The exact value of tan(105°) is -2 - √3.
What is Tangent function?Tangent function of an angle in a right angled triangle is defined as the ratio of the opposite side to the adjacent side.
Given that, we have to find the exact value of tan(105°).
We know that,
105° = 60° + 45°
tan(105°) = tan (60° + 45°)
We know,
tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
So,
tan (60° + 45°) = (tan 60 + tan 45) / (1 - tan (60) tan (45))
tan 60 = √3 and tan 45 = 1
tan (60° + 45°) = (√3 + 1) / (1 - √3)
Multiplying both numerator and denominator by (1 - √3),
= (√3 + 1)² / (1 - 3)
= -(3 + 2√3 + 1) / 2
= -(4 + 2√3) / 2
= -(2 + √3)
= -2 - √3
Hence the value of tan(105°) is -2 - √3.
Learn more about Tangent Functions here :
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Please answer this question
Answer:
number: 2
Step-by-step explanation:
Find the measure of each angle indicated.
2)
50°
?
A) 60°
B) 50°
C) 130°
D) 940
Solve the equation for all real solutions:
16n^2-10n-5=6n
Answer:
5/4 and - 1/4
Step-by-step explanation:
16n^2-10n-5=6n
16n^2-16n-5=0
(4n+1)(4n-5)
4n=-1 4n=5
n= -1/4 n= 5/4
Can somebody please help me
Answer:
Step-by-step explanation:
the shaded area would be
200*75=15,000 ft^2
from this are we have to subtract the are of the house and of the garage
house= 40*40=1600
garage=24*30=720
house and garage= 1600+720=2320
15,000-2320=12,680
Answer:
12680 ft²
Step-by-step explanation:
First we will find the area of the house and then the garage.
They're both rectangles so we should use this formula [tex]A=l*w[/tex].
Area Of The House:
[tex]A=l*w\\A=40*40\\A=1600ft^2[/tex]
Area Of The Garage:
[tex]A=l*w\\A=24*30\\A=720ft^2[/tex]
Adding the two areas:
Now we have to add the two together to find how much of the space they take up in the yard.
[tex]1600+720=2320[/tex]
Area Of The Yard:
[tex]A=l*w\\A= 200*75\\A=15000ft^2[/tex]
Subtracting The Two Areas To The Yard's Area:
[tex]15000-2320=12680ft^2[/tex] and that is it!
An airplane can seat up 175 passengers
okay okay 123
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
175-87=88 so 88 is where the dot needs to be located so we have option A and option B
For ≤ and ≥ , use a closed dot
For > and < , use a open dot
she said AT LEAST 175
so we would use a closed dot
I have to take care of my sister's cat while she is on vacation. The cat is a very picky eater and will only eat a certain cat food, available at two stores.
Gristede's sells 12 cans for $18
PetSmart sells 20 cans for $26
Which store is offering the best deal on cat food?
Make sure to explain how you were able to determine which store offers the best deal on the cat food.
What us the equivalent ratio for 4:3
Answer:
PetSmart is offering the best deal
Step-by-step explanation
For Gristede's we get 18 and divide it by 12 which would give us $1.50 per can
For PetSmart we get 26 and divide it by 20 which would give us $1.30 per can
You are renting a cabin that changes you a processing fee along with a daily rate. The total charge for this cabin is represented by the equation y=4x+35,where y represents the total cot and x represents the length of stay in days. How much would you be charged for 20 days at this cabin
Answer:
y= 115
Step-by-step explanation:
Step one:'
given data
The total charge for this cabin is represented by the equation
[tex]y=4x+35[/tex]
we are told that y represents the total cost and x represents the length of stay in days
Required:
the value of y when x= 20
Step two:
substitute
[tex]y=4(20)+35\\\\y=80+35\\\\y=115[/tex]
A proportional relationship between y and x. When x = 3, y=−4 .
What is the constant of proportionality, k?
Enter your answer as a simplified or improper fraction in the box.
k =
Answer:
k = 4/3
Step-by-step explanation:
Formula for k: y/x
If y = 4 and x = 3, then we use the formula (y/x) in order to find the constant of proportionality:
k = 4/3
If y=32 when x=8, find y when x=30.
