The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
How to convert sine of an angle to some angle of cosine?We can use the fact that:
[tex]\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)[/tex]
to convert the sine to cosine.
Which trigonometric functions are positive in which quadrant?In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.In second quadrant(π/2 < θ < π), only sin and cosec are positive.In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)
Here, the given function is:
[tex]y= 3\cos(2(x + \pi/2)) - 2[/tex]
The options are:
[tex]y= 3\sin(2(x + \pi/4)) - 2[/tex][tex]y= -3\sin(2(x + \pi/4)) - 2[/tex][tex]y= 3\cos(2(x + \pi/4)) - 2[/tex][tex]y= -3\cos(2(x + \pi/2)) - 2[/tex]Checking all the options one by one:
Option 1: [tex]y= 3\sin(2(x + \pi/4)) - 2[/tex][tex]y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2[/tex]
(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.
This option if would be true, then from option 1 and this option, we'd get:
[tex]-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0[/tex]
which isn't true for all values of x.
Thus, this option is not same as the given function.
Option 3: [tex]y= 3\cos(2(x + \pi/4)) - 2[/tex]The given function is [tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]
This option's function simplifies as:
[tex]y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2[/tex]
Thus, this option isn't true since [tex]\sin(2x) \neq \cos(2x)[/tex] always (they are equal for some values of x but not for all).
Option 4: [tex]y= -3\cos(2(x + \pi/2)) - 2[/tex]The given function simplifies to:[tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]
The given option simplifies to:
[tex]y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2[/tex]
Thus, this function is not same as the given function.
Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
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Answer:
a
Step-by-step explanation:
Which of the following rational functions is graphed below?
5
10
A. F(X) =
OB. F(x)=
O C. F(x) =
D. F(X) =
(x + 1)
(x + 2)(x-2)
(x+1)
(x-1)(x+2)
2x
x(x - 2)
(x-1)
x(x-2)
ڈے
Answer:
B. F(x) = (x+1)/(x-1)(x+2)
Step-by-step explanation:
See attached graph. Note how the two vertical lines at x = -2 and 1 match plot B
The following graph is of the rational function [tex]F(x) = \frac{x+1}{(x-1)(x+2)} \\[/tex]
What are asymptotes?
An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance.
The rational function does not exist at x = 1 and x = -2 ( as observed in graph). Thus, the denominator of the function consist (x-1) and (x+2). It is only in option B, thus it is correct.
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Gary has 24 sweets. He eats 3/8 of them.
Ben has 30 sweets. He eats 2/5 of them. Who has the most sweets left?
no of sweet gave to peny is 24×3/8 = 9 sweets
rest was ate by him
so the sweet ate by him is 24-9 = 15 sweet
hope this helps you kindly mark me as brainliest and follow me
Based on the amount of sweets eaten by Gary and Ben, the person with more sweets left is Ben.
Who has more sweets left between Ben and Garry?The sweets left by Gary are:
= 24 - (24 x 3/8)
= 24 - 9
= 15 sweets
The sweet left by Ben are:
= 30 - (2/5 x 30)
= 30 - 12
= 18 sweets
In conclusion, Ben has more sweets left.
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I NEED THIS ASAP!!
Solve for X and find the angle relationship!!
(WILL GIVE BRAINIEST)
THIS IS RLY IMPORTANT
Answer:
Vertical anglesx = 1484°Step-by-step explanation:
The indicated angles are vertical angles since formed by two intersecting lines.
We know the vertical angles are congruent. Use this property to find the value of x and the angle measure
6x = 3x + 426x - 3x = 423x = 42x = 42/3x = 14The angle measure
6*14 = 84Opposite angles are equal
6x=3x+426x-3x=423x=42x=42/3x=14Answer number 6 pleaseeeee
Answer:
20 peopleStep-by-step explanation:
25% = 1/4 of 100
100 represents 200 people here, that means that if 25 = 1/4 to 100, then it is 1/8 to 200. 25x8=200
If 25% = 50, since 50x4=200 and 1/4 = 25% of 100%.
50... ok......
50 = 25%
Now, because there are 5 parts in 25, let's divide 5 by 50, that is 10. That means that 5 = 10 in that 50. 5% = 10 people
So, if 25-15=10
and then 5% = 10 people
5%+5%=10
10+10=20
That means, that 20 people more liked the movie than disliked it.
Which expression is equivalent to cube root of 216 x superscript 27 ? 6x3 6x9 72x3 72x9
The expression which is equivalent to cube root of 216 x superscript 27 is 6 times 3 (6x3).
How to find the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
To find the equivalent expression, simplify the given equation with the help of mathematical operations.
