What is the vertex of the function defined as
g(x) = f(x – 5) + 3?

Answer:

[tex]\displaystyle \tan\frac{5\pi}{12}=2+\sqrt{3}[/tex]

Step-by-step explanation:

Tangent Half Angle

Given an angle θ, then:

[tex]\displaystyle \tan {\frac {\theta }{2}}=\frac {\sin \theta }{1+\cos \theta}[/tex]

We are required to find:

[tex]\tan\frac{5\pi}{12}[/tex]

But it cannot be found in tables of main angles. We can use the angle

[tex]\theta = \frac{5\pi}{6}[/tex]

And use the formula above to find the required operation. Hence:

[tex]\displaystyle \tan\frac{5\pi}{12}=\tan\frac{\frac{5\pi}{6}}{2}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac {\sin \frac{5\pi}{6} }{1+\cos \frac{5\pi}{6}}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac {\frac{1}{2} }{1-\frac{\sqrt{3}}{2}}[/tex]

Operating:

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac {\frac{1}{2} }{\frac{2-\sqrt{3}}{2}}[/tex]

Simplifying:

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{1}{2-\sqrt{3}}[/tex]

Rationalizing:

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{1}{2-\sqrt{3}}\cdot \frac{2+\sqrt{3}}{2+\sqrt{3}}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{2+\sqrt{3}}{2^2-\sqrt{3}^2}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{2+\sqrt{3}}{4-3}[/tex]

Finally:

[tex]\boxed{\displaystyle \tan\frac{5\pi}{12}=2+\sqrt{3}}[/tex]

Answer:

Step-by-step explanation:

Changing to slope-intercept form:

5x + 2y = 12         {subtract 5x from both sides}

2y = -5x + 12         {divide both sides by 2}

y = -⁵/₂ x + 6

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y =-⁵/₂ x + 1    ⇒     m₁ =  -⁵/₂

-⁵/₂× m₂ = -1      ⇒   m₂ = ²/₅

So, any line perpendicular to 5x + 2y = 12 must have slope m =²/₅

The equation of the hyperbola is:

[tex]\frac{x^2}{8} - \frac{y^2}{8} = 1[/tex]

-----------------------------------------

They are both in the x-axis, and the center is (0,0), which means that the equation is:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

-----------------------------------------

Directrices at [tex]x = \pm 2[/tex] means that:

[tex]\frac{a^2}{c} = 2[/tex]

-----------------------------------------

Foci at [tex]x = \pm 4[/tex] means that:

[tex]c^2 = 4^2 = 16 \rightarrow c = 4[/tex]

Thus:

[tex]a^2 = 2c = 2(4) = 8[/tex]

-----------------------------------------

For b, we have that:

[tex]a^2 + b^2 = c^2[/tex]

[tex]8 + b^2 = 16[/tex]

[tex]b^2 = 8[/tex]

-----------------------------------------

Thus, since a and b have been found, the equation of the hyperbola is:

[tex]\frac{x^2}{8} - \frac{y^2}{8} = 1[/tex]

A similar problem is given at https://brainly.com/question/20409089

Step-by-step explanation:

Since all 3 sides of the triangle is equal, it is not only an isosceles, but an equilateral triangle.

x = 8sin60° = 6.928 or sqrt48.

That is a question about triangles.

In my answer I will show 2 ways to solve that question, ok? Let's go.

The line segment x divide the biggest triangle in 2 equals right triangles.

Let's choose one of them and note that is a triangule with hypotenuse equals to 8 and one cathetus equals to half of 8.

The Pythagoras's theorem says that:

[tex]\boxed{a^2 = b^2 + c^2}[/tex]

a is the hypotenuse and b and c are cathetus.

So, in our case, we know the hypotenuse and one cathetus, let's substitute that in the expression:

[tex]a^2 = b^2 + c^2\\8^2 = 4^4 + c^2\\64 = 16 + c^2\\c^2 = 64 - 16\\c^2 = 64 -16\\c^2 = 48\\c = \sqrt{48}\\c= 4\sqrt{3}[/tex]

Therefore, the value of x is [tex]4\sqrt{3}[/tex].

That way to solve the question is a consequence of the previous way.

That triangle has all the sides equals, so it is a equilateral triangle.The line segment x is the height of that triangle. And we can find the equilateral triangle height using that expression:

[tex]\boxed{h = \frac{S\cdot \sqrt{3} }{2} }[/tex]

h is the height and S is the triangle's side.

