Recall the double angle identities:
cos(2θ) = 1 - 2 sin²(θ)
sin(2θ) = 2 sin(θ) cos(θ)
With some rewriting, we can get
cos(4θ) - cos(2θ) = 2 cos²(2θ) - 1 - cos(2θ) = (2 cos(2θ) + 1) (cos(2θ) - 1)
and
sin(4θ) + sin(2θ) = 2 sin(2θ) cos(2θ) + sin(2θ) = sin(2θ) (2 cos(2θ) + 1)
The numerator and denominator both share a factor of 2 cos(2θ) + 1; canceling them leaves us with
(cos(2θ) - 1) / sin(2θ)
Replace cos(2θ) = 1 - 2 sin²(θ) and sin(2θ) = 2 sin(θ) cos(θ) :
((1 - 2 sin²(θ)) - 1) / (2 sin(θ) cos(θ))
-2 sin²(θ) / (2 sin(θ) cos(θ))
- sin(θ) / cos(θ)
- tan(θ)
so the answer is C.
Answer:
(cos4θ-cos2θ)/(sin4θ+sin2θ)
-[2sin((4θ+2θ)/2)sin(2θ-4θ)/2)]/[2sin((4θ+2θ)/2)cos (4θ-2θ)/2)]-sinθ/cosθ-tanθC. -tanθ is your answer.
Which is the height of the lighthouse?
Answer:
Step-by-step explanation:
tan 26° = [tex]\frac{x}{90}[/tex] ⇒ x = 90tan26° ≈ 43.9 ft. (This answer for the picture)
sin 26° = [tex]\frac{h}{100}[/tex] ⇒ h = 100sin26° ≈ 43.9 ft (This answer for the text)
h = √(100² - 90²) ≈ 43.589 ft. (Pythagorean theorem)
PLEASE HELP!! solve |2x-2| ≥6.
x ≤ -2 OR x ≥ 4
__________________________________________________________
Step-by-step explanation:We are given the inequality:
|2x - 2| ≥ 6
Getting rid of the Modulus:
Since 2x-2 is in modulus:
|2x-2| = -(2x-2) OR 2x-2
(since the modulus of both these values is 2x-2)
Hence, our inequality can be written in 2 different ways:
2x-2 ≥ 6 (if 2x-2 ≥ 1)-(2x - 2) ≥ 6 (if 2x-2 < 0)__________________________________________________________
Solving these 2 inequalities:
Solving inequality 1:
2x - 2 ≥ 6
2x ≥ 8 [adding 2 on both sides]
x ≥ 4 [dividing both the sides by 2]
This is the solution of the inequality if: 2x-2 ≥ 0
Solving Inequality 2:
-(2x-2) ≥ 6
It can be rewritten as:
2 - 2x ≥ 6
2 ≥ 6 + 2x [adding 2x on both the sides]
-4 ≥ 2x [Subtracting 6 from both sides]
x ≤ -2 [Dividing both sides by 2]
This is the solution of the given inequality if: 2x-2 < 0
__________________________________________________________
Solution of the given Inequality:
Therefore, the solution of the given inequality |2x-2| ≥ 6 are:
x ≥ 4 (if 2x-2 ≥ 0)
x ≤ -2 (if 2x-2 < 0)
Hence, option C is correct!
What is the domain of the square root function graphed below?
Answer:
The domain of the graph must be [tex]x\ge \:-4[/tex].
Therefore,
[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]
Hence, option a is true.
Step-by-step explanation:
From the graph, it is clear that the graph is heading towards positive infinity from x=-4.
The point x=-4 is included in the graph as the starting point of the graph i.e. x=4 is showing a closed circle on x=4, and heading towards positive infinity onward.
i.e. [-4, ∞)
Hence, the domain of the graph must be [tex]x\ge \:-4[/tex].
Therefore,
[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]
Hence, option a is true.
2x+7y=1
y=4x−8
Is (4,8)(4,8)left parenthesis, 4, comma, 8, right parenthesis a solution of the system?
hello :
2x+7y=1 ...(*)
y=4x−8...(**)
(4;8) means x= 4 and y= 8
put this values in (*) and(**) :
2(4)+7(8) =1 62=1 false
8=4(4)-8 8=8 true
so :(4;8) is not solution for this system.
2/3 times 4/7 Plz thx
Answer:
8/21
Brainliest? :)
Step-by-step explanation:
does anyone know how to get these dumb restrictions off this chromebook
Answer:
You must force restart the chromebook. It is probably a school computer so you wont be able to get the software/extenstions back. Sadly there is nothing you can do. If you have another computer you can use Chrome remote desktop to connect to it and control it.
