This can be proved by using identities of trigonometry.
Prove that cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1:Given that,
sin x + sin²x = 1 ⇒ sin x = 1 - sin²x
⇒ sin x = cos²x (∵sin²x + cos²x = 1)
We have to prove that,
cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1
LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x
= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x
= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³
= (sin²x + sin x)³ (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)
= 1³ = 1 = RHS
LHS = RHS
Hence the equation is proved since both sides of the equation are equal.
Learn more about trigonometric identities here:
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The six sided of number cube are labeled 1,2,3,4,5 and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on heads and roll a number greater than 2?
heads = 1/2
>2 = 2/3
2/3 x 1/2 = 1/3
Answer:
1 / 3Select the correct answer.
Identify the vertex of the function graphed below.
A.
(0,-2)
B.
(3,1)
C.
(1,1)
D.
(2,2)
Answer:
I think the answer is B
Step-by-step explanation:
Answer:
think it d
Step-by-step explanation:
because when i pick (3,1) it was wrong so that why it think it D
Write the equation of the line that passes through the points (1,4) and (1,-3).
y = -7x+11
X=1
y = 7x - 3
WILL GIVE BRAINLIEST!!!!!!!
2(x+1)^2=12
Answer:
Step-by-step explanation:
PROBLEM SOLVING A math club is having a bake sale. Find the area of the bake sale sign
TT IS
SWEET!
412ft
Math Club Baka Ina this Saturday
729 ft
The area of the sign is square feet.
The area of the bake sale sign is 6 ft²
Area
Area is the amount of space occupied by a two dimensional object.
Rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel.
The area of a rectangle = length * breadth
The area of the bake sale sign = length * breadth = [tex]\sqrt{4} *\sqrt[6]{729} = 6\ ft^2[/tex]
Find out more on Area at: https://brainly.com/question/25689052
Choose SSS, SAS, or AA to prove
the triangles are similar.
A. SSS
B. SAS
C. AA
Choose SSS, SAS, or AA to prove the triangles are similar.
A. SSS
B. SAS
C. AA
Answer :As, all sides are given so we can use SSS to prove the triangles are similar.
So, correct option is A.
Explanation :Given : Sides of 1st triangle = 24, 32 and 40Sides of 2nd triangle = 27, 36 and 45To Prove :Triangles are similarProof :As, all three sides are given so let's check ratio of all three sides.
1. [tex] \tt \cancel{\dfrac{24}{27}} = \dfrac{8}{9}[/tex]
2. [tex] \tt \cancel{\dfrac{32}{36}} = \dfrac{8}{9}[/tex]
3. [tex] \tt \cancel{\dfrac{40}{45}} = \dfrac{8}{9}[/tex]
As, all sides are in equal ratio.
So, by SSS
∆1 ~ ∆2
At a certain store a half gallon jug of milk cost 2.95 and a gallon jug of milk costs 5.95. Which milk has cheaper price?
Answer:
The first milk
Step-by-step explanation:
2.95 × 2 = 5.90
The first milk has cheaper price.
Whos HAPPYYYYY today
Answer:
meeeeeeeeeeee super happy
Número de departamento vendidos en un edificio cualitativa o cuantitativa.
Answer:The nucleus / large central vacuole contains
genetic material of a eukaryotic cell.
Step-by-step explanation:The nucleus / large central vacuole contains
Giselle's as a wallet containing four $5 bills, five $10 bills and three $20 bills. She pulls out two bills, one at a time without the first bill being returned to the wallet. Find the probability that both bills that she pulls out will be $5 bills.
Answer:
the answer is 4/12
Step-by-step explanation:
-2(6) + 3(5 – 4· 2)
Answer:
-21
Step-by-step explanation:
There are (2^6)^3• 2^0bacteria in a sample. What is the total number of bacteria in the sample?
Answer:
262,144
Step-by-step explanation:
2^0 = 1
(2^6)^3 = 2^18 = 262,144
Answer: 262,144.
Step-by-step explanation: (26)3(20)
=(643)(20)
=262144(20)
=(262144)(1)
=262144
A square cake sits on a circular cake stand. The circular cake stand has a diameter of 24 inches. The cake measures 16 inches on each side. How many square inches of the cake stand are visible?
Answer:
196.12 in^2
Step-by-step explanation:
circular cake stand area=(24/2)^2(3.14)=452.12 in^2
square cake=16x16=256 in^2
452.12-256=196.12 in^2
Solve each inequality for the variable. Show your work. 3x-7>4x+2
Step-by-step explanation:
3x-4x>2+7
-x>9
x>-9
Plz mark me as a brainlist
Help If the side lengths of a cube are 16 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?
16 ⋅ 3
16 ⋅ 16 ⋅ 16
163
316
Answer: I believe the answer is 6.3 I will research more and get a definite answer just dam me for the answer!
Step-by-step explanation:
:)
Help me PLEASE! I will give Brainliest to the first correct answer.
Jada’s dog was 5 and 1/2 inches tall when it was a puppy. Now her dog is 14 and 1/2 inches taller than that. How tall is Jada’s dog now?
