If
[tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]
Prove that:
[tex] \tan(165) = \sqrt{3} - 2[/tex]
Please solve this question.
Answers
Answer: see attachment
Step-by-step explanation:
Given: cos 330 = √3/2
Prove that tan (165) = √3 - 2
![If [tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]Prove That:[tex] \tan(165) = \sqrt{3} - 2[/tex]Please](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/DiNKcFSF6IWnOXeW8JIutemZlAjk9lS1.png)
![If [tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]Prove That:[tex] \tan(165) = \sqrt{3} - 2[/tex]Please](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/PKGx81XJ157AhA0Yju0BJVLL7ThE6ceZ.png)
Step-by-step explanation:
cos330° = cos(360° - 30°) = cos(2π - 30°)
Using, cos(2π - x) = cosx, x < 90°
=> cos(2π - 30°)
=> cos(30°)
=> √3/2 , proved
(ii): tan(165°) = tan(180° - 15°) = tan(π - 15°)
Using, tan(π - x) = - tanx
=> tan(π - 15°)
=> - tan15°
=> - (-√3 + 2)
=> √3 - 2 proved
For tan15° :
Using, tan2x = 2tanx/(1 - tan²x)
tan30° = 2tan15°/(1 - tan²15°)
1/√3 = 2tan15° / (1 - tan²15°)
1 - a² = 2√3 a {a = tan15°}
Solving this we get, a = -√3±2
As a = tan15°, it can't be -ve, thus
a = tan15° = -√3 + 2
Related Questions
STORAGE COSTS According to a certain prediction equation, the cost of 200 square feet of storage space is $60. The cost of 325 square feet of storage space is $160. Find the slope of the prediction equation (in decimal form). Use the prediction equation to calculate the cost of 520 square feet. (use slash symbol to separate both answers, do not space)
Answers
Answer: for the first one it would be y=.8x-100 and the other answer would be 180
Let me know ASAP pls if it’s correct I found the answer online
Answer:
Full answer is
.8 for 1st one
and 360 for 2nd one
Step-by-step explanation:
Correct answer was given after wrong one.
z=1+4i
Find the angle 0(theta) in degrees that z makes in the complex plane.
Round your answer, if necessary, to the nearest tenth. Express 0(theta) between -180 and 180 degrees.
Answers
Answer:
76.0 degrees
Step-by-step explanation:
Just got it right on the Khan Academy quiz.
A 38-ounce bottle of juice drink contains 6 percent water. Than computed 6 percent of 38. His work is shown below.
6 percent of 38 0.6 times 38 = 22.8
Which statement explains Than’s error?
Than did not multiply 0.6 and 38 correctly.
Than did not use 0.06 for 6 percent.
Than did not move the decimal point three places to the left in the answer.
Than did not use 6 for 6 percent.
Answers
Answer:
C
Step-by-step explanation:
Answer:
it b or c
Step-by-step explanation:
If the perimeter of the regular pentagon is 75 cm what is the length of each side
Plz help nowww
If you wanna be crowed a brainliest:-)
Answers
Answer:
15 (mark me brainliest if you want and lmk if you need more help understanding)
Step-by-step explanation:
perimeter is (l*w)*2
if a pentagon is 5 sided, you do 75/5 which is 15.
each side has 15 cm
plz simplify and answer 3x+7x−28+31−8x for x=2043
Answers
Answer:
4091
Step-by-step explanation:
Given the equation;
3x + 7x − 28 + 31 − 8x
First, we would collect like terms;
3x + 7x − 8x − 28 + 31
Simplifying, we have;
[tex] 2x + 5[/tex]
For x = 2043;
2(2043) + 5 = 4086 + 5 = 4091.
the ratio of berries to oranges is 10:1 if there are 25 oranges, how many berries are there?
Answers
Answer:
250 berries
Step-by-step explanation:
There are 10 berries to every orange there is. It is given that there are 25 oranges. Simply multiply 10 with 25:
10 x 25 = 250
There are 250 berries.
~
Answer:
There are 250 berries.
Step-by-step explanation:
There are 10 berries per 1 orange.
We have 25 oranges.
To find out how many groups of berries to oranges there will be I will divide 25 by 1.
[tex]25/1=25[/tex]
[tex]x*y=z[/tex]
x = Amount of groups
y = Amount of berries per group
z = Amount of berries total.
Substitute values:
[tex]25*10=250[/tex]
There are 250 berries total!
evaluate (2x^2+y^2)3
Answers
Answer:
8[tex]x^{6}[/tex] + 12[tex]x^{4}[/tex]y² + 6x²[tex]y^{4}[/tex] + [tex]y^{6}[/tex]
Step-by-step explanation:
This can be expanded using the binomial theorem or by multiplying the factors.
In case you are not aware of the theorem, will do multiplication.
Given
(2x² + y²)³ = (2x² + y²)(2x²+ y²)(2x² + y²)
Expanding the second pair of factors
Each term in the second factor is multiplied by each term in the first factor, that is
2x²(2x² + y²) + y²(2x² + y²) ← distribute both parenthesis
= 4[tex]x^{4}[/tex] + 2x²y² + 2x²y² + [tex]y^{4}[/tex] ← collect like terms
= 4[tex]x^{4}[/tex] + 4x²y² + [tex]y^{4}[/tex]
Now multiply this by the remaining factor (2x² + y²)
(2x² + y²)(4[tex]x^{4}[/tex] + 4x²y² + [tex]y^{4}[/tex])
= 2x²(4[tex]x^{4}[/tex] + 4x²y² + [tex]y^{4}[/tex]) + y²(4[tex]x^{4}[/tex] + 4x²y² + [tex]y^{4}[/tex]) ← distribute both parenthesis
= 8[tex]x^{6}[/tex]+ 8[tex]x^{4}[/tex]y² + 2x²[tex]y^{4}[/tex] + 4[tex]x^{4}[/tex]y² + 4x²[tex]y^{4}[/tex] + [tex]y^{6}[/tex] ← collect like terms
= 8[tex]x^{6}[/tex] + 12[tex]x^{4}[/tex]y² + 6x²[tex]y^{4}[/tex] + [tex]y^{6}[/tex]
Sam and Bruno were computing how many kilometers they rode in the 3 bike trips they took last month. In order, they rode 45.7, 40.9, and 38 miles. Their solutions are shown. Sam's Solution Bruno's Solution 45.7 + 40.9 + 38.0 = 124.6 miles. 124.6 times 0.621 = 77.38 kilometers. 45.7 + 40.9 + 38.0 = 124.6 miles. 124.6 divided by 0.621 = 200.64 kilometers. If one kilometer equals 0.621 miles, which is the best solution to find the total number of kilometers they rode? Why is it correct? Bruno is correct. When going from a larger unit to a smaller unit you need to divide. Bruno is correct. When going from a smaller unit to a larger unit you need to divide. Sam is correct. When going from a larger unit to a smaller unit you need to multiply. Sam is correct. When going from a smaller unit to a larger unit you need to multiply.
Answers
Answer:
Bruno is correct. When going from a larger unit to a smaller unit you need to divide
Step-by-step explanation:
Sam's calculation:
45.7 + 40.9 + 38.0 = 124.6 miles. 124.6 × 0.621 = 77.38 kilometers.
Bruno's calculation:
45.7 + 40.9 + 38.0 = 124.6 miles. 124.6 divided by 0.621 = 200.64 kilometers.
1 kilometer = 0.621 miles.
Bruno is correct. When going from a larger unit to a smaller unit you need to divide
We will divide a larger value by a smaller value to get the smaller units
Answer:
Bruno is correct. When going from a larger unit to a smaller unit you need to divide
Step-by-step explanation:
What is the value of x?
Answers
Answer:
150
Step-by-step explanation:
Answer: 70
Step-by-step explanation: because 40 + 70 is 110. There is a sum of 180 degrees in a triangle. And 180- 110= 70.
pls give me brainliest
CAN SOMEBODY PLZ ANSWER ALL THESE CORRECT THANKS!!!!
(Only if u know how to do this)
WILL MARK BRAINLIEST :D
Answers
Answer:
ok look at comments for answers
Step-by-step explanation:
Answer:
24. -3, -1, 0, +1, +3
25. -4, -3, -2, +1, +2
26. -1, 0, +5, +7, +8
27. -7, -4, 0, +2, +3
28. -3, -2, -1, +4, +6
29. -11, -7, -4, +1, +3
:)
14. A cable company charges a $30 base installation fee plus $10 for every hour it takes to install all the equipment in your house. Write an equation in slope-intercept form that models the price of your installation as a function of the amount of time it takes.