The expression given in the problem is,
[tex]\sqrt[3]{216\times {27}}[/tex]
Let the expression which is equivalent to the above expression is n. Thus,
[tex]n=\sqrt[3]{216\times {27}}\\n=\sqrt[3]{216}\times \sqrt[3]{27}\\n=\sqrt[3]{6\times6\times6}\times \sqrt[3]{3\times3\times3}\\n=6\times3[/tex]
Thus, the expression which is equivalent to cube root of 216 x superscript 27 is 6 times 3 (6x3).
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Answer:
A
Step-by-step explanation:
What is the range of possible sizes for side x?
Ur mommy may know this
Step-by-step explanation:
she has been to school right?
If one mile is aprox 1.6 kilometers the how many miles is the race
What is the equation of the line that passes through the point (8,-6) and has a
slope of o?
The slope or gradient has this formula when two points are given: m = y1 −y x1 −x In this case we have the points (-6,-8) and (-7,y) and m=-8.
You are considering buying the house next to your home in order to fix it up and
sell it to make a profit. Ypu estimate that you will need to invest about $8,000 to
make necessary repairs and upgrades. After these improvements, you should
be able to sell it for $215,000. If the general guideline for flipping is to buy at
least 20% below the market value, what is the most you should be willing to pay
for the home?
Answer:
s
Step-by-step explanation:
Which represents a perfect cube? 6 times 6 times 6 6 6 6 3 times 3 times 3 times 3 3 3 3 3 3
The expression that represents a perfect cube is expressed as: 6 × 6 × 6
What is a Perfect Cube?A perfect cube, x, is such that x × x × x = x³ = ∛x.
Thus, we have:
6 × 6 × 6 = 216
Cube root of 216 = ∛216
∛216 = 6
We can then conclude that the expression that represents a perfect cube is: 6 × 6 × 6
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Answer:
6x6x6
Step-by-step explanation:
Which letter will correspond to the location of the following points when plotted on the number line below?
Answer:
A, E, B, D, C
Step-by-step explanation:
1) 6 is A
2) √83 = 9.11, so it is E
3) √40 = 6.3, so it is B
4) √64 = 8, so it is D
5) 7.5 is C
solve the volume for the triangular prism
Answer:
9.5 cubic units
Step-by-step explanation:
You need to multiply everything together and divide by 2.
5 x 2 x 1.9/2 = v
19/2 = v
9.5 cubic units
If 6 and 10 are factors of a number, identify four other factors of the number
Answer:
1 2 3 5
Step-by-step explanation:
1 and 2 go into 6 and 10. 3 goes into 6 and 5 goes into 10
Katie is selling lemonade for $1.50 per cup. She decides to put them on sale for $0.90. What percent discount did she give on her lemonade? *
Answer:
40%
Step-by-step explanation:
1.50 - 0.90 = 0.60
0.60 cents are saved.
[tex]\frac{0.60}{1.50} = 0.4[/tex]
0.4 = 40%
hope this helps :)
Taub missed 14 questions on her multiple choice math final that had a total of 200 problems. What percentage of questions did Taub answer correctly?
Answer:
81%
Step-by-step explanation:
200-38= 162
162/200= 81/100
81%
Answer:
93%
Step-by-step explanation:
100 x 186= 200 * x
18600/200 = 200x/200
93%=x
186/200 = 0.93
convert decimal to percent
0.93 x 100= 93%
Omar wants to simplify the following expression. What should be his first step? 6 x (3 + 9) - 5
*
1 point
Multiply 6 by 3
Subtract 5 from 9
Add 3 to 9
Subtract 5 from 6
Answer:
(c) Add 3 to 9
Step-by-step explanation:
The order of operations tells you that quantities in parentheses are evaluated first.
Here, that means the first step is finding the sum 3+9.
Is 2x 4/3 equal to 4x 2/3
[tex]2x \times \frac{4}{3} = 4x \times \frac{2}{3}[/tex]
[tex] \frac{8x}{3} = \frac{8x}{3} [/tex]
Both are equivalents
A recipe calls for 2/5 cup of sugar for every 3/10 teaspoon of vanilla. What is the unit rate of cups per teaspoon?
Answer:
4/3 cups/tsp
Step-by-step explanation:
You want cups / tsp = 2/5 c / 3/10 tsp = 2/5 * 10/3 c/tsp = 20/15 = 4/3
Help me plssss!
