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]
Please help please please help me please please
Answer:
8.88
Step-by-step explanation:
With reference angle 42°
hypotenuse (h) = 12
base (b) = x
Now
cos 42° = b / h
0.74 = x / 12
x = 0.74 * 12
x = 8.88
Answer:
the answer is 48 I think
Step-by-step explanation:
I did it by sub 90 and 42
Antonio tried to evaluate an expression. Here is his work: (57–8+5)÷9(17–14) = (49+5)÷93 Step 1 = (49+5)÷27 Step 2 = 54÷27 Step 3 = 2 Step 4 Is Antonio's work correct?
Answer:
Antonio's work is correct but his method is not
Step-by-step explanation:
(57–8+5)÷9(17–14) = (49+5)÷9
Antonio work:
Step 1 = (49+5)÷27
Step 2 = 54÷27
Step 3 = 2
Correct working:
Step 1:
Addition first
-8 + 5 = -3
= (57 - 3) ÷ 9(3)
Step 2:
= 54 ÷ 27
Step 3:
= 2
Antonio's work is correct but his method is not
He subtracted first when he is supposed to add first according to the rule of BODMAS
B - bracket
O - off
D - division
M - multiplication
A - Addition
S - subtraction
what percent of 18 is 24
SIDE NOTE:its not 75%
Select the three situations that model a sum of zero.
Explain your answer.
Answer:
Step-by-step explanation:
1,2,4
3,000 is 1/10 of?-
300
300,000
3,000
30,000
Answer:
30,000
Step-by-step explanation:
3,000 times 10 is 30,000, therefore 30,000/10=3,000
Answer:
Step-by-step explanation:
3000 of 1/10
3000*0.1=300
The coach of a track team is standing on
the outside of a circular track. What is the
maximum distance he can be from one of
his track teammates if the distance from the
coach to the center of the track is 52.4
· feet? Explain how you know your answer is
correct.
,.....................
Add. Express your answer in simplest form. 225+445 = $$
4n - 3 = -2n + 9 when n = 2
Answer:
Step-by-step explanation:
4n-3=-2n+9, we move the variables in one side and numbers on the other side
4n+2n=9+3
6n=12
divide by 2
n=2
10x + 5 - 2x + 9x.
HELP IMMEDIATELY PLEASEEE
Answer: 17x+5
Combine 10x to the 9x which would be 19x then subtract the 2x which gives you 17x+5
Answer: 17x+5
Step-by-step explanation:
10x+5-2x+9x
10x-2x+9x+5
17x+5
Help out pls ill mark u brainliest
Answer:
B = 119
C = 119
Step-by-step explanation: 180 - 61
B and C are vertical angles
how do I solve this
Answer:
4 hours
Step-by-step explanation:
120-72=48
48÷12=4
Answer:
4
Step-by-step explanation:
The total amount was $120.
A portion of the $120 was for parts.
The rest of the $120 was for service. Service cost $12 per hour.
Start with $120.
Subtract $72 to find the amount spent on service.
$120 - $72 = $48
$48 was spent on service.
The service costs $12 per hour.
$48/($12/hour) = 4 hours
Answer: 4 hours
Check:
$72 in parts + 4 hours * $12/hour = $72 + $48 = $120
4 hours is correct.
A school band is buying new jackets and hats. A jacket
costs $100 and a hat costs $40. The expression 100j + 40h
represents the cost of į jackets and h hats. How much will 5
new jackets and 8 new hats cost?
Answer:
it will cost 1820
Step-by-step explanation:
add 100 + 40=140 x 13=1820
Hoped it helps
Find the value of x I’d appreciate if you could explain as well if not that’s fine
How many groups of ten are there in 230
Answer:
23
Step-by-step explanation:
230/10=23
since it got deleted last time -_-
Please help me ASAP!!
Answer:
First one is 6
Second on is 45
When the British system of units was first developed, what was the most
common object used as a basis for measuring length?
A. Animals
B. The king's castle
C. The human body
D. Automobiles
find the constant of proportionality (r) in the equation y=rx
Answer:
5
Step-by-step explanation:
The constant of proportionality (r) in the equation y=rx is 3
How to determine the constant of proportionality?The equation of the function is given as:
y = rx
Make r the subject
r = y/x
From the table, we have:
y = 36 when x = 12
So, the equation becomes
r = 36/12
Divide
r = 3
Hence, the constant of proportionality (r) in the equation y=rx is 3
Read more about constant of proportionality at:
https://brainly.com/question/24309476
#SPJ2
Brainliest to right answer
Answer:
4,-2
Step-by-step explanation:
The line passes through the Y Axis and slopes 4 and -2.
