What is the value of tan theta in the unit circle below? A.1/2 B.sqrt3/3. C.sqrt3/2. D.sqrt3

B) 50+36×=$212 ; 4.5. That is the answer.

The equation symbolizes the above situation is $50 + $36x = $212 and the landscapers work at 4.5 hours

Let's use "x" to represent the number of hours The Garden Expert worked in Emma's yard. We know that the landscaper charges $36 per hour for the actual work and a $50 consultation fee. Therefore, the total cost "C" for the service can be represented as:

C = 36x + 50

Emma owes the landscaper $212, so we can set up the equation as follows:

212 = 36x + 50

Now, let's solve for "x":

First, subtract $50 from both sides to isolate 36x:

212 - 50 = 36x

162 = 36x

Next, divide both sides by 36 to solve for x:

x = 162 / 36

x = 4.5

Hence the correct option is (b).

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Answer:

A

Step-by-step explanation:

Multiply them according to the problem.

[tex]6x+2y=6 \\ \\ -3(6x+2y)=(6)*-3 \\ \\ -18x-6y=-18 \\ \\ \\ 7x+3y=9 \\ \\ 2(7x+3y)=(9)*2 \\ \\ 14x+6y=18[/tex]

As you can see, the only terms in the two equations that can cancel out are [tex]-6y[/tex] and [tex]6y[/tex].

Answer:

D

Step-by-step explanation:

1.  Replace "f(x)" with "y:"  y = (x + 1)/x

2.  Interchange x and y:  x = (y + 1)/y

3.  Solve this result for y:                                     1

     xy = y + 1, or xy - y = 1, or y(x -1) = 1, or y = --------

                                                                            x-1

4.  Replace "y" with:

        -1               x

      f     (x) = -----------   This matches answer choice D.

                       x - 1

Answer:

D

Step-by-step explanation:

ANSWER

[tex]\tan(\sin^{ - 1}( \frac{x}{2} )) = \frac{x}{ \sqrt{4 - {x}^{2} } } \: \:where \: \: x \ne \pm2[/tex]

EXPLANATION

We want to find the exact value of

[tex] \tan( \sin^{ - 1}( \frac{x}{2} ) ) [/tex]

Let

[tex]y = \sin^{ - 1}( \frac{x}{2} )[/tex]

This implies that

[tex] \sin(y) = \frac{x}{2} [/tex]

This implies that,

The opposite is x units and the hypotenuse is 2 units.

The adjacent side is found using Pythagoras Theorem.

[tex] {a}^{2} + {x}^{2} = {2}^{2} [/tex]

[tex]{a}^{2} + {x}^{2} = 4[/tex]

[tex]{a}^{2} = 4 - {x}^{2}[/tex]

[tex]a= \sqrt{4 - {x}^{2}} [/tex]

This implies that,

[tex] \tan(y) = \frac{opposite}{adjacent} [/tex]

[tex]\tan(y) = \frac{x}{ \sqrt{4 - {x}^{2} } } [/tex]

But

[tex]y = \sin^{ - 1}( \frac{x}{2} )[/tex]

This implies that,

[tex]\tan(\sin^{ - 1}( \frac{x}{2} )) = \frac{x}{ \sqrt{4 - {x}^{2} } } \: \:where \: \: x \ne \pm2[/tex]

The answer is:

[tex]f'(2)=-1[/tex]

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

[tex]f(x)=\frac{4}{x}[/tex]

It's a quotient, so, we need to use the following formula to derivate it:

[tex]f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }[/tex]

Then, of the given function we have that:

[tex]u=4\\v=x[/tex]

So, derivating we have:

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]

Hence,

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]

Now, evaluating with x equal to 2, we have:

[tex]f'(2)=\frac{-4}{(2)^{2} }[/tex]

[tex]f'(2)=\frac{-4}{4}[/tex]

[tex]f'(2)=-1[/tex]

Therefore, the answer is:

[tex]f'(2)=-1[/tex]

Have a nice day!

ANSWER

[tex]f'(2) = -1[/tex]

EXPLANATION

The given function is

[tex]f(x) = \frac{4}{x} [/tex]

Recall that:

[tex] \frac{c}{ {a}^{ m} } = c {a}^{ - m} [/tex]

We rewrite the given function using this rule to obtain,

[tex]f(x) = 4 {x}^{ - 1} [/tex]

Recall again that,

If

[tex]f(x)= a {x}^{n} [/tex]

then

[tex]f'(x)=n a {x}^{n - 1} [/tex]

We differentiate using the power rule to obtain,

[tex]f'(x) = - 1 \times 4 {x}^{ - 1 - 1} [/tex]

[tex]f'(x) = - 4 {x}^{ - 2} [/tex]

We rewrite as positive index to obtain,

[tex]f'(x) = - \frac{4}{ {x}^{2} } [/tex]

We plug in x=2 to obtain,

[tex]f'(2) = - \frac{4}{ { (2)}^{2} } = - \frac{4}{4} = - 1[/tex]

ANSWER

[tex]\frac{9x - 2}{3x + 5} [/tex]

EXPLANATION

We want to find the difference;

[tex] \frac{9x}{3x + 5} - \frac{2}{3x { + 5}} [/tex]

This are like fractions or equivalent fractions.

We keep one of the denominators and subtract the numerators.

The difference is:

[tex]\frac{9x - 2}{3x + 5} [/tex]

Note that, we cannot simplify this further.

So we live the difference as it is.

Answer:

The correct answer is,

(9x - 2)/(3x + 5)

Step-by-step explanation:

It is given two expression with variable x

9x/(3x + 5) and 2/(3x + 5)

To find the difference

Here the denominators of two expression are same, so we can write,

9x/(3x + 5) - 2/(3x + 5) = (9x - 2)/(3x + 5)

Therefore the correct answer is

(9x - 2)/(3x + 5)

In quadrant II, if sinΘ = 1/2, the value of cosΘ is -√(3/4).

In quadrant II, sine is positive and cosine is negative. Since sinΘ = 1/2, we can use the Pythagorean identity to find the value of cosΘ:

sin²Θ + cos²Θ = 1

Plugging in the value of sinΘ and solving for cosΘ, we get:

(1/2)² + cos²Θ = 1

1/4 + cos²Θ = 1

cos²Θ = 3/4

Taking the square root, we get:

cosΘ = ±√(3/4)

Since Θ lies in quadrant II where cosine is negative, the value of cosΘ is:

cosΘ = -√(3/4)

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Arc GHE is 40 + 80 or 120 so arc GFE is 360 (total measurement in a circle) - 120 which is 240. The circumference of a circle is 2*pi*r so in this case it will be 2*pi*5 or 10pi (you can also write it as approximately 31.4). The area of a circle is pi*r² so it'll be pi*5² or 25pi (you can write it as approximately 78.5 also). The equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius. Input your values. The equation of this circle is (x+1)² + (y-2)² = 6² (The radis is 6 because the diameter is 12)

I hope this helps!

A full circle is 360 degrees.

You are given the angles for GH, HE and FE, subtract those from 360 to find the angle for FG:

360 - 110 - 80 - 40 = 130 degrees.

Now for the arc GFE add FG and FE:

Arc GFE = 130 + 110 = 240 degrees.

Circumference = 2 x PI x r

Using 3.14 for PI:

Circumference  = 2 x 3.14 x 5 = 31.4 mm or 10PI

Area = PI x r^2 = 3.14 x 25 = 78.5 mm^2 or 25PI mm^2

Equation of a circle with center at (-1,2) and diameter of 12:

The equation is written as (x-x1)^2 + (y-y1)^2 = r^2

x1 and y1 are the values of the center (-1,2) and r is the radius, which would be half the diameter.

The equation is: (x+1)^2 + (y-2)^2 = 36

Please ignore the x above,,

Answer: 30%

Step-by-step explanation:

Given: the number of employees in the office = 80

The number of employees are managers = 24

Then, the percent of employees are manger is given by :-

[tex]\dfrac{\text{Number of mangers}}{\text{Total employees}}\times100\\\\=\dfrac{24}{80}\times100\\\\=30\%[/tex]

Hence, the percent of the employees are managers = 30%

Answer:

  35.9 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

  tan(U) = VW/WU

  tan(65°) = (77 ft)/WU

  WU = 77 ft/tan(65°) ≈ 35.9 ft

Answer:

It is parallel

Step-by-step explanation:

See the first equation equals the last equation, I just realized that.

