Answer:
Step-by-step explanation:
From what I can come up with with no actual factual information is that the equation is
[tex]\frac{1+sin^4x-cos^4x}{1-sin^6x-cos^6x}=\frac{2cos^2x}{3}[/tex] I'm going with that because it actually solves pretty easily, which is usually the way this goes. Begin by cross multiplying:
[tex]3(1+sin^4x-cos^4x)=2cos^2x(1-sin^6x-cos^6x)[/tex] and distribute:
[tex]3+3sin^4x-3cos^4x=2cos^2x-2cos^2xsin^6x-2cos^8x[/tex] and then break up the powers of sin into squared sines:
[tex]3+3[sin^2x*sin^2x]-3cos^4x=2cos^2x-2cos^2x[sin^2x*sin^2x*sin^2x]-2cos^8x[/tex] and use the Pythagorean identity to change those sines into cosines:
[tex]3+3[(1-cos^2x)(1-cos^2x)]-3cos^4x=2cos^2x-2cos^2x[(1-cos^2c)(1-cos^2x)(1-cos^2x)]-2cos^8x[/tex]
and the FOIL out those terms inside the square brackets:
[tex]3+3[1-2cos^2x+cos^4x]-3cos^4x=2cos^2x-2cos^2x[1-3cos^2x+3cos^4x-cos^6x]-2cos^8x[/tex]
and distribute again on both sides to get rid of the brackets entirely:
[tex]3+3-6cos^2x+3cos^4x-3cos^4x=2cos^2x-2cos^2x+6cos^4x-6cos^6x+2cos^8x-2cos^8x[/tex]
and combining like terms cancels a lot of that out to leave:
[tex]6-6cos^2x=-6cos^6x+6cos^4x[/tex] and get everything on one side to factor:
[tex]0=-6cos^6x+6cos^4x+6cos^2x-6[/tex] and factor out the -6:
[tex]0=-6(cos^6x-cos^4x-cos^2x+1)[/tex] and now we'll factor by grouping, so grouping everything together to get ready for that:
[tex]0=-6[(cos^6x-cos^4x)-(cos^2x+1)][/tex] and begin the factoring:
[tex]0=6[cos^4x(cos^2x-1)-1(cos^2x-1)][/tex] and continuing the factoring:
[tex]0=-6(cos^2x-1)(cos^4x-1)\\0=-6(cos^2x-1)(cos^2x-1)(cos^2x+1)[/tex] and by the Zero Product Property (and we won't list that duplicated factor cuz it's not necessary):
[tex]cos^2x-1=0[/tex] or [tex]cos^2x+1=0[/tex]
Solving the first:
[tex]cos^2x=1[/tex] so
x = 0 + 2kπ and solving the second one:
[tex]cos^2x=-1[/tex] which is not solvable over the real number system.
So x = 0 + 2kπ
and I really hope that's what you were looking for!
What’s the answer to this? Please send help
Answer:
But I see no attachment....pls recheck
For each line, determine whether the slope is positive, negative, zero, or undefined.
Line 1
Line 2
Line 3
Line 4
O Positive
O Negative
Zero
Undefined
Positive
O Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
O Positive
O Negative
O Zero
O Undefined
For line 1 slope is negative, for line 2 slope is undefined, for line 3 slope is positive and for line 4 slope is zero.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
The slope of a line is a measure of its steepness and direction. To determine the sign of the slope, we need to look at the direction of the line:
If the line is slanting upwards from left to right, the slope is positive.If the line is slanting downwards from left to right, the slope is negative.If the line is vertical, the slope is undefined (since the denominator of the slope formula, which is the difference in x-coordinates, is zero).If the line is horizontal, the slope is zero (since the numerator of the slope formula, which is the difference in y-coordinates, is zero).Therefore, Lines 1, 2, and 4 have negative slopes, undefinable slopes for lines 2 and 3, and positive slopes for lines 3 and zero for lines 4.
Learn more about Linear equations here:
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Jessica spent half of her allowance going to the movies. She washed the family
car and earned 9 dollars. What is her weekly allowance if she ended with
17 dollars ?
Answer:
16 dollars.
Step-by-step explanation:
She ended with 17 dollars after earning 9 dollars, so her amount of money before earning this was 17 - 9 = 8 dollars. This is half of her weekly allowance, so her weekly allowance is double this or 16 dollars.
If two functions, f(x) and g(x), are inverse functions, what must the composition of f(g(x)) and g(f(x)) both equal?
A. 0
B. 1
C. f(x) = g(x)
D. x
==========================================================
Explanation:
The composition of the original function with its inverse will cancel out the operations to yield the input as the output.
Consider the example functions shown below
f(x) = x+5g(x) = x-5The first function adds 5 while the second function does the complete opposite and subtract 5. The two functions are inverses of each other.