Answer:
slope = - [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 4) and (x₂,y₂ ) = (1, - 3) ← 2 points on the line
m = [tex]\frac{-3-4}{1+3}[/tex] = - [tex]\frac{7}{4}[/tex]
Find the 91st term of the arithmetic sequence 5, -14, -33, ...
Answer:
-1704
Step-by-step explanation:
5, -14, -33
it goes down by 19 each time
nth term: -19n+25
91st term is 91 times -19=-1729+25=-1704
In ΔTUV, the measure of ∠V=90°, VT = 45 feet, and TU = 90 feet. Find the measure of ∠T to the nearest degree.
Answer:
60 on delta math
Answer:
60
Step-by-step explanation:
delta math answer
Alicia, Quentin, and Rosalyn are siblings. Alicia is the oldest sibling. Quentin is four years younger than Alicia. Rosalyn is two years older than Quentin. The sum of the siblings’ ages, in years, is 48. How old is Alicia?
Answer:
Alicia is 18years
Quentin is 14years
Rosalyn is 16years
Step-by-step explanation:
Let the age of Alicia be x
Let the age of Quentin be y
Let the age of Rosalyn be z
If the sum of the siblings’ ages, in years, is 48 then;
x+y+z = 48.... 1
If Rosalyn is two years older than Quentin then;
z =y+2 ..... 2
Also if Quentin is four years younger than Alicia then;
y = x-4 ... 3
From 3:
x = y+4 ... 4
Substitute 2 and 4 into 1 to have:
y+4+y+y+2 = 48
3y + 6= 48
3y = 48-6
3y= 42
y = 14
Since x= y+4
x = 14+4
x = 18
Since z = y+2
z = 14+2
z = 16year
This means that;
Alicia is 18years
Quentin is 14years
Rosalyn is 16years
Animals hair grows at a rate of 1 •10^-5 miles per hour.How many miles will animals Jaír grow after 500 hours?Express answer scientific notation
Answer:
0.005
Step-by-step explanation:
10^-5 =0.00001
0.00001x1= 0.00001
0.00001x 500=0.005 miles
change 9.65kg into grams
Answer:
9650
Step-by-step explanation:
Step-by-step explanation:
=(9.65×1000) grams
=9650grams
hope it helps.
HELP AS SOON AS POSSIBLE PLEASE!
Answer: A is correct
Step-by-step explanation:
all possible chances between two people are 100 different possibilities. Once you add the possibilities, you can see there is 15 balloons with the medium prize. Multiply 15 by 2 and you'll get 30/100, which simplifies to 3/10
Which function has a greater rate of change? Function 1 Function 2 X-1 -2 -3 2 3 y 3 5 7-3-5 A) Function 1 B) Function 2 C) Neither, they are equal D) Neither, one is nonlinear ОА OB ОС
Answer:
Step-by-step explanation:
Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created?
A store buys an item for $94. The store then prices the item to sell to customers. What is the selling price (in dollars) the store sells the item to customers for after applying a 62% markup? If necessary, round the answer to the closest hundredth.
Answer:
$152.28
Step-by-step explanation:
In order to determine the markup, multiply the original price by 62%
94 x 62% = 94 x .62 = 58.28
In order to determine the sale price, add the markup to the original price.
94 + 58.28 = $152.28
Given quadrilateral RSTU, what is the measure of angle R? HELPPPPPPP PLEASEEEEE!!!!!!
Answer: did you ever get the answer?
Step-by-step explanation:
Answer:
Step-by-step explanation:
?
triangle ABC has perimeter 22cm
AB= 8cm
BC= 5cm
by calculation deduce whether triangle ABC is right-angled triangle
9514 1404 393
Answer:
not a right triangle
Step-by-step explanation:
The perimeter is 22, so we have ...
AB +BC +CA = 22
8 + 5 + CA = 22
CA = 22 -13 = 9
If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.
AB² +BC² = 8² +5² = 64 +25 = 89
This is not the same as ...
CA² = 9² = 81
The triangle is not a right triangle.
_____
Additional comment
If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)
Who is drinking the fastest
Answer: Caiden
Step-by-step explanation:
For Caiden, at the second minute, the water is already at 7 ounces. However, Bella is still at 8 ounces. And Caiden is drinking at a speed of 2.5 ounces per minute while Bella is drinking at a speed of 2 ounces per minute.
Hope that helped!
Help plss I will mark as brainlest if correct
Answer:
ok
Step-by-step explanation:
Answer:
if im not mistaken it should be y=0x+-3
Step-by-step explanation:
well i took the points -8.,0 an -3,0 an got the slope of 0 , so i did the formula y=mx+b m is slope wich is 0 so y=0x+? so i looked at where the line passes through the y axis an it went through at -3 therefore your answer is y=0x+-3