So, we know that the side of our triangle is 8. Let's change S value in the expression:

[tex]h = \frac{S\cdot \sqrt{3} }{2} \\h = \frac{8\cdot \sqrt{3} }{3} \\h = 4\sqrt{3}[/tex]

Thus, the value of x is [tex]4\sqrt{3}[/tex].

Note that in the 2 ways we find the same result, so that answer is correct.

I hope I've helped. :D

Enjoy your studies! \o/

Answer:

its multipled by 12

Step-by-step explanation:

Answer:

1 ft = 12

Step-by-step explanation:

The length in inches is equal to the feet multiplied by twelve

Answer:

481.5

Step-by-step explanation:

The music art museum is divided into 6 sections

Each section contains the same timert of tiles

There are 2889 tails total

Therefore the number of tiles in each section can be calculated as follows

= 2889/6

= 481.5

Hence there are 481.5 tiles in each section

Answer:

-7 × 10

Step-by-step explanation:

Explanation:

6.3

×

10

5

is the same value as

63

×

10

4

So we have:

63

×

10

4

9

×

10

3

ddd

→

ddd

63

9

×

10

4

10

3

ddddddddd.d

→

ddd

63

9

×

10

If the sum of the digits is exactly divisible by 3 then the actual number is also exactly divisible by 3

→

6

+

3

=

9

so we will divide both top and bottom by 3 to simplify the fraction.

ddddddddd.d

→

ddd

63

÷

3

9

÷

3

×

10

Note that:

63

÷

3

9

÷

3

=

21

÷

3

3

÷

3

=

7

1

=

7

so we have:

(

6.3

×

10

5

)

÷

(

9

×

10

3

)

=

7.0

×

10

Negative version works the same exact way but with a negative sign

The scientific notation of (6.3 × 10⁻⁵) / (9 × 10⁻³) on simplifying is 7 × 10⁻³.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It is also known as the standard form in the UK and scientific form, standard index form, and standard form.

Given:

The expression is (6.3 × 10⁻⁵) / (9 × 10⁻³),

The values in the negative power in the numerator go to the denominator and vice versa,

(6.3 × 10⁻⁵) / (9 × 10⁻³) = (6.3 × 10³) / (9 × 10⁵)

Divide the 6.3 by 9 as shown below,

(6.3 × 10⁻⁵) / (9 × 10⁻³) = 0.7 / 10²

(6.3 × 10⁻⁵) / (9 × 10⁻³) = 0.7 × 10⁻²

(6.3 × 10⁻⁵) / (9 × 10⁻³) = 7 × 10⁻³

To know more about scientific notation:

https://brainly.com/question/18073768

SPJ2

Answer:

140x+36

Step-by-step explanation:

hope this helps :)

Answer:2600

Step-by-step explanation: 25%=1/4

650×4=2600

Answer:

Step-by-step explanation:

if g(x)=3x-8

replace x with -2

g(-2)=3(-2)-8=-6-8=-14

Answer:

[tex]4^{6}[/tex]  

4096

Step-by-step explanation:

i tried

Answer:

[tex]4^{6}[/tex]

Step-by-step explanation:

4 x 4 x 4 x 4 x 4 x 4 it's really just counting how many 4's there are. In this case there are 6 and the number being repeated 6 times is 4 so we only put it as [tex]4^{6}[/tex]. I know I'm late just wanted to answer :'D

Answer:

x = 14[tex]\sqrt{2}[/tex]

y = 14

z= 14[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Notice that the top triangle is a 45-45-90 triangle and the triangle below is a 30-60-90 triangle.

Using the fact that the top triangle is a 45-45-90 triangle and also an isosceles triangle, we can see that x will be the same as its respective leg, 14[tex]\sqrt{2}[/tex]

Now, we must find a side length of the bottom triangle. We can use the Pythagorean Theorem to find the third side of the top triangle, which is also a side of the bottom triangle. We can find that the third side must be 28. We can now use this to find the other sides of the bottom triangle.

Since y is opposite to the 30 degree angle, it is half of the hypotenuse. The hypotenuse which we found earlier is 28, therefore, y is 14. z is then 14[tex]\sqrt{3}[/tex] using either Pythagorean Theorem or special right triangle properties for 30-60-90.

Selling price of a bicycle = 2850

Profit percentage = 14%

We know that :

[tex]\color{plum}\tt{Cost \: \: price = \frac{Selling \: \: price \: \times \: 100}{100 \: \: + \: \: profit \: \%} }[/tex]

Then, the cost price of this bicycle :

[tex] = \tt \frac{2850 \times 100}{100 + 14} [/tex]

[tex] = \tt \frac{285000}{114} [/tex]

[tex] =\color{plum} \tt2500[/tex]

Thus, the cost price of this bicycle = 2500

In another scenario :

Profit percentage = 8%

Cost price of the bicycle = 2500

Then, Selling price will be equal to :

Let x be the selling price of the bicycle.

[tex] = \tt2500 = \frac{\: x \: \times 100}{100 + 8} [/tex]

[tex] = \tt2500 = \frac{100x}{108} [/tex]

[tex] =\tt 100x = 2500 \times 108[/tex]

[tex] = \tt100x = 270000[/tex]

[tex] =\tt x = \frac{270000}{100} [/tex]

[tex] =\color{plum}\tt x = 2700[/tex]

Therefore, the selling price with a profit of 8% will be = 2700

Answer: You do this by dividing the minutes worked by 60. You then have the hours and minutes in numerical form, which you can multiply by the wage rate

Step-by-step explanation:

Answer:

You do this by dividing the minutes worked by 60. You then have the hours and minutes in numerical form, which you can multiply by the wage rate. For example, if your employee works 38 hours and 27 minutes this week, you divide 27 by 60.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:its right

Answer:

70%

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

147/x * 210/100

147*100= 14700

14700/210 = 70

70%

Answer:

x=4

Step-by-step explanation:

x

=

4

or

x

=

−

4

Explanation:

First divide throughout by  

2

to get

x

2

=

16

Now take the square root on both sides to get

x

=

±

4

.

You may now substitute the values of  

x

=

4

and

x

=

−

4

back into the original equation and check that it satisfies the equation which it does.

Answer:

It is all 4

Step-by-step explanation:

Answer:

all 4 , the next one is A

Step-by-step explanation:

Answer:

Here I just did the Workin out. don't worry it's correct. Have a nice day!!

Answer:

1542

Step-by-step explanation:

Answer:

I would say zero or undefined

Step-by-step explanation:

Answer:

c, zero slope

Answer:

k=12

Step-by-step explanation:

k=29-17

29-17=12

Answer:

32 people got off

Step-by-step explanation:

For the 10th stop, we can get the total number of people that have gotten off

Mathematically, this is the product of the mean and the number of stops

= 10 * 6.3 = 63 people

Now, for the 11th stop, the total becomes

11 * 8.6 = 94.6

Hence;

(94.6-63) = 31.6

since there are no fractional humans, the number of people getting off is 32

Given:

Vertices of a triangle ABC are A(-3,0), B(3,0) and C(0,4).

To find:

The intersection point of all the medians of the triangle ABC.

Solution:

We know that, intersection point of all the medians of a triangle is called centroid.

The formula of centroid is

[tex]Centroid=\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)[/tex]

Vertices of a triangle ABC are A(-3,0), B(3,0) and C(0,4).

[tex]Centroid=\left(\dfrac{-3+3+0}{3},\dfrac{0+0+4}{3}\right)[/tex]

[tex]Centroid=\left(\dfrac{0}{3},\dfrac{4}{3}\right)[/tex]

[tex]Centroid=\left(0,1.333...\right)[/tex]

Round each coordinate to the nearest tenth.

[tex]Centroid=\left(0,1.3\right)[/tex]

The coordinates of required point are (0,1.3). Therefore, the correct option is C.

Answer:

rko

Step-by-step explanation:

Answer:

Step-by-step explanation:

styls clash baaaabyyy

Answer:

use math

Step-by-step explanation:

Answer:

A point is a coordinate pair

A ray is a starting point but no end point (so it goes on forever)

A segment is a line connecting two points

(I'm in 9th still learning-ish)

Answer:

Step-by-step explanation:

63 hours

hope it helps

Answer:

a little more than 16 1/2 hours but you should round it up to 17 hours

Step-by-step explanation:

If she can only work hours and not half hours or anything, the answer would be 17 hours and she will have a little more than $900 because 16 hours would be too little time.

(sorry if this is confusing but i hope it helped)