Find the exact value of tan π/12.
[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]
-10-9-8-7 -6 -5 -4 -3
-2.1
0
1 2 3 4 5
6
7 8 9 10
3) Which inequality matches the graph?
A) X > .2
B) X <-2
C) x = -2
D) 3.2
Answer:
I think its D
Step-by-step explanation:
The dot starts on -2 and decreases so the answer would = -2 or be less than -2 :)
Help, im incredibly confused
[tex]f[/tex](x) = 0.20x + 35 : 29.5
HELP PLEASE TAKING A TEST RIGHT NOW
the graph shows a system of equations
what is the solution to the system of equations?
a. -3, 2
b. 3, -2
c. 3, 2
d. -3, -2
Brent buys a dinning table that costs $150 before tax. The sales tax is 8% . How much tax did he pay?
Answer:
12
Step-by-step explanation:
its just twelve beliebe me
Write an equation in slope-Intercept form for the line with slope 2 and y-Intercept - 1. Then graph the line.
Answer:
Solution given in the photo
What number group includes only the counting number and 0
Answer:
Integers
The set of numbers including all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero)
Help help help help math math
can anyone slove this question pls
we have: -10/4 = -2.5 ⇒ -2 > -2.5 > -3
ANSWER : -2 and -3
ok done. Thank to me :>
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answer:
c. copy an angle.
there's no angle in this as far as I can see.
Mrs. Traynor's class is taking a field trip to the zoo. The trip will cost $26 for each student. There are 22 students in her class. Use compatible numbers to estimate the total cost of the field trip.
Answer:
$572
Step-by-step explanation:
Since she has to pay $26 for her 22 students, you need to multiply to find the answer$26 * 22 = 572Therefore, she has to pay $572Help help math math math please
Answer:
x = 5
Step-by-step explanation:
2x+15 = 4x+5 (because they are corresponding angles)
10 = 2x
x = 5
Answer:
x = 5
Step-by-step explanation:
Camden has a loyalty card good for a 17% discount at his local hardware store. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?
Answer:
0.83Step-by-step explanation:
Let the price is x.
With 17% discount it becomes:
x - 17% of x =x - 0.17x = 0.83xThe number we need is 0.83
Solution,
Assume That The Price is x
When Will Put It in Equation,
[tex] \frak{ \bigstar}{ \rm{ {We \: Will \: Get,}}}[/tex]
[tex]{ \longmapsto{ \sf{x-17 \% \: of x =}}}[/tex][tex]{ \longmapsto { \sf{x-0.17x}}}[/tex]0.83Hence, Required Price is “0.83”
What is the diameter of circle 0?
Answer:
8
Step-by-step explanation:
diameter is the radius times 2
A jeans maker is designing a new line of jeans. These jeans will sell for $410 per unit and cost $328 per unit in variable costs to make. Fixed costs total $120,000. If 5,000 units are produced and sold, income equals:
Answer:
$290,000
Step-by-step explanation:
Total cost = total variable cost + fixed cost
= 5000×328 + 120000
= 1640000+120000
=1760000 $
The jeans maker earns in total = 5000 × 410
= 2050000 $
So the income is
= 2050000 – 1760000 = 290000 $ ( Answer)
If the number of units is 5,000. Then the income will be $290,000.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A pants producer is planning another line of pants. These pants will sell for $410 per unit and cost $328 per unit in factor expenses to make. Fixed costs complete $120,000.
Let 'x' be the number of units. Then the equation is given as,
Income = Selling cost - Variable cost - Fixed cost
Income = $410 x - $328 x - $120,000
Income = $82 x - $120,000
If the number of units is 5,000. Then the income is calculated as,
Income = $82 (5,000) - $120,000
Income = $410,000 - $120,000
Income = $290,000
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A recipe requires 1/3 cup of water for every 2/5 cups of sugar. How much
sugar would you need for a full cup of water?