We see that,
f(x) = x+5
f(g(x)) = g(x)+5
f(g(x)) = x-5+5
f(g(x)) = x
and you should find that g(f(x)) = x for similar steps.
No matter what the x input is, the output will be identical to the input.
For instance, if we plug in x = 7, then adding 5 to it gets us 12. Then undoing that operation to subtract 5 gets us back to 7 again. This is one example showing why both f(g(x)) and g(f(x)) both equal x, where f and g are inverses of each other.
0.125, 2/5, 65%, 0.5, 1/4, 80%, 0.232 in order from greatest to least
Express each percent as a fraction or mixed number in simplest form.
120%
++pls explain how to do this if you know
Answer:
120/100
Step-by-step explanation:
120÷20= 6
100÷20=5
6/5 = 1⅕
The total bill (parts and labor) for the repair of a car was $458. The cost of parts was $339. The cost of labor was $34 per hour. How many hours of labor did it take to fix the car?
Answer:
3.5 Hours MARK ME AS BRAINLIEST PLEASE
Step-by-step explanation:
Take 458, and subtract 339 from it. Then, divide that by 34.
Answer:
3 and a half hours
Step-by-step explanation:
Subtract 399 from both sides
119 = 34h
Divide both sides by 34
3.5 = h
Identify whether or not the following features are represented in the above diagram for each feature that is represented write the name(s) denoted it in the diagram
The geometric features of objects are the objects features that are constructed by the aid of elements of geometry
The definition of the geometrical features are as follows
A ray is a line having a single starting point and a straight extension, having no end pointA vertex is the meeting point of two or more linesAn angle is formed by two rays that have a common vertexParallel lines are two lines that are always the same distance from each otherParallel planes are two planes that have equal distance from each otherCoplanar points are points on the same planeCollinear points are points on the same lineSegment addition postulate states that segment AC can include a third point B, when AB + BC = ACPerpendicular lines are two lines that intersect at 90°
Based on the above definitions, the values in the table are as follows;
[tex]\begin{array}{lcl} \mathbf{Feature}&& \mathbf{Denoted \ in \ diagram (s)}\\ \\Ray&&\\\\Vertex&&\\\\Angle&&\\\\Parallel \ lines &&\\\\Parallel \ planes &&\\\\Coplanar \ points&&\mathbf{C, \ F, A, N, B}\\\\Collinear \ points&&\mathbf{A, N, B}\\\\Segment \ addition \ postulate&&\mathbf{AN + NB} = AB\\\\Perpendicular \ lines&&\end{array}\right][/tex]
The features in the diagram are;
Coplanar points: C, F, A, N, B
Collinear points: A, N, B
Segment addition postulate: AN + NB = AB
Learn more about geometric features here:
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i need help with this question
Answer:
-14.50, -8/4, 4.2, 15/2, 12.072, 12.25
6x + 3y - 9 when
x = 6, y = 9
Answer:
63
Step-by-step explanation:
6x + 3y - 9
x = 6
y = 9
6(6) + 3(9)
36 + 27
= 63
b. The number of cats your teammates have as pets: 0, 1, 3,2
Ok so 1.2 is the answer you get if you divide them
and you can also say one because its counting by ones
Five times the sum of a number and 7 is 8
How would I graph y = 5/3 x -9
Factorise: (Using Algebraic Identities)
64x^3-(4x-3y)^3
Answer:
9y(16x2−12xy+3y2)
Step-by-step explanation:
Factor 64x3−(4x−3y)3
144x2y−108xy2+27y3
=9y(16x2−12xy+3y2)
Answer:
9y(16x2−12xy+3y2)
what is 6x^2+2x ?
please help will mark brainliest
Answer:
38x
Step-by-step explanation:
[tex]6x^{2}+2x\\=\\36x+2x\\=\\38x[/tex]
Chow,...!
HELP WITH B, C, & D PLS: g(x) = 2x2 + 5x + 1, find: -3g(3)
hi please help i’ll give brain
Answer:
The GCF is going to be 2
Step-by-step explanation:
This Is how I find the GCF of 3 numbers. I find the prime factorization first, then I find the common factors and multiply them. Here
The prime factorization of 8, 2 × 2 × 2 = 8
The prime factorization of 18, 2 × 3 × 3 = 18
The prime factorization of 70, 2 × 5 × 7 = 70
The one and THE only common factor is 2, which is going to be the GCF
Factor this polynomial completely.
6x2 + 7x - 20
3. Determine the value of x if:
3.1. 75x -15 =5x + 125
3.2. 6(3x - 2) = 7(x + 3) +2
3.3.10/x-3= 8
3.4. x + 7 = 5x - 13
3.5. 20x +4 =4x - 46
Step-by-step explanation:
3.1.
your question
75x-25=5x+125
collect like terms
70x=150
Divide both side by the coefficient of x
70x/70=150/70
70 ti cancel 70 on x side to leave x alone
:. x=150/70 or 2.14
3.2.