Lines AB and CD are straight lines. Find x and y. Give reasons to justify your solution
Answer:
x = 18
y = 54
Step-by-step explanation:
90 - 72 = 18
18 + 2x = 3x
18 = x
2(18) = 36
3(18) = 54
72 + y + 54 = 180
126 + y = 180
y = 54
Answer:
54
Step-by-step explanation:
could you explain this to me and tell me the answer. Thank you so much!!
Answer:1+3=4 4+2=6 5+6=11
Step-by-step explanation:
Answer:
1+3=4, 2+4=6, 5+6=11
Step-by-step explanation:
when made into a cube, (assuming 2 is on the top,) 1 is on the left side and 3 is on the right. 2 is on the top and 4 is on the bottom. 5 is on the north side (the front I guess, but north is the way I can explain it best) and 6 is on the south (the back).
what is ─7 ─ 4b = ─5b sovled for the variable
Answer:
b = 7
Step-by-step explanation:
Add 4b to both sides
You then get -b = -7
You want to multiply both sides by -1 because you can't have a negative variable
Answer:
b = 7
Step-by-step explanation:
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What is an equation of the line that passes through the points (-5, 4) and (5, -8)?
Answer:
Y= -1.2x-2
Step-by-step explanation:
17.75X + 24 = 18.95x + 18
i need bro with this problem
Answer:
what is the question ????
PLEASE HELP IT'S ON A TEST!
What is an equation of the line that passes through the point (2, 4) and is perpendicular to the line whose equation is y = 2x + 1?
Answer:
y=-1x+6
Step-by-step explanation:
desmos
i feel happy after 3 years of being emotionless. witch proportion can be used to solve the following percent problem? what is 50% of 70?
a. x/70=50/100
b. x/50=70/100
c. 50/70=x/100
d. 70/x=50/100
34 points for answering
Please help me with this question and explain it
Answer:
(1, 1)
Step-by-step explanation:
Multiply x and y by 0.25 to find the new coordinates after dilation
solve for x.
√x + 20 = 9
possible answers:
17
61
81
101
Answer: 61
Step-by-step explanation:
[tex]\sqrt{x+20}=9\\\\x+20=81\\\\x=\boxed{61}[/tex]
The value of x will be 61.
What is mathematical expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mathematical expression is,
⇒ √x + 20 = 9
Now,
Solve the expression for the value of x as;
The mathematical expression is,
⇒ √x + 20 = 9
Take square on both side, we get;
⇒ (√x + 20 )² = 9²
⇒ x + 20 = 81
Subtract 20 both side, we get;
⇒ x + 20 - 20 = 81 - 20
⇒ x = 61
Therefore, The value of x will be 61.
Learn more about the mathematical expression visit:
https://brainly.com/question/16583268
#SPJ2
1.43 x 10 to the 9 power
Answer:
1430000000
Step-by-step explanation:
The graph of a function is shown: scatterplot of the following points: negative 3 and 2, negative 2 and negative 1, 2 and negative 1, and 3 and 3 Which of the following correctly identifies the set of outputs? (4 points)
A. {−3, −2, 3}
B. {−1, 2, 3}
C. {(−3, 2), (−2, 1), (3, 3), (3, −1)}
D. {(2, −3), (1, −2), (3, 3), (−1, 3)}
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
i did flvs
PLEASE PLEASE PLEASE HELP ME!!!!!!!!!!!!!
Answer:
c
Step-by-step explanation:
the graph has a y intercept of (0, -4) and a slope of 3
the equation is y = 3x - 4
Which ordered pair is part of the solution set of the inequality 5-y5-3x? Oa (3,-5) Ob. (-3,-5) Oc. (2,-1) Od (-2,-1)
Answer:
ob
Step-by-step explanation:
need to know how to find the area of this figuer
What is a term I’m doing this math
Answer:
A term is one part of an equation in math, for example 9x+2x=3. a term would be 9x
Step-by-step explanation:
I need help dividing these decimal numbers
1. 4.75 ÷ 5 =
2. 0.5 ÷ 2 =
3. 10.26 ÷ 2 =
4. 0.36 ÷ 9 =
5. 0.4 ÷ 20 =
6. 3.5 ÷ 7 =
7. 0.88 ÷ 4 =
8. Kari is making copies at a local copy store of the program for her school play. She makes 52 copies and the total cost is $6.24. How much did the store charge her per copy?