A. y=30x+10
B. y=10x+30
C. y=10x-30
D. y=30x-10
Answers
Y= $10( hours) + $30
So you multiply $10 (x) how many hours worked plus $30 charge for base . Will give you the (y)
Here are the values of the first 5 terms of 3 sequences: : 30, 40, 50, 60, 70, . . . : 0, 5, 15, 30, 50, . . . : 1, 2, 4, 8, 16, . . . For each sequence, describe a way to produce a new term from the previous term. If the patterns you described continue, which sequence has the second greatest value for the 10th term? Which of these could be geometric sequences? Explain how you know.
Answers
Answer:
1,2,4,8,16.
Step-by-step explanation:
they are a square root of 2 for each question. it will eventually get up higher then additive.
The sequence that has the second greatest value for the 10th term is
1, 2, 4, 8, 16, . . .
The geometric sequences in the given sequences is 1, 2, 4, 8, 16, . . .
What is a sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Now the given sequences are,
30, 40, 50, 60, 70, . . . :
0, 5, 15, 30, 50, . . . :
1, 2, 4, 8, 16, . . .
For sequence 30, 40, 50, 60, 70, . . . :
we have common difference, d = 10
So, this is an arithmatic sequence.
So, Tn = a1 + (n-1)d
Hence, 10th term of the series,
T10 = 30 + (10-1)10
T10 = 30 + 9*10
T10 = 30 + 90
T10 = 120
For sequence 0, 5, 15, 30, 50, . . .
This is a recurssive sequence
Hence each term of the series is given as,
0
5 = 5*1
15 = 5*(1 + 2)
30 = 5*(1 + 2 + 3)
50 = 5*(1 + 2 + 3 + 4)
.
.
.
.
.
10th term = 5*(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
10th term = 225
For sequence 1, 2, 4, 8, 16, . . .
Here common ratio, r = 2
also, Tn = ar^(n-1)
So, T10 = 1*2^(10-1)
or, T10 = 1*2^9
or, T10 = 512
Therefore,
The sequence that has the second greatest value for the 10th term is
1, 2, 4, 8, 16, . . .
and The geometric sequences in the given sequences is
1, 2, 4, 8, 16, . . .
More about geometric progression :
https://brainly.com/question/14256037
#SPJ2
HELPP ME PLEASEEE
ill give brainiest to whoever answers first
Answers
Answer:
the answer is d
Step-by-step explanation:
it would be 9.7 x 10^3
Is (4, 10) a solution of 5x + 10y = 120? Explain how you know. How
could you check using the equation? Using the graph?
Answers
Answer: No, it is not.
Step-by-step explanation:
If you solve and graph the equation, the point (4,10) falls below the line, not satisfying the equation.
A rectangular room is covered in 5 12 square feet of carpet. If the length of the room is 16 feet,
what is the width of the room?
Answers
Answer:
long
Step-by-step explanation:
14ft
Find the slope of the line that passes through the points (4,10) and (6,9)
Answers
64x^2y-y factor the expression
Answers
Answer:
y(8x+1)(8x-1)
Step-by-step explanation:
Find the average rate of change for the function over the given interval.
2) y = 6x3 - 6x2 - 8 between x = 2 and x = 4
Answers
Answer:
132
Step-by-step explanation:
The average rate of change over a function can be given by: f(b)-f(a)/b-a. Where b is the second part of the interval and a is the first part.
y = 6x^3-6x^2-8
____
x = 2
6(2)^3-6(2)^2-8
6(8)-6(4)-8
48-24-8
24-8
16
____
x = 4
6(4)^3-6(4)^2-8
384-96-8
288-8
280
_____
280-16/4-2 = 264/2 = 132
In the figure, polygon ABCD is transformed to create polygon A'BCD.
This transformation is a
by a factor of
Answers
Answer:
This transformation is a horizontal stretch by a factor of 2 .
Step-by-step explanation:
The transformation is a horizontal stretch by a factor of 2 .
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
According to the given figure, vertices of rectangle ABCD are:
A=(3,0) B=(1,0) C=(1,2) and D=(3,2)
After the transformation of square ABCD we get a rectangle A′B′C′D′.
whose vertices are, A'=(6,0) B'=(2,0), C'=(2,2) and D'=(6,2)
(Here A', B', C' and D' are transformed from points A, B , C and D respectively.
In horizontal stretch by a factor k the point (x,y) in a graph f(x) is transformed to the (kx,y).
And after seeing the coordinates of vertices of square ABCD and rectangle A′B′C′D′
it is clear that there is no change in the y-coordinates in all the vertices of both square ABCD and rectangle A′B′C′D'.
Moreover, the x-coordinates are increasing by multiplying 2. Therefore it is a horizontal stretch by factor 2.
Hence, this transformation is a horizontal stretch by a factor of 2 .
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
j + 150 × 50 is a(n) ______ expression, because ______.
Answers
what do i put? meh need help
Answers
Answer:
2/2 = 1 i think pls check
Step-by-step explanation:
4 divided by 2 = 2
and 6 divided by 3 = 2
so yea 2/2
and 2/2 = 1
Given:
b (x) = x2+7x
Find
B(7)
Answers
Answer:
Step-by-step explanation:
b(7) = 7^2 + 7(7)
B(7) = 49 + 49
B(7) = 98
Sandra is selling cookie dough for a fundraiser. She has a minimum fundraising goal of $150. If Sandra's mom gave her a $45 contribution without buying anything and Sandra can sell a box of cookie dough for $5 each, which inequality below represents the minimum number of cookie dough boxes she can sell
Answers
Answer:
At least 21 cookieStep-by-step explanation:
Firstly she needed to raise $150
and each cookie $5
let the number of cookie be x
let the expression for the fund raising be
150=5x
given that the mom gave her $45
then she need
150-45=5x
105=5x
x=105/5
x=21
Therefore she need to sell at least 21 cookie
f(x) = 3x - 8 and g(x) = -x - 4. Find (f + g)(x) and (f + g)(5).
Answers
Answer:
(f+g)(x) = 3x - 8 -x -4
(f+g)(x) = 2x-12
(f+g)(5) - substitute 5 into x
(f+g)(5) = 2(5)-12
(f+g)(5) = 10-12
(f+g)(5) = -2
Step-by-step explanation:
−2z+3+7z=−12
i need help
Answers
Answer:
= − 3
Step-by-step explanation:
Answer:
z=-3
Step-by-step explanation:
-2z+3+7z=-12
5z+3=-12
5z=-12-3
5z=-15
z=-3
:)
(5.31 x 103) – (2.8 x 103)
Answers
Answer:
258.53
Step-by-step explanation:
Hope This Helps!
Plz Mark Brainliest!
Answer:
I believe it is 258.53 ,,,,
10 POINTS!!!
PLEASE HELP:(
I know it’s really easy but i’m super confused. Can anyone help???
Answers
Answer:
t=1/5d
Hope this helps! :)
in health class the students were asked what grains they preferredin the breakfeast cereal. What is the probibility that a random chosen student in the health class is listed out as their favorite grain?
Answers:
A: 20%
B: 35%
C: 14%
D: 30%
Answers
The equation of line q is 5y - 4x = 10. Write an equation of the line that is perpendicular to q and passes through the point (-15, 8)
Answers
Answer:
y = -5/4x - 10.75
Step-by-step explanation:
First, put the equation in slope intercept form by isolating y:
5y - 4x = 10
5y = 4x + 10
y = 4/5x + 2
Perpendicular lines have opposite reciprocal slopes, so the slope will be -5/4
Plug in the slope and the given point into y = mx + b to find b:
y = mx + b
8 = -5/4(-15) + b
8 = 18.75 + b
-10.75 = b
Plug in the slope and y intercept into y = mx + b
y = mx + b
y = -5/4x - 10.75
Answer:
5x + 4y + 43 = 0
Explanation:
y=mx+b
m=slope
b=y intercept
perpendicuar lines have slopes that multiply to get -1
so
solving for y
add 4x both sides and divide by 5 to get
y=4/5x+2
slope is 4/5
perpendicular means the slopes multiply to get -1
so
4/5 times what=-1?
what=-5/4
so
y=(-5/4)x+b
find b
given the point (-15,8)
8=(-5/4)(-15)+b
8=75/4+b
-43/4=b
y=(-5/4)x-43/4
convert to standard form:
5x + 4y + 43 = 0
Isaaq put 2b + 3 dollars in the bank in the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week he doubled what was in the bank and put that amount in the bank. If he now has $477 in the bank, how much did he put in the bank the first week? Please add an numerical explanation
Answers
Answer:
The answer is $159
Step-by-step explanation:
2b + 3 - Day 1
4b + 6 - Day 2
6b + 9 - Day 3
477=6b+9
-9 -9
468=6b
78=b
(2x78) + 3 = 159
The answer is $159
