Answers
Answer:
2. ☑ A [tex]\displaystyle f(x) = tan\:\frac{1}{2}x[/tex]
☐ B [tex]\displaystyle f(x) = tan\:2x[/tex]
☐ C x = [tex]\displaystyle 2tan\:x[/tex]
1. ☐ A [tex]\displaystyle \frac{\pi}{2}[/tex]
☐ B [tex]\displaystyle \pi[/tex]
☑ C [tex]\displaystyle 2\pi[/tex]
Explanation:
[tex]\displaystyle \boxed{f(x) = -cot\:(\frac{1}{2}x - \frac{\pi}{2})} \\ \\ y = Acot(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A[/tex]
OR
[tex]\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A[/tex]
Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS the tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cot\:\frac{1}{2}x,[/tex] in which you need to replase "tangent" with "cotangent", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cotangent graph [photograph on the right] is shifted [tex]\displaystyle \pi\:units[/tex] to the left, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \pi\:units,[/tex] which means the C-term will be positive, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pi} = \frac{\frac{\pi}{2}}{\frac{1}{2}},[/tex] but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is [tex]\displaystyle y = -cot\:(\frac{1}{2}x - \frac{\pi}{2}).[/tex] Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are [tex]\displaystyle -\pi = x\:and\:\pi = x.[/tex] From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{2\pi} = \pi + \pi.[/tex] So, the period of this function is [tex]\displaystyle 2\pi.[/tex] Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = 0.[/tex]
Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.
I am delighted to assist you at any time.
Related Questions
Hello! I’ll take any help !!
Answers
Answer:
√73
Step-by-step explanation:
a^2+b^2=c^2
8^2+3^2=c^2
64+9=c^2
√73 =√c^2
√73 =c
Problems 1 - 6, evaluate each expression for the given values of the variables.
1 5a + 4b - 3a - 7b+ 4a; a = -3 and b = 4
2. c6-1)-cm; b=5 and c= -2
3. 5x – 2xy + 3y: x=-5 and y=-2
4. -K -(7k - 4m); k=-2 and m = 4
5. 3(6x + 5y) - 2y: x = 3 and y=-3
6. 5(3m – n) – 4(2m- n); m=-8 and n=-11
Problems 7 - 14, combine like terms and simplify completely
Answers
Step-by-step explanation:
1) 5a+4b-3a-7b+4a
Add terms having 'a' and 'b' separately
=6a-3b
Now subtitute values of a and b :
=6(-3)-3(4)
=-18-12
=-30
2)c(6-b)-c²
=6c-bc-c²
Subtitute values of b and c:
= 6(-2)-(5)(-2)-(-2)²
=-12+10-4
=-6
3)5x²-2xy+3y
Subtitute values of x and y:
=5(-5)²-2(-5)(-2)+3(-2)
=5(25)-20-6
=125-20-6
=99
4)-k²-(7k-4m)
Subtitute values of m and k:
=-(-2)²-{7(-2)-4(4)}
=-4-(-14-16)
=-4-(-30)
=-4+30
=26
5)3(6x+5y)-2y
Subtitute values of x and y:
=3{6(3)+5(-3)}-2(-2)
=3(18-15)+4
=3(3)+4
=9+4
=13
6)5(3m-n)-4(2m-n)
Subtitue values of m and n:
=5{5(-8)-(-11)}-4{2(-8)-(-11)}
=5(-40+11)-4(-16+11)
=5(-29)-4(-5)
=-145+20
=-125
Note:If you have any question about it you can friendly ask.Thanks
please help me with this ixl it would be much appreciated
Answers
Answer:
q=2,6
r=8,6
s=8,10
t=2,10
Answer:
Q= (-2, -6)
R= (-8, -6)
S= (-8, -10)
T= (-2, -10)
Step-by-step explanation:
Since the rotation is 180 degrees, change all of the numbers to the opposites/negatives.
Then, since the rotation is counterclockwise, switch all of the x and y values.
I hope this helps!
pls ❤ and mark brainiest pls!
a tank is 4÷5 full of water. after drawing off 190 litees of water,it is just 1÷6 full. what is the capacity of the tank
Answers
Hey there! I'm happy to help!
Let's have the capacity be c. The tank is currently at 4/5c. We subtract 190 and then we are at 1/6c. Let's set this up as an equation and solve it.
4/5c-190=1/6c
We want to get the c all by itself to see the capacity of the tank. Let's get all of the c values on the left side of the equation and the numbers on the right by using inverse operations.
4/5c-190=1/6c
Add 190 to both sides.
4/5c=1/6+190
Subtract 1/6 from both sides.
19/30c=190
Divide both sides by 19/30.
c=300
So, the capacity of the tank is 300 liters of water.
Have a wonderful day and keep on learning! :D
what is 2 ÷ 3 = as a fraction???
Answers
Answer:
[tex]2 \div 3 \\ \frac{2}{3} [/tex]
Can someone plzzz explain.
Why do you only need a single counterexample to show that a conditional statement is false?
Answers
Answer:
For a conditional (if-then) statement, a counterexample must be an instance which satisfies the hypothesis , but not the conclusion .
Step-by-step explanation:
How many solutions does the system have?
8x + 2y = 14
82 + 2y = 4
Answers
you can solve the equestion by many rules , but in my point of view the easiest rule is subtraction/addition and subtition method .
Ans X=11.5
Y = -39
8x+2y=14 eqn.......1
82+2y=4 eqn .......2
2y= -78 (4-82)
y = - 39
putting value of y in eqn ..1
we get,
8x+ 2×(-39) =14
8x= 14+78
8x=92
x = 92÷8
x=11.5
it's a subtition method..
Joey’s brother is 4 years younger than twice his age. If the sum of their ages is 8. How old is Joey?
Answers
1,7,5,3,6,2
J+B=8
J=6
Joey is 6
5. Mrs. Perkins hosts a birthday party for her son and 7 guests. She orders 2 cookies and a
cupcake for each child. The cost of the cupcake is $2.75, and the total bill is $46.00. What is the
cost of a cookie?
Answers
Answer:
Below.
Step-by-step explanation:
In total there are 8 kids. Each cupcake is 2.75 so 8x2.75= 22 now the total is 46.00 So? 46-22 = 24. 24 divided by 2 = 12.
I Divided by 12 because they said cost of each individual cookie.
Answer:
$1.375
Step-by-step explanation:
7guests + 1son = 8children
8 (children) x 2.75 (dollars-per-cupcake) = 22
46 (total cost) - 22 (dollars spend on cupcakes) = 24
24 (left) / 16 (number of cookies needed (each child gets two)) = 1.375
Please help I will mark brainlyest thank you
Answers
Answer:
3
Step-by-step explanation:
the reason being, is that three is the most repeated number (it is repeated 6 times!)
hope this helps!!
Answer:
The Tables Mode is: 3
Step-by-step explanation:
Mode is the number in a table or set of data that appears most. In this case, there are 6 number 3's, 4 number 6's, and 3 number 0's. But the number with the most is 3. So that is your answer.
Hope this helped! Let me know if you have any questions! :)
Jade purchased a game controller for $14.65 including tax. How much did she get from a twenty-five dollar bill?
Answers
Answer:
$5.35
Step-by-step explanation:
20-14.65=5.35
geometry #1 please will give brainliest
Answers
Step-by-step explanation:
If two lines, segments, or rays intersect at right angles, then they are perpendicular. If two angles are complementary, then their measures add up to 90 degrees. If two angles' measures add up to 90 degrees, then they are complementary. If two angles are supplementary, then their measures add up to 180 degrees.
[tex]f(x) = 2x^{2} +5x-2[/tex]
Answers
Answer:
[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5} [/tex]
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} + 5x - 2[/tex]
[tex]f(x) = 2( {x}^{2} + \frac{5}{2} x) - 2[/tex]
[tex]f(x) = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2[/tex]
[tex]f(x) + 2 \times \frac{25}{16} = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2[/tex]
[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - 2 - \frac{25}{8} [/tex]
[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5} [/tex]
step by step
6x+1<9-2x
2x-1 less than or equal to 5x+20
3-(2x-7) less than or equal to 34-6x
Answers
Answer:
6x+1<9-2x
6x+2x<9-1
8x<8
x<1
2x-1 ≤ 5x+20
2x-5x≤20+1
-3x≤21
x≥-7
3-(2x-7) ≤ 34-6x
3-2x+7 ≤ 34-6x
-2x+6x ≤ 34-3-7
4x ≤ 24
x ≤ 6
How many solutions are there to the equation below?
6x+8 - 2x(7 - 2) = 2(6+1)
A. 0
B. 1
C. infinitely many
Answers
Answer:
B one solution
Step-by-step explanation:
Answer:
B - one solution
Step-by-step explanation:
6x+8−2x(7−2)=2(6+1)
Subtract 2 from 7 to get 5.
6x+8−2x×5=2(6+1)
Multiply 2 and 5 to get 10.
6x+8−10x=2(6+1)
Combine 6x and −10x to get −4x.
−4x+8=2(6+1)
Add 6 and 1 to get 7.
−4x+8=2×7
Multiply 2 and 7 to get 14.
−4x+8=14
Subtract 8 from both sides.
−4x=14−8
Subtract 8 from 14 to get 6.
−4x=6
Divide both sides by −4.
x=−46
Reduce the fraction −46 to lowest terms by extracting and canceling out 2.
x=−23
hope it helps :)
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
5y=4x+2
Step-by-step explanation:
First the slope, the slope is 4/5. Using the slope intercept form, the line of equation is y-2=(4/5)(x-2), 5y-10=4x-8, 5y=4x+2
Solve for X: -2x - 4 > 7
(9th grade Algebra 1)
Answers
Answer:
x is less than -6
Step-by-step explanation:
Add 4 to both sides
-2x is greater than 12
Divide both sides by -2 and don't forget to change the sign
x is less than -6
Answer:
x < - 6
Step-by-step explanation:
Given
- 2x - 4 > 8 ( add 4 to both sides )
- 2x > 12
Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
x < - 6
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
Answers
Answer:
The first choice.
Step-by-step explanation:
It pass through the x axis at x = 3, so a factor must be (x - 3).
Answer:
The first option is correct :)
~Hope this helps
can someone answer these 2 questions
Answers
Explanation:
1).
a. f(1) = 2(1)^2 - 3(1) + 1
= 2 - 3 + 1
= 0
b. g(2) = 4(2) - 2
= 8 - 2
= 6
c. f(-3) = 2(-3)^2 - 3(-3) + 1
= 2(9) + 9 + 1
= 28
d. f(-4) = 2(-4)^2 - 3(-4) + 1
= 2(16) + 12 + 1
= 45
2).
When x = -8
y = -3/4x + 2
= -3/4(-8) + 2
= 6 + 2
= 8
When x = -4
y = -3/4(-4) + 2
= 3 + 2
= 5
When x = 0
y = -3/4(0) + 2
= 2
When x = 4
y = -3/4(4) + 2
= -3 + 2
= -1
A plane traveled 1000 miles each way to Albuquerque and back. The trip there was with the wind. It took 10 hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?
Answers
100 mph going there, 50 coming back
Hellpp pleaseeeeeeee
Answers
Answer:
4th option
Step-by-step explanation:
The translation shifts Δ ABC → Δ A'B'C'
Consider the x- coordinates of A and A'
A has x- coordinate 1
A' has x- coordinate - 3
Then 1 to - 3 is a shift of 4 units left
Answer:
4 units lefts
Step-by-step explanation:
First you have to take 2 similar points, we will take A' and A and counts the squares between them. Since the dashed A is the new translation, we know the translation is left, all we do now is count the squares which is 4.
A puppy gained 1/2 ounce in weight every day. At this rate, how long did it take the puppy to gain 16 ounces?
Answers
Answer:
It took 32 days into the puppy was 16 ounces
Step-by-step explanation:
i hope this was helpful
Answer:
32 days to gain 16 ounce
Step-by-step explanation:
I. If y = [tex]\frac{1}{2}x[/tex]
when y is total weight, x is day
Perform 16 = 1/2x
16 * 2 = x
x = 32
Write 81 in exponential form
Answers
Answer:
3 exponent 4
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\bullet\rm{\ Exponential\ form \ is \ basically \ a \ number \ that \ is \ expressed \ within \ the \ exponent.}[/tex]
[tex]\star\rm{\ Example: a^b, whereas\ \underline{a} \ is \ the \ \bold{base} \ \& \ \underline{b} \ is \ the \ \bf exponent}[/tex]
[tex]\huge\boxed{\square }\huge\textsf{ Answering your question }\huge\boxed{\square{}}[/tex]
[tex]\large\boxed{= 81}[/tex]
[tex]\large\boxed{= 3 \times3 \times 3 \times3}[/tex]
[tex]\large\boxed{= 9\times9}[/tex]
[tex]\large\boxed{= \bf 3^4}[/tex]
[tex]\huge\boxed{\mathsf{\rm Answer: \mathsf{3^4}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A new cars salesperson, sold an average of $32,130 per day for the first 4 days she worked. The next 5 days she worked, she sold an average of $31,173. How much did she sell on average per day over the entire time she worked??
Answers
Answer:
$31,598.33
Step-by-step explanation:
she worked 4+5=9 days.
due the total average we need the total of sales and divide it by the length of the observation period (9 days).
how much did she sell in total on the first 4 days ?
well, the average times 4 = 32130×4 = $128520
how much did she sell in total during the following 5 days ?
31173×5 = $155865
so, the daily average is
($128520 + $155865) / 9 =$284385 / 9 = $31,598.33
a) If 8 workers can complete a piece of work in 18 days, how many workers are required to complete the work in 12 days? b) 20 labourers comnloto the . 1 T
Answers
Answer:
12 workers are required to complete the work in 12 days
The function fis defined by f(x) = 5^x. What is the value of f(3)?
O 15
O 25
O 53
O 125
Answers
Answer:
125
Step-by-step explanation:
If the function is f(x) = 5^x and you need to know the value of f(3), you just need to put 3 in place of x:
f(3) = 5^3 = 5•5•5 = 125
1. The volume of a cube is 27 cubic inches. How long is its side? 3
Answers
If I'm not wrong, it should be 27cm^3. Hope this helps!!
Answer:
3
Step-by-step explanation:
[tex]\sqrt[3]{27}[/tex]
So the question is "Write down four common multiples of 2 and 3"
Step by step explaination :(
Answers
Answer:
The common multiples of 2 and 3 are 6,12,18,24
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...
Common multiples of 2 and 3 include 6, 12, 18, and 24.
Reorder the numbers and combine like terms to simplify. 4.5 + 2 1/2 + 6.0 - 5 1/2
A. 8.5
B. 7.5
C. -7.5
D. 7m
Answers
Answer: B
Step-by-step explanation:
4.5+6=10.5
2 1/2 - 5 1/2 = 2.5 - 5.5 = -3
10.5 - 3 = 7.5
Your college professor tells you he will give you a 30%-30%-40% split on grades between homework, quizzes, and test. However which ever category you have the highest average and will be able to 40% category. What will your final grade be if your homework average of 62, your quiz average is 93, and your test average 60?
Answers
Here we want to calculate percentages of different values to find your final grade, we can conclude that your final grade will be 73.8
We know that:
you have an average of 62 in homework
you have an average of 93 on quiz
you have an average of 60 on test.
Your final grade will be a 30%-30%-40% of the above average scores, such that the 40% will be of the highest average.
We can see that the highest one is on quiz, then your final grade will be:
the 40% of your average quiz grade plus the 30% of your average homework grade plus the 30% of your average test grade.
This will be:
[tex]g = \frac{40 \%}{100 \%}*93 + \frac{30 \%}{100 \%}*62 + \frac{30 \%}{100 \%}*60\\\\g = 0.4*93 + 0.3*62 + 0.3*60 = 73.8[/tex]
We can conclude that your final grade will be 73.8
If you want to learn more, you can read:
https://brainly.com/question/19179977