9. Janelle cuts a piece of rope that is 20.44 feet long into four equal sections. How long is each new section of rope?
10. Camden's mom pays $206.45 for him to go to camp each summer. If the camp is five days long, how much does each individual day cost?
Answer:
1.) 0.95
2.) 0.25
3.) 5.13
4.) 0.04
5.) 0.02
6.) 0.5
7.) 0.22
8.) 0.12 cents
9.) 5.11 feet long
10.) $41.29 per day
Step-by-step explanation:
what is the smallest six-digit number you can make that is divisible by five
Answer:
100000
Step-by-step explanation:
Maths class
Answer:
500.000 cos it's firstly multiplies by 5
What is square root of 144
Find the regression equation, letting the first variable be the predictor (x) variable. Find the best predicted Nobel Laureate rate for a country that has 78.8 Internet users per 100 people. How does it compare to the country's actual Nobel Laureate rate of 2 per 10 million people
The table is missing, so i have attached it.
Answer:
Regression equation is;
y = 0.2028x - 8.443
The predicted value is not at all close to the actual novel rate
Step-by-step explanation:
The internet users will be the x-values while the novel laureates will be the y-values.
Thus, sum of x values is;
Σx = 79.5 + 79.6 + 56.8 + 67.6 + 77.9 + 38.3 = 399.7
Sum of y values is;
Σy = 5.5 + 9 + 3.3 + 1.7 + 10.8 + 0.1
Σy = 30.4
Σx² = 79.5² + 79.6² + 56.8² + 67.6² + 77.9² + 38.3²
Σx² = 27987.71
Σy² = 5.5² + 9² + 3.3² + 1.7² + 10.8² + 0.1²
Σy² = 241.68
Σxy = (79.5 × 5.5) + (79.6 × 9) + (56.8 × 3.3) + (67.6 × 1.7) + (77.9 × 10.8) + (38.3 × 0.1)
Σxy = 2301.16
The regression line will be;
y = b1(x) + b0
b1 is expressed as;
b1 = [nΣxy - (Σx • Σy)]/[nΣx² - (Σx)²]
Where n is number of given data which is n = 6.
Thus;
b1 = [(6 × 2301.16) - (399.7 × 30.4)]/[(6 × 27987.71) - (399.7)²]
b1 = 1656.08/8166.17
b1 = 0.2028
b0 is expressed as;
b0 = [(Σy • Σx²) - (Σx • Σxy)]/[nΣx² - (Σx)²]
b0 = [(30.4 × 27987.71) - (399.7 × 2301.16)]/[(6 × 27987.71) - (399.7)²]
b0 = -68947.268/8166.17
b0 = -8.443
Thus, regression equation is;
y = 0.2028x + (-8.443)
y = 0.2028x - 8.443
Best predicted value is given as;
y¯ = (Σy)/n
y¯ = 30.4/6
y¯ = 5.067 per 10 million people.
The predicted value is far greater than the actual value of 2 per 10 million people.
Thus, we can say that the predicted value is nowhere close to the actual value
Which equation results from isolating a radical term and squaring both sides of the equation for the equation /c - 2 - /c=5?
Answer:
D. c - 2 = 25 + c + 10√c
Step-by-step explanation:
Hope this helps!! Have a great day!! ❤
10 points solve ASAP!!!! Solve for x:
-8x + 10 = 82
a
x = 9
b
x = -9
c
x = 92/8
d
x = -92/8
Answer:
The answer should be b: x=-9
Answer:
b. -9
Step-by-step explanation:
-8x+10=82
-10 -10
-8x=72
divide both side by -8
x=-9
A four-digit perfect square number is created by placing two positive two-digit perfect square numbers next to each other. What is the four-digit square number?
Answer:
1681
Step-by-step explanation:
In a four digit perfect square, the first two digits and last two digits taken seperately are also perfect squares.
Therefore, the answer is 1681 because 1681=41*41 and
16=4*4 and 81=9*9
Number 7 thanks ASAP ASAP
Answer:
Price is $1088 (agrees with answer B)
Step-by-step explanation:
Notice that the linear equation that represents this relationship can be estimated via finding the slope and y-intercept using a couple of the given points on the plane (for example (5, 140), and (10, 200), which results in;
Price = 12 x + 80
where "x" is the number of computers shipped.
Then, to ship 84 computers, we have the following price:
Price = 12 (84) + 80 = 1088
Then the price is $1088.