[tex]-124x+102=-126x-90[/tex]
Answer:
x=-96
Step-by-step explanation:
isolate x by moving -124x to the other side by adding -124x to -126x = -2x
then it will look like: 102= -2x-90
add 90 to both sides: 192= -2x
divide both sides by -2 to isolate x
x= -96
Which products result in a difference of squares? select three options. (x minus y)(y minus x) (6 minus y)(6 minus y) (3 x z)(negative 3 x z) (y squared minus x y)(y squared x y) (64 y squared x squared)(negative x squared 64 y squared)
The three (3) products that resulted in a difference of squares are:
(3 + xz)(-3 + xz) (y² - xy)(y² + xy)(64y² + x²)(-x² + 64y²)How to determine the difference of squares?In Mathematics, the standard form for a difference of two (2) squares is given by a² - b² = (a + b)(a - b).
(3 + xz)(-3 + xz) = (3 + xz)(xz -3)
(3 + xz)(xz -3) = 3xz - 9 + x²z² - 3xz.
(3 + xz)(xz -3) = x²z² - 9
Therefore, x²z² - 9 ≡ a² - b²
(y² - xy)(y² + xy) = y⁴ + xy³ - xy³ - x²y²
(y² - xy)(y² + xy) = y⁴ - x²y²
Therefore, y⁴ - x²y² ≡ a² - b².
(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²)
(64y² + x²)(-x² + 64y²) = 4096y⁴- 64y²x² + 64y²x² - x⁴
(64y² + x²)(-x² + 64y²) = 4096y⁴ - x⁴
Therefore, 4096y⁴ - x⁴ ≡ a² - b².
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Answer:
Step-by-step explanation:
p.557(3-6 all): Similar Triangles and Indirect Measurement
I need helppp :/ please
Answer:
3. 200ft
4. 21ft
5. 37.5m
6. 4.2ft
Step-by-step explanation:
3. use proportions:
[tex]\frac{h}{50} = \frac{50}{12.5}[/tex]
50(50) = 12.5h
h = 200ft
4.
[tex]\frac{h}{6} =\frac{7}{2}[/tex]
6(7) = 2h
h = 21ft
5.
[tex]\frac{25}{8} =\frac{x}{12}[/tex]
25(12) = 8x
x = 37.5m
6.
[tex]\frac{9}{15} =\frac{h}{7}[/tex]
9(7) = 15h
h = 4.2ft
The histogram shows the distribution of heights, in inches, of 100 adult men.
6 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
Height (inches)
Based on the histogram, which of the following is closest to the interquartile range, in inches, of the distribution?
2
B
5
9
D
D
12
15
Based on the histogram, the interquartile rangle of the distribution is 5 inches.
What is the interquartile range?The interquartile range is the difference between the third quartile of a data set and the first quartile of the data set.
First quartile = 1/4 x ( n + 1)
= 101 / 4 = 25.25
25.25 on the histogram is 66
Third quartile = 3/4 x (n + 1)
303 / 4 = 75.75
75.75 on the histogram is 71
Interquartile range = 71 - 66 = 5
Please find attached the image of the histogram. To learn more about histograms, please check: https://brainly.com/question/14473126
Simplify the following.
I need to see a step by step answer on both questions to see how it actually works.
Answer:
See below ~
Step-by-step explanation:
27. (B)
3a/5b + 4a/15bTake the LCM to be 15b3a(3) + 4a / 15b13a/15b27. (C)
(3²)³ × 3⁰ ÷ 3⁴3⁶ x 1 ÷ 3⁴3²3 x 39Answer:
1,
[tex] \frac{13a}{15b} [/tex]
2,
[tex]9[/tex]
Step-by-step explanation:
[tex] \frac{3a}{5b} + \frac{4a}{15b} [/tex]
[tex] \frac{45a}{75b} + \frac{20a}{75b} [/tex]
[tex] \frac{13a}{15b} [/tex]
2,
[tex] {3}^{6} \times {3}^{0} \div {3}^{4} [/tex]
[tex]729 \times 1 \div 81[/tex]
[tex]729 \div 81 = 9[/tex]
5. In the given sequence 32, 28, 24, 20, What rule is applied?
a. 10[tex]n[/tex]
b. 4[tex]n[/tex]
c. [tex]n[/tex]- 4
d. ([tex]n[/tex]+ 5) / 8
Answer:
C
Step-by-step explanation:
A number is n, therefore you can start off with 32 and subtract 4 getting you 28. Subtract 4 and you get 24, and again 20.
please help me...asap
Answer:
Your answer is D. 5 children, 12 teens, and 3 adults.
Step-by-step explanation:
45 children, 108 teens, and 27 adults.
x - children , y-teens, z-adults
45x + 108y + 27z
GCF for 45, 108, 27 is 9 so factory out 9 to all.