Answer:

1,048,576

Step-by-step explanation:

We can tell that this is a geometric sequence because each new term is a multiple of the previous term.  The common ratio is -2.

The pertinent formula is a(n) = -2 · (-2)^(n-1).

Thus, the 20th term of this sequence is a(20) = -2 · (-2)^(20-1), or

a(20) = -2 · (-2)^19, or 2^20, which comes out to 1,048,576 (same as the fourth possible answer).

Answer:

The answer is perfect square.

Step-by-step explanation:

A number whose square roots are integers or quotients of integers - perfect square.

The square of a number is a number multiplied by itself. Like 2 x 2 , 5 x 5 etc.

The perfect squares are the squares of the whole numbers like : 1, 4, 9, 16, 25, 36,  and so on.

(x-3)(x+3) this is the answer

Answer:

(x + 3)(x - 3)

Step-by-step explanation:

x² - 9 ← is a difference of squares and factors as

x² - 9 = (x + 3)(x - 3)

Answer:

the answer is $50 for the full price of the sweater

Step-by-step explanation:

if you know $20 is 40% what is 20% it is $10 and then multiple it by 5 because  20 times 5 is 100 and you get 50

Answer:

$50

Step-by-step explanation:

Sale on sweater = 40% .

Money saved = $20 .

Let original price be x then ,

=> 40% of x = $20

=> 40x/100 = $20

=> x = $20 *100/40

=> x = $ 50

Answer:

B

Step-by-step explanation:

In one complete rotation the wheel rotates 360°

Assuming the seats are equally spaced around the wheel then the

angle between each seat = [tex]\frac{360}{15}[/tex] = 24°

The angle measurement between each bucket is 24 degrees if the Ferris wheel has 15 seat buckets option (B) 24° is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

A Ferris wheel has 15 seat buckets.

The total angle of the wheel is 360 degrees, which is a complete revolution of the wheel.

The angle measurement between each bucket is:

= 360/15

= 24 degree

Thus, the angle measurement between each bucket is 24 degrees if the Ferris wheel has 15 seat buckets option (B) 24° is correct.

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Problem

If you deposit $500 into an account paying 12% annual interest compounded yearly , how much money will be in the account after 10 years?

Result

The amount is $1552.92 and the interest is $1052.92.

Problem

If you deposit $500 into an account paying 12% annual interest compounded yearly , how much money will be in the account after 20 years?

Result

The amount is $4823.15 and the interest is $4323.15.

Problem

If you deposit $500 into an account paying 12% annual interest compounded yearly , how much money will be in the account after 30 years?

Result

The amount is $14979.96 and the interest is $14479.96.

Final answer:

The investment grows to $1,555.88 in 10 years, $4,822.49 in 20 years, and $14,974.46 in 30 years.

Explanation:

To calculate the future value of an investment with compound interest, you can use the formula A = P(1 + r/n)[tex]^{(nt)}[/tex], where:

P is the principal amount (the initial amount of money)

r is the annual interest rate (decimal)

n is the number of times that interest is compounded per year

t is the time the money is invested for, in years

For your case, where you invest $500 at 12% compounded annually, this becomes:

A = 500(1 + 0.12/1)[tex]^{(1t)}[/tex]

Calculating for 10, 20, and 30 years:

A = 500(1 + 0.12)¹⁰ = $1,555.88 after 10 years

A = 500(1 + 0.12)²⁰ = $4,822.49 after 20 years

A = 500(1 + 0.12)³⁰ = $14,974.46 after 30 years

Answer: 10 inches per year.

If the snake is now 3 foot 9 inches, we can add up how many inches that is by converting feet to inches. 1 foot=12 inches, so 3 feet is 36 inches. We then add the 9 inches.

36+9= 45

Since the snake had already accomplished being 5 inches at birth, we can subtract 5 from 45.

This gives us 40.