Answer:
20 inches tall
Step-by-step explanation:
First, I did 1/2+1/2=1. Then, I did 5+14=19. So, 19+1=20.
Simplify.
6⁴
౼
6²
simplify that
Answer:
6⁴/4²
Since, a^m/a^n = a^m-n
→ 6^4-2
→ 6^2
→ 6*6 = 36 Ans.
Here is an inequality: -x > 18. List some values for x that would make this inequality true.
Answer:
some examples x could equal:
x = -19
x = -20
x = -50
x = -100
so on
Step-by-step explanation:
remember negative x negative = positive
so any negative value beneath -18 will satisfy this because it will turn positive when multiplied by that outer minus sign.
hope this helped
Find the equation of the line which passes through (0,8) and (1,12)
Answer:y =4x + 8
Step-by-step explanation:
X-0/0-1 = y-8/8-12
Or,-4x = -y +8
So, y-4x = 8
Can someone help me on this is for today pls!!!
Answer:
C
Step-by-step explanation:
The answer must be in square inches, not inches, so a and b are automatically wrong.
Couple of ways of doing it - the large triangles are congruent, so the area of each is the same. Since the area of a triangle is 1/2 base times height, the area of the 2 large triangles is just base times height, which is 18 * 11 or 198
Same principle for the smaller triangles at the top, area is 8 times 11, or 88. Add them up, you get 286 sq inches.
help????????????????????
Answer:
x=11
Step-by-step explanation:
12x+2 and 2x+112 are opposite exterior angles so they are congruent
Answer:
x=11
Step-by-step explanation:
12x + 2 and 2x + 112 are vertical angles meaning that they are equal to each other so we set up an equation that says 12x + 2 = 2x + 112 and solve for x
12x+2=2x+112
step one subtract 2 from each side
12x=2x+112
step 2 subtract 2x From each side
10x=110
step three divide each side by 10
x=11
Find the value of x in the following figure.
Answer:
x = 8
Step-by-step explanation:
180-(89+57)= 180-146 = 34
(5x -6) = 34
5x = 34 + 6
5x = 40
x = 40 ÷ 5
x = 8
pls help me plssssss
Answer:
1
Step-by-step explanation:
It's the correct spelling.
What is the slope of the line that passes through these two points (15,20) and (20,25)
Answer:
The slope Is 1.
Step-by-step explanation:
If you graph the two points it shows that the graph is done.
Answer:
slope = 1
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 ) = (15, 20) and (x₂, y₂ ) = (20, 25)
m = [tex]\frac{25-20}{20-15}[/tex] = [tex]\frac{5}{5}[/tex] = 1
y=3x+−7
Find the slope.
A. 7
B. -7
C. 3x
D. 3
Answer:
D.3
Step-by-step explanation:
In the equation for a line in the form y=mx+c, m represents the slope.
Therefore the slope is 3.
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + - 7 ← is in slope- intercept form
with slope m = 3
The question is in the picture
Answer:
(8, - 7)
Step-by-step explanation:
Since, (8, 7) is reflecting over x-axis, so after reflection, x- coordinate will remain same and y-coordinate changes from 7 to -7.
Therefore,
[tex] J(8,\: 7) \rightarrow J'(8,\: - 7)[/tex]
Answer:
-8,7 is the ans of the question
Zoltan read 15 pages of his book in 6 minutes. At this rate, how many pages can he read in 10 minutes?
Answer:
25 pages in 10 minutes.
Which properties justify the steps taken to solve the system? {2a+7b=03a−5b=31 10a+35b=0; 21a−35b=217 31a = 217 a = 7 2(7)+7b=0 14 + 7b = 0 7b=−14 b=−2 what are each of the steps taken?
9514 1404 393
Explanation:
2a+7b=0 . . . . . . . . given [eq1]
3a−5b=31 . . . . . . . .given [eq2]
10a+35b=0 . . . . . . multiplication property of equality 5×[eq1] = [eq3]
21a−35b=217 . . . . .multiplication property of equality 7×[eq2] = [eq4]
31a = 217 . . . . . . . . addition/substitution properties of equality [eq3]+[eq4]
a = 7 . . . . . . . . . . . . division property of equality (÷31)
2(7)+7b=0 . . . . . . . .substitution property of equality; a=7 in [eq1]
14 + 7b = 0 . . . . . . . properties of real numbers
7b=−14 . . . . . . . . . . addition property of equality; add -14
b=−2 . . . . . . . . . . . . division property of equality (÷7)
Every time Kristina bakes a batch of brownies, she uses 1/8
a cup of chocolate. If she has 3/4
cup(s) of chocolate remaining, how many batches of brownies can Kristina make?
Answer:
6 batches
Step-by-step explanation:
3/4 divided by 1/8 = 6/8 divided by 1/8 = 6 batches
Find the midpoint of the line segment from (4,5) to (-4,4)
9514 1404 393
Answer:
(0, 4.5)
Step-by-step explanation:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
((4, 5) +(-4, 4))/2 = (4-4, 5+4)/2 = (0, 9)/2 = (0, 4.5)\
The midpoint is (0, 4.5).