[tex]\frac{45}{9} ,\frac{108}{9} ,\frac{27}{9} \\5,12,3[/tex]
5 children, 12 teens, and 3 adults.
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{It seems like all of your numbers are apart of the 9 factors. So, we will }\\\large\text{DIVIDE each of your numbers by 9 until we find out the total}\\\large\text{population (also known as your result to this equation)}[/tex]
“[tex]\large\text{45 children, 108 teens, \& 27 adults}[/tex]”
[tex]\large\textbf{Equation \# 1.}\\\\\large\boxed{\rm{\dfrac{45\ children}{9\ children}}}\\\\\\\large\boxed{= \rm{45 \ children \div 9 \ children}}\\\\\\\large\boxed{\rm{= 5\ children\ in\ total}}[/tex]
[tex]\large\textbf{Equation \# 2.}\\\\\large\boxed{\rm{\dfrac{108\ teens}{9\ teens}}}\\\\\\\large\boxed{= \rm{108\ teens \div 9 \ teens}}\\\\\\\large\boxed{= \rm{12 \ teens \ in \ total}}[/tex]
[tex]\large\textbf{Equation \# 3.}\\\\\\\large\boxed{\rm{\dfrac{27\ adults}{9\ adults}}}\\\\\\\large\boxed{\rm{= 27\ adults \div 9 \ adults}}\\\\\\\large\boxed{\rm{= 3\ adults\ in\ total}}[/tex]
[tex]\huge\textbf{Therefore, your answer is:}\\\\\huge\boxed{\textsf{Option D. 5 children, 12 teens, 3 adults}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the equation of the lines a and b
Step-by-step explanation:
A ) 3x-2
B ) -4x+5
I HOPE IT HELPED YOU
Solve 2(9-x) = 3 ( x +16 )
Answer: x=-6
Step-by-step explanation:
Let's solve your equation step-by-step.
2(9−x)=3(x+16)
Step 1: Simplify both sides of the equation by distribution
[tex]2(9-x)=3(x+16)\\(2)(9)+(2)(-x)=(3)(x)+(3)(16)\\18+-2x=3x+48\\-2x+18=3x+48\\[/tex]
Step 2: Subtract 3x from both sides.
[tex]-2x+18-3x=3x+48-3x\\-5x+18=48[/tex]
Step 3: Subtract 18 from both sides.
[tex]-5x+18-18=48-18\\-5x=30[/tex]
Step 4: Divide both sides by -5.
[tex]\frac{-5x}{-5} =\frac{30}{-5} \\x=-6[/tex]
One of the diagonals of a rhombus is 15 cm long. if the rhombus has an area of 60 cm², find the length of the other diagonal.
Answer:
8.5
Step-by-step explanation:
area of a rhomus = (1/2)(product of its diagonals)
let the other diagonal be a
(1/2)(15a) = 60
15a= 120
a = 8
So let's find the hypotenuse of one of the right-angled triangles formed by the intersection of its diagonals
base = 4, height = 7.5
if h is the hypotenuse,
h^2 = 4^2 + 7.5^2
h = 8.5
Solve for x . 8x-3 & 4x+3
8x-3+4x+3=180
?x+_=180
Answer:
x = 15
Step-by-step explanation:
the 2 angles are a linear pair and sum to 180° that is
8x - 3 + 4x + 3 = 180
12x = 180 ( divide both sides by 12 )
x = 15
The angles are supplementary angles. Then the value of the variable 'x' will be 15.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The angles are 8x - 3 and 4x + 3. And they are supplementary angles. Then the equation is given as,
8x - 3 + 4x + 3 = 180
Simplify the equation, then we have
8x - 3 + 4x + 3 = 180
12x + 0 = 180
x = 15
The angles are supplementary angles. Then the value of the variable 'x' will be 15.
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Identify the slope and y-intercept of each of the following lines. Then graph each line.
y = 5
Answer:
Below!
Step-by-step explanation:
Since the "y" variable is on the L.H.S, we can rewrite y = 5 in slope intercept form to determine the slope and the y-intercept.
⇒ y = 5⇒ y = 0x + 5Now, let's compare the equation of the line with the formula.
⇒ y = 0x + 5 and y = mx + bThus, we will obtain the following equations:
⇒ y = y⇒ m (Slope) = 0⇒ x = x⇒ b (Y-intercept) = 5============================
Thus, the slope is 0 and the y-intercept is 5. Since the slope is 0, the line will be a horizontal line that intersects the y-intercept.
In this case, the y-intercept is 5. Thus, the line will be a horizontal line, intersecting the y-intercept (5). (Refer to graph).
If we simplify
y=0x+5Hence..
slope=m=0y inetrcept=5Graph attached