6×(3x-2)=7×(x+3)
multiply by the bracket
18x-12=7x+21
collect like terms
18x+7x=21+12
25x=33
divide by the coefficient of x
25x/25=33/25
x=33/25 or 1.32
3.3.
10/x-3=8
cross multiply(know that 8 is /1)
x‐3×8=10×1
8x-24=10
8x=10+24
8x=34
divide both sides by coefficient of x
8x/8=34/8
8x=34/8 or 4.25
3.4.
x+7=5x-13
collect like terms
7+13=5x-x
20=4x
divide both sides by the coefficient of x
20/4=4x/4
5=x
:.x=5
3.5.
20x+4=4x-46
collect like terms
20x-4x=-46-4
16x=-52
divide both sides by the coefficient of x
16x/16=-52/16
:.x=52/16 or 3.25
(2x+y)^2- (y-2x)^2
pleaseee help me
Which names are other ways to name _1? Select each correct answer.
y
pfy
pyf
p
yfp
ypf
f
Answer:
your answer is F
I hope it's helps you
construct a quadrilateral KLMN in which KL=LM=KM=5cm,KM=8cm and LN =6 cm
Answer:
Step-by-step explanation:
There are 2 possibilities.
1) Put a point L.
2) draw the circle of center L and radius 5 :C1
3) Put on point M on this circle
4) Draw the circle of center m and radius 8:C2
5) C1 and C2 intersect in K
2) Para realizar um campeonato de vôlei em uma escola o professor de educação física decidiu dividir os 96 alunos em grupos. Sabendo que cada equipe para esse esporte deve ser composta por 6 pessoas, quantas equipes o professor conseguiu formar?
Answer:
Answer:
16
Step-by-step explanation:
96÷6=16
is 5 (10) the same as 5 (3+7)
Answer:
[tex]yes \\ because \\ 5 \times (10) = 50 \\ and \: 5(3 + 7) = 5(10) = 50 \\ than k\: you[/tex]
Answer:
yes, because 3+7 is equal to 10
Step-by-step explanation:
What numbers are 3 units from -2 on a number line?
A number line ranging from negative 10 to positive 10
Select from the drop-down menus to correctly complete the statements.
______is 3 units left from -2 on a number line.
______- is 3 units right from -2 on a number line.
The answers are
-1
-5
1
5
please hurry
Answer:
___-5___is 3 units left from -2 on a number line.
___1___- is 3 units right from -2 on a number line
If n - 72 = 36, then what is the value of n?
N - 72 = 36
To solve for n add 72 to both sides of the equation:
N = 108
Answer:
108
Step-by-step explanation:
Add 72+ 36 you will get your answer
The answer is 108
Therefore n= 108
Find the median and mode of 14 ,25, 14, 28, 18, 17, 18, 14, 23 22, 14 and 18
Answer:
Ascending order - 14, 14, 14, 14, 17, 18, 18, 22,
23, 25, 28
Median = ( n+1/2)
= ( 11+1/2)
= 12/2 = 6th term
Here, in order 6th term is 18, so 18 is median.
Mode is frequently occurring number.
Here frequently occurring number is 14 i,e 4 times.
Hence, 14 is mode.
Answer:
mode ; 14
median; 18
Step-by-step explanation:
Ans; 14, 14 , 14 ,14, 17 , 18 , 18 , 18 ,22, 23 , 25 , 28
mode ; 14
[tex]median = \frac{n}{2} = \frac{18 + 18}{2} = \frac{36}{2} \\ \\ median = 18[/tex]
I hope I helped you^_^
what is the rule division property of radicals?
Answer:
Divide the numbers from within the radicals.
How many times greater is the value of the 7 in 70,048 than the value of 7 in 17,992?
Answer:
10 times
Step-by-step explanation:
The value of the 7 in 70,048 is 70,000
The value of the 7 in 17,992 is 7,000.
If you divide 70,000 by 7,000, you get 10.
The first 7 is 10 times greater than the 2nd.
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:10 times
Step-by-step explanation:
The value of 7 in 70,048 stands for 7 Ten thousand which is equal to 70,000
Also 7 in 17,992 stands for 7 thousand which is equal to 7,000
So we divide to know how much the lesser value is in the grater vale giving us
70,000/7,000 =10
Therefore, the value of 7 in 70,048 is 10 times than the value of 7 in 17,992
See similar answer here: https://brainly.com/question/13200619
Carly spent more than 180 minutes this week on her computer. She
spent 45 minutes on Sunday and the same number of minutes each
of the other 6 days. What is the minimum number of minutes that
Carly spent on her computer each of the other 6 days? Write and
solve an inequality.
Answer:256
Step-by-step explanation: