanation:

1. Rewrite the function as a linear equation:

y = -5x - 4

2. Swap x and y:

x = -5y - 4

3. Solve for y:

x+4 = -5y - 4+4

x + 4/-5 = -5y/-5

[tex]\frac{x+4}{-5}[/tex] = y  can be rewritten as [tex]-\frac{1}{5} x+\frac{4}{5}[/tex]

4. Write in inverse notation:

f(x) = [tex]-\frac{1}{5} x+\frac{4}{5}[/tex]

Therefore, B is the answer.

Answer:

(x+2)/(x−3)

Step-by-step explanation:

((x-2)/(x+3))+((10x)/(x+3)(x-3))

((x-2)(x-3)+10x)/(x+3)(x+3)

Brainliest if you can please

Step-by-step explanation:

Take the natural logarithm of both sides;

8x+9 = ln (14)

Transposition;

8x= ln(14)-ln(e⁹)

[tex]x = \frac{ ln(14) - ln( {e}^{9} ) }{8} [/tex]

[tex]x = \frac{1}{8} ( ln(14) - 9)[/tex]

Answer:

117.29 cubic feet

Step-by-step explanation:

* means multiplied by

V=π*r^2*(h/3)

V=π*4^2*(7/3)

V=3.14*16*(7/3)

V≈117.29

Answer:23.6ft

Step-by-step explanation:

SOHCAHTOA

sin(80)=(o/24)

Multiply both sides by 24 and 24 on the right side will cancel out.

24sin(80)=23.6ft

The height of the wall where the ladder reaches will be 23.64 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.

The height of the wall where the ladder reaches is given as,

sin 80° = h / 24

h = 24 x sin80°

h = 23.64 feet

The height of the wall where the ladder reaches will be 23.64 feet.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ2

Answer:

10.38

Step-by-step explanation:

Answer:

3(3r - 4)(3r + 4)

Step-by-step explanation:

I can't see the writing very clearly.

This is the correct solution:

27r^2 - 48                   Divide through by 3:

= 3(9r^2 - 16)               9r^2- 16 is the difference of 2 squares so:

= 3(3r - 4)(3r + 4)

Answer:

970,060

Step-by-step explanation:

i think this is correct-

Edit: i just realised the number was 907,060 ._.

976

Step-by-step explanation:

Answer:

Pauline made $8 per hour last week.

Step-by-step explanation:

$280÷35=$8

Answer:

Yes

Step-by-step explanation:

There are two green regions and two red regions which makes four regions in total. If there is an equal probability to land on each region, it means that the probability to land on a green region is 2/4 because there are two green regions out of the four total regions. You could also simplify it to 1/2.

Answer:

25 one degree turns

Step-by-step explanation:

if one degree is one degree than 25 degrees are 25 one degree turns since 25 divided by 1 equals 25

Answer:

25

Step-by-step explanation:

If x is in quadrant I, then both sin(x) and cos(x) are positive. The angle x/2 also belongs to quadrant I, and hence each of sin(x/2), cos(x/2), and tan(x/2) are positive.

Recall that for all x,

cos²(x) + sin²(x) = 1

and multiplying through both sides by 1/cos²(x) = sec²(x) gives another flavor of this identity,

1 + tan²(x) = sec²(x)

It follows that

sec(x) = √(1 + tan²(x)) = √937/19

which immediately gives us

cos(x) = 19/√937

and from the identity above we find

sin(x) = √(1 - cos²(x)) = 24/√937

Recall the half angle identity for cos :

cos²(x) = (1 + cos(2x))/2

which means

cos(x/2) = + √[(1 + cos(x))/2] = √[1/2 + 19/(2√937)]

Then

sin(x/2) = + √(1 - cos²(x/2)) = √[1/2 - 19/(2 √937)]

and by definition of tan,

tan(x/2) = sin(x/2) / cos(x/2) = 1/12 √[649/2 - 19 √937/2]

Just to be clear, the solutions are

[tex]\cos\left(\dfrac x2\right) = \sqrt{\dfrac12 + \dfrac{19}{2\sqrt{937}}}[/tex]

[tex]\sin\left(\dfrac x2\right) = \sqrt{\dfrac12 - \dfrac{19}{2\sqrt{937}}}[/tex]

[tex]\tan\left(\dfrac x2\right) = \dfrac1{12} \sqrt{\dfrac{649 - 19\sqrt{937}}2}[/tex]