Since the snake was born 4 years ago we divide 40 by 4.

40÷4= 10

Answer:

73.21% annual percentage rate.

Step-by-step explanation:

3 foot 9 inches = 45 inches

45 = 5(1 + r)4

9 = (1 + r)4

91/4 = 1 + r

r = 0.73205

therefore,

r = 73.21%

Answer:

2x+6=24

Step-by-step explanation:

Janeka forgot to divide by 2 to get the radius and then square and multiply by pi.

since the diameter is 20 the radius would be 10. so i the equation you would replace the 20 with 10 bc she but the diameter in instead of the radius which r=radius

the answer is

615500

hope this helps

Simplify the expression using the definition of an imaginary number i = sqrt -1

i32 = 1

i25 = i

i86 = -1

i51 = -i

Answer:

Sample answer for Edmentum

Like and Rate!

Step-by-step explanation:

Answer:

33.6 cm

Step-by-step explanation:

We can use the formula for arc length to solve this.

[tex]s=r\theta[/tex]

Where

s is the arc length

r is the radius

[tex]\theta[/tex] is the angle subtended by the arc (in radians)

The problem gives us theta = 2.8 radians and radius of the circle as 12 cm. We plug these into the formula and figure out the arc length (to 1 decimal place):

[tex]s=r\theta\\s=(12)(2.8)\\s=33.6[/tex]

2nd answer choice is right.

he can either send one half or the other half.

Answer:

70

Step-by-step explanation:

Given : There are 8 people on the debate team.

To Find: In how many ways can the coach choose 4 members to send to competition?

Solution:

We will use combination over here

Formula : [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now There are 8 people on the debate team and the coach have to choose 4

So, n = 8

r = 4

So, number of ways of choosing 4 people out of 8 = [tex]^8C_4[/tex]

                                                                                    = [tex]\frac{8!}{4!(8-4)!}[/tex]  

                                                                                    = [tex]\frac{8!}{4!4!}[/tex]  

                                                                                    = [tex]70[/tex]  

Hence there are 70 ways of choosing 4 members out of 8 to send to competition

Answer:

[tex]\$1,920[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5*12=60\ months\\ P=\$1,200\\r=0.01[/tex]

substitute in the formula above

[tex]A=\$1,200(1+0.01*60)[/tex]

[tex]A=\$1,200(1.6)=\$1,920[/tex]

Answer:  b) 16%

Step-by-step explanation:

The mean is 290 so on a normal bell curve that would be a z-score of 0.

The standard deviation is 10 so 290 - 10 = 280 is a z-score of -1.

A z-score from the left to -1 is 15.9%

Answer:

17.54 ft

Step-by-step explanation:

Moving along the line from (–4.2, –6.4, 4.5) to (7.1, 2.2, 5.8), x increases by 11.3, y by 8.6 and z by 10.3.

Applying the Pythagorean Theorem twice, we get

(length of clothesline) = √( 11.3² + 8.6² + 10.3²), or 17.54 ft.

Answer:

[tex]\sqrt{109}[/tex]

Step-by-step explanation:

The side of the house is a side of the right triangle.

The ladder is 3 feet away, so it forms a triangle with sides 3, 10, x.

We're trying to find the hypotenuse, which is given by Pythagoras' Theorem:

[tex]a^2 + b^2 = c^2\\3^2 + 10^2 = x^2\\109 = x^2\\x = \sqrt{109}[/tex]

Four possible coplanar points based on the image are B,E,D; Q,B,E; D,Q,B; and, E,D,Q.

This word refers to points that share the same plane. Remember a plane is a surface that goes in one direction.

In the image, all points over the surface are coplanar. Based on this, some coplanar points are:

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Answer:

The best describes the transformation is right 3 units, down 1 unit ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ f(x) = x²

- The change from x² to (x - 3)² means the graph shifted 3 units

  to the right

- The value -1 means the graph shifted down 1 unit

∴ The graph of f(x) = x² is shifted 3 units to the right and 1 unit

   down and the resulting function is f(x) = (x - 3)² - 1

* The best describes the transformation is right 3 units, down 1 unit

Answer:

C

Step-by-step explanation: