Find the least common denominator for these fractions. Enter your answer in
the space provided.

[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]

so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs

[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]

[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]

Answer:

Focus on planting trees and and getting healthier soil, improve energy efficiency and not use so much pesticides using natural ways to plant things.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x=25/6

Step-by-step explanation:

3x+11=9x-14

11=6x-14

25=6x

x=25/6

Answer:

[tex]x=\cfrac{25}{6}[/tex]

or

[tex]x=4.16[/tex]

Step-by-step explanation:

[tex]3x+11=9x-14[/tex]

[tex]3x+11-11=9x-14-11[/tex]

[tex]3x=9x-25[/tex]

[tex]3x-9x=9x-25-9x[/tex]

[tex]-6x=-25[/tex]

[tex]\cfrac{-6x}{-6}=\cfrac{-25}{-6}[/tex]

[tex]x=\cfrac{25}{6}[/tex]

Have a good day!

Answer:

It's A bar graph but I got to see the question to be for sure but its a bar graph and it helps you  measure rates of things from numbers , months , years etc .

Step-by-step explanation:

Answer:

Integers

The set of numbers including all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero)

Answer with step-by-step explanation:

A: 207

We know that percentage is out of 100, so we can divide 460 by 100 to find 1%, which is 4.6. We also know 45% percent of teenagers like comedies, so we multiply 4.6 by 45, or 207. 207 teenagers like comedies.

B. 80 teenagers

We know that 50% of teens Hannah surveyed like thrillers. We also know that 40 teenagers like thrillers. Using multiplication, we can multiply 40 by 2, since 50% is half, we need to multiply by 2 to get the total number of teenagers. Hannah surveyed 80 teenagers.

C. Jamie went to the candy store and spent his entire allowance of $20 on candy. His friends gave him $5 more dollars, so he bought candy with that too. He spent 125% of his allowance on candy.

The number of teenagers who like comedy is 207, and The total number of teenagers Hannah surveyed is 100.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

Netan surveyed 460 teenagers, He found that 45% of the teenagers surveyed like comedies,

(a) Calculate the number of teenagers who like comedy as shown below,

The number of teenagers who like comedy = 45 × 460 / 100

The number of teenagers who like comedy = 207

(b) Calculate the total number of teenagers as shown below,

The total number of teenagers × 50% = 40

The total number of teenagers = 40 × 100 / 40

The total number of teenagers = 100

To know more about percentages:

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Answer:

the answer u r looking for is 144

Step-by-step explanation:

if u know who this is i will follow u

hint: its from avatar tla

only the first person that answers!!!

Answer:

x = 21

Step-by-step explanation:

2x+78 = 5x+15,

because corresponding angles will allow (2x+78) to move diagonally from 5x+15.

from built geometry knowledge,

angles diagonal from one another equal,

because (example) the angle above it would be 180-(2x+78),

then 5x+15 = 180 - [180-(2x+78)], which would ultimately be 5x+15 = 2x+78.

so, 2x+78 = 5x+15

78-15 = 5x-2x

63 = 3x

21 = x

Answer:

15 installments

Step-by-step explanation:

3900 = Σ [tex]\left \ {{x=n} \atop {x=1}} \right.[/tex]   400 - 20*(n - 1)

Answer:

i have no clue

Step-by-step explanation:

i said this bc apparently i have to help someone to get help and i just wanna finish this math homework lol

Refer to the attachment for the graph.

[tex]\mathbb{MIREU} [/tex]

Answer:

2a(7b+5)

Step-by-step explanation:

yeah-ya....... right?

Answer:

34

Step-by-step explanation:

20% of 70 + 80% of 25 = 14 + 20 = 34.

Answer:

61

Step-by-step explanation:

Assuming a linear relationship between the percent chance for rain and the number of attendees, the number is 20% of the way from 70 (0% chance) to 25 (100% chance).

The expected number of people with a 20% chance of rain would be 61.

(hope it helps)

Answer: [tex]\frac{19}{14}[/tex] in improper form and [tex]1\frac{5}{14}[/tex] in mixed fraction form.

Step-by-step explanation: [tex]\frac{6}{7}[/tex] + [tex]\frac{1}{2}[/tex] = ? First you have to find the LCM (Least Common Multiple) of 7 and 2; also known as the LCD (Least Common Denominator). The LCM of 7 and 2 is 14 so you have to multiply both of the fractions by the number that equals 14, remember to multiply it for the numerator too. [tex]\frac{6}{7}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{12}{14}[/tex] Then [tex]\frac{1}{2}[/tex] x [tex]\frac{7}{7}[/tex] = [tex]\frac{7}{14}[/tex] Now you add [tex]\frac{12}{14}[/tex] and [tex]\frac{7}{14}[/tex] together. You leave the denominator as 14 because you found the LCD of 7 and 2 already, so you add 12 and 7 together which gives you 19. The answer would be [tex]\frac{19}{14}[/tex] in improper fraction form and [tex]1\frac{5}{14}[/tex] in mixed fraction form.

The sum of the fraction 6/7 and 1/2 is 19/14

Given:

sum of 6/7 and 1/2

Sum means addition(+)

= 6/7 + 1/2

The least common denominator is 7 × 2 = 14

= 6/7 + 1/2

= (12+7) / 14

= 19/14

Therefore, the sum of 6/7 and 1/2 is 19/14

Learn more about fraction:

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Answer:

A. 2 pounds of carrots per $1

Step-by-step explanation:

[tex]\frac{5 pounds }{2.5 dollars}=\frac{2pounds }{1 dollars}[/tex]

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

[tex]\sqrt 10y[/tex]

Step-by-step explanation:

10*[tex]\sqrt{y}[/tex] is [tex]\sqrt 10y[/tex]

[tex]\sqrt{100y}[/tex]

Step-by-step explanation:

Recall that

[tex]10 = \sqrt{100}[/tex]

So we can write our original expression as

[tex]10\sqrt{y} = \sqrt{100}\sqrt{y}[/tex]

[tex]\;\;\;\;\;\;\;\;\;=\sqrt{100y}[/tex]

Answer:

y = 18 when x = 3

Step-by-step explanation:

y is directly proportional to x^2, meaning:

[tex]y=ax^2[/tex]

where a is the proportion between them. We're given the values for both x and y, so plug those in and solve for a:

[tex]8=a(2)^2\\8=a4\\2=a\\a=2[/tex]

Now you can use a to solve for y when x is 3:

[tex]y=ax^2\\y=(2)(3)^2\\y=2(9)\\y=18[/tex]

Answer:

it is 2^21

Step-by-step explanation:

Answer:

2^21

Step-by-step explanation:

add 3 and 18 together

dont change 2

Answer:

about 5.1 units

Step-by-step explanation:

to find the length between two points you can use the pythaogorean theorem

5^2 + 1^2 = c^2

25 + 1 = c^2

26 = c^2

c is about 5.09901

rounding to the nearest tenth we get 5.1

Answer:

#5. C 4

#4. J 0.3 meters

Step-by-step explanation:

No. 5

f(-7) = -3-(-7)

f(-7) = 4

C

No. 4

s = sqrt(0.09)

s = 0.3 meters

Answer:

9π + 18

Step-by-step explanation:

The circumference of a circle is pi times diameter, so 9 x 2 = 18 inches, which is the diameter. That will be the flat side of the semicircle. Then the circumference of the whole circle will be 18π. To find the curved side of the semi-circle, divide this by 2, so you get 9π. Therefore the answer is 9π + 18. The rough answer to 3 decimal places is 46.274

Answer:

Step-by-step explanation:

Answer:

$572

Step-by-step explanation:

Answer:

syuare root 270 to get 16.4 then subtract 6 to get 10.4

Answer:

tank 1 : 19 gallons

tank 2 : 42 gallons

Step-by-step explanation:

tank 1 : x

tank 2 : 2x+4 ( 4 more than twice the other )

x + ( 2x + 4 ) = 61

3x + 4 = 61 [ add x + 2x = 3x ]

3x = 57 [ subtract 4 on both sides ]

x = 19 [divide 3 on both sides ]

tank 1 : 19 gallons

tank 2 : 42 gallons

Answer:

P=14

Step-by-step explanation:

Since P depends on two variables x and y as the sum of the two, then;

P = 3+ 11

P = 14

[tex]f[/tex](x) = 0.20x + 35 : 29.5