What is the Factor of :
10x + 15
Answer:
The factor of : 10x+15 is
Step-by-step explanation:
10x+15
5(2x+3)
Graph the line that passes through the points (-2, - 7) and (5,0) and determine
the equation of the line.
what is the variable to 3x-5
Answer:
3 (2x + 3) + 11 = –2 (2x - 6) - 18
Answer:
-15
Step-by-step explanation:
this is because when a negative multiplies with a positive ....it gives an answer of negative
Need help resolving the following quadratic expressions:
a) 4x -4x -15 = 0
b) 2y +7y + 3 +0
Answer:
first answer for (a) is -15=0
second answer for (b) is =9y+3
Step-by-step explanation:
its juss so easy
which graph represents a function? please help
Answer:
C
Step-by-step explanation:
Answer:D
Step-by-step explanation: a function has only one output value for each input value
find the values of x and y
Answer:
61=x cortical opposite angle
61=y corresponding angle
Answer:
61=x and 61=y
Step-by-step explanation:
I think that bout right
Area of a right triangle (7,6)
Answer: The answer is 21
Step-by-step explanation:
The area formula is 1/2 bh so if you take if you put the numbers into formula it = a=1/2(6)(7)
What is the value of 0?
Answer:
[tex]\huge\boxed{\sf \theta = 36.9\°}[/tex]
Step-by-step explanation:
[tex]\sf cos \theta = adjacent/ hypotenuse\\\\where \ adjacent = 4 , hypotenuse = 5\\\\cos \theta = 4 / 5\\\\cos \theta = 0.8\\\\\theta = cos^{-1} 0.8\\\\\theta = 36.9\°\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807please answer if u know
Answer:
9 dollars
Step-by-step explanation:
let x be per mile
the equation for solving this would be 0.5x + 3(flat fee)=amount you have to pay
The x is 12 since you have to go 12 miles
0.5(12)+3=amount you have to pay
6+3=amount you have to pay
$9=mount you have to pay
What is the measurement of
127^*
A.13
В.35
С.53
D.73
Answer:
C
Step-by-step explanation:
Because if you do the multiplication then you would know that it was c
x
1
2
3
4
5
y
13
16.9
21.97
28.56
37.13
Graph the function shown by the table. Is the function linear or nonlinear?
Yes
NO
PLEASE HELP ME!!!!!!!!!!!!!!$!!!!!!!!
Graph the line that has a slope of -9 and includes the point (1, -1).
Answer:
Step-by-step explanation: you didnt put a Graph in your question
An item sells for $30 and is on sale for 15% off and the sales tax is 8.2%. What is the final cost to the nearest cent? (Calculate the discounted cost first and then find the tax on the discounted cost.)
Answer:
$27.59
Step-by-step explanation:
You multiply 30 dollars by 0.85 (1-0.15, with the 0.15 being for the 15 percent off). Which gets you to $25.50, and you then multiply it by 1.082 (the 1.082 being the tax, and the .082 part equating to the 8.2% tax percentage).
No need to show work just need answer.
Use the distributive property to write an equivalent expression. 2.5 ( w + 3 )
Answer:
2.5w + 7.5
Step-by-step explanation:
2.5(w+3)
2.5w+7.5
HELPP PLEASEEEEE 42 POINTS !!! what is 6( -3w + 1/3) =
Answer:
2 - 18w or -18w + 2
Step-by-step explanation:
6(-3w + 1/3)
Multiply using distrubutive property
-18w + 6(1/3)
Multiply 6 * 1/3 to get 6/3 or 2
-18w + 2
This is optional, but put the variable term on the right
2 + (-18w)
2 - 18w
What is the circumference of the circle below?
Answer:
Step-by-step explanation:
circumference C=2*3.14*r
C=2*3.14*18m=113.04 m
Answer:
113.04 meters.
Step-by-step explanation:
Use the formula
2 times pi times r
r=radius of the circle
or Pi times D
d= diameter of the circle.
The radius is 18 meters.
So, do 2 times 18 times pi.
a company will clean jarrel carpets for a total of $71 jarrel has a coupon for 20% of the total how much will jarrel save when he used the coupon?
Answer: 14.2 I hope im Right but it’s a simple question
Step-by-step explanation:
Answer:
do whatever your instincts are telling you to do
Step-by-step explanation:
anything helps !!! :))))
i need help
this is due today at 4
Answer:
Hi The Answer is A.
Step-by-step explanation:
The Answer is A Because of the funter travel of the X.
x*y=z
Hope This Helps.
:)
My name is John henry.
PLEASE HELP ASAP!!
j^4-5j^3+10j
Answer:
B) j(j^3-5j^2+10)
Step-by-step explanation:
Given: [tex]j^4-5j^3+10j[/tex]
Factor out j: [tex]j(j^3-5j^2+10)[/tex]
We cannot factor out anymore, so the final answer is B) j(j^3-5j^2+10)