Answer:
1 1/5
Step-by-step explanation:
QRS is similar to XYZ.of QR=5,QS=7,and XY=30 find the value of XZ
How do you dived a fraction with a number like for an a example:
4/10 divided 2 = ?
Please explain step by step to get marked as brainliest!
Step-by-step explanation:
I assume you mean how do you divide a fraction by a whole number
In order to divide a fraction by a whole number we must use the KFC rule or the "Keep, flip, change" rule
The "Keep" means we keep the first fraction the same.
Next, we "flip" the second fraction (or in this case number; however it can be made into a fraction by putting it over 1). So now we have 4/10 divided by 1/2
Then we "change" the symbol so instead of dividing the fraction, we change the divide to a multiply.
Lastly, you just multiply the fractions as you usually would and you should end up with 4/20 which simplifies to 1/5 if my maths is correct.
Hope this helps.
Answer:
you can use KCF for this answer as well
Step-by-step explanation:
2 as a fraction would be 2/1
you need 4/10 divided by 2/1
applying KCF, you change it to be 4/10 multiplied by 1/2
solve to get 4/20 or simplified 1/5
hope this helped :)
Helppppopleaseee????
Answer:
LQ = 5
Median = 6
Step-by-step explanation:
[tex]\frac{n+1}{2}[/tex] gives us 5.5, so we do the average of position 5 and 6. This gives us 6, so the median is 6.
Now we find the median of the bottom half of the numbers, which is 5, so the LQ is 5.
Now we find the median of the upper half of the numbers, which is 7, so the UQ is 7.
A hole needs to be at least 40 feet below ground level. This means it needs to be more than 2 times its current depth.
represented by the inequality 2d<-40, where d is the current depth of the hole.
Select from the drop-down to correctly interpret the solution of this inequality.
The current depth of the hole is Choose.
feet below ground level
The current depth of the hole is at least 20 feet below ground level.
Inequality is an expression that shows the non equal comparison of numbers and variables.
Let d represent the current depth of the hole.
To be at least 40 feet below ground level, he need more than 2 times its current depth.
2d < -40
d < -20
Hence the current depth of the hole is at least 20 feet below ground level.
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Answer:
20 feet below
Step-by-step explanation:
identify a potential sustainable agriculture practice to reduce the impact of the large-scale intensive agriculture on
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:
A rectangular swimming pool is 4 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 1800 cubic feet.
Find the dimensions of the pool.
Answer:
19 x 23.5 x 4
Step-by-step explanation:
4 * x * (x + 4.5) =1800
Divide both sides by 4
x * (x + 4.5) = 450
Use distributive property
x^2 + 4.5x = 450
Move all terms to one side
x^2 + 4.5x - 450 = 0
Use quadratic formula to solve a = 1, b = 4.5, c = -450
-4.5 +- [tex]\sqrt{4.5^2 - 4 * 1 * -450}[/tex]/2
=-4.5 + - [tex]\sqrt{1820.25}[/tex] / 2
= -4.5 +- 42.664 / 2
=19.08 and -23.582. You can't have a negative length, so it is 19.08, or 19
19 x 23.5 x 4
The ratio of good guys to bad guys was 15 to 4. If there were 75 good guys, how many bad guys were there ?
[tex]\begin{array}{ccll} \stackrel{guys}{good}&\stackrel{guys}{bad}\\ \cline{1-2} 15&4\\ 75&x \end{array}\implies \cfrac{15}{75}=\cfrac{4}{x}\implies \cfrac{1}{5}=\cfrac{4}{x}\implies x = 20[/tex]
Number of bad guys = 12
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given,
Ratio of good to bad guys = 15:4 = 15/4
No. of good guys = 75
Let the no. of guys be x
⇒ 15:4 = 75:x
⇒ 15/4 = 75/x
Cross multiplying
15 x = 75×4
x = (75/15)×4
No. of bad guys = (75/15)×4
= 3 × 4
No. of bad guys = 12
Hence, there are 12 bad guys.
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71.841 to the nearest tenth
71.8
Step-by-step explanation:71.841:
The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.
How?In order to round, we need to remember how to round numbers:
If the digit is less than 5, the number to the left stays the same.If the digit is greater than, or equal to 5, the number to the left rounds up, or increases by 1. Solve:First, 4<5, meaning that 4 is less than 5.
#1 above is stating that the number to the left of 4 stays the same.
If we use that rule:
71.8 is our answer.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
On a number line, point O is at -7, and point P is at 8. Point N lies between points O and P. If the ratio of ON to NP is 4:8, where does point N
lie on the number line?
Point N is at
on the number line.
Answer:
N is at -2 on the number line
Step-by-step explanation:
The location of point N can be found by writing the segment lengths as a proportion.
ON : NP = 4 : 8
8(ON) = 4(NP) . . . . . . . . "cross multiply"
2(N -O) = (P -N) . . . . . divide by 4, show lengths ON and NP
2(N -(-7)) = 8 -N . . . . . use given values of O and P
3N = -6 . . . . . . . . . . . add N-14 and simplify
N = -2 . . . . . . . . . . divide by 3
Point N is at -2 on the number line.
If the ratio of ON to NP is 4:8, point N lie on the -2 at the number line.
Point O is at -7.
Point P is at 8.
The ratio of ON to NP is 4:8.
The ratio 4:8 simplifies to 1:2. This means that ON is one-third of the total distance from O to P, and NP is two-thirds of the total distance.
The total distance from O to P is the sum of the distances between O and N, and between N and P.
As the ratio of ON to NP is 1:2, and the total distance is 15 (8 - (-7) = 15), we can set up the following equation:
ON/NP = 1/2
ON/(15 - ON) = 1/2
Now we can solve for ON:
2 × ON = 15 - ON
3 × ON = 15
ON = 5
So, ON is 5 units away from O.
Now O is at -7, point N is at -7 + 5 = -2 on the number line.
So, N is at -2.
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Solve the proportion where necessary, round to the nearest hundredth 12/13 = X/13
Answer:
12
Step-by-step explanation:
12 / 13 = x / 13
Cross Multiply,
12 * 13 = 13 * x
x = ( 12 * 13 ) / 13
x = 12
I NEED HELP ON QUESTION B AND C ASAP.
Answer:
See belowStep-by-step explanation:
Part BAssumed the dimensions of the top and bottom parts are identical.
Since the cylindrical part has total height of 1.8 cm and the hemisphere volume is transferred to bottom part and the cone part is still full, the value of h is the difference of the total height of cylinder and full part of the top section of cylinder:
h = 1.8 cm - 0.3 cm = 1.5 cmPart CFind the volume of sand in the bottom part. It consists of a hemisphere and a cylinder of 1.5 cm height.
V(cylinder) = πr²h = 3.14*(2.6/2)²*1.5 ≈ 7.96 cm³V(hemisphere) = 2/3πr³ = 2/3*3.14*(2.6/2)³ ≈ 4.6 cm³Total sand in the bottom part:
7.96 + 4.6 = 12.56 cm³Time taken:
12.56 / 0.05 = 251.2 seconds = 4 min 11.2 secondsA company claims that their new bottle holds 40% more laundry soap.
If their original container held 53 fluid ounces of soap, how much does the new container hold?
plz show work too plz
Answer:
74.2
Step-by-step explanation:
53 x .4 = 21.2
21.2 + 53 = 74.2
A movie theater charges $9.75 per ticket. Monday through Thursday they make on average $2720.25 daily. How many
customers do they have on an average Tuesday?
a. 279 customers
c. 70 customers
b. 272 customers
D. 26552 customers
Answer:
Your anwser would be A mark brainliest please and thank you
Step-by-step explanation:
y = -5x+1 linear or nonlinear