The general equation of a cosine function with an amplitude of 3, a period of 4 π, and a horizontal shift of negative π is [tex]f(x) =3cos(0.5x+\pi )[/tex].
What is a function?A function is a rule that relates two variables.
The parent function is:
[tex]f(x)=cosx[/tex]
We know the period of the parent function is 2π and the amplitude is 1.
For an amplitude of 3, we need to multiply the parent function by 3.
So, the function with amplitude 3 will be given by:
[tex]f(x) =3cosx[/tex]
For a period of 4π, we need to make the argument of the parent function half.
So, [tex]f(x) = 3cos(0.5x)[/tex]
A horizontal shift of negative π means, f(x) will become f(x+π)
So, [tex]f(x) =3cos(0.5x+\pi )[/tex].
Therefore, the general equation of a cosine function with an amplitude of 3, a period of 4 π, and a horizontal shift of negative π is [tex]f(x) =3cos(0.5x+\pi )[/tex].
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Answer:
Option C. y + 3cos (0.5(x+ pi))
:)
Can someone please help me I I’ll give u brainest
Answer:
b. translation, rotation
Step-by-step explanation:
When a shape is translated, that just means nothing about it has changed except it's location on the coordinate plane. This is that happened with shape 1 - it was translated, and that created shape 2.
When a shape is rotated, that just means it is turned (or rotated) at a specific point. This is what happened to shape 2 that changed it to shape 3.
The other two transformations that aren't shown in this specific example are dilation, which means that the shape either shrinks or grows, and reflection, which means that the shape is reflected across the y-axis or the x-axis.
I included a picture with all four transformation examples in it. I hope this helps! Have a lovely day!! :)
(a) Make y the subject of 3y - 2x = 5.
(b) Hence, find the value of y when x= -2.
Answer:
a) 5/2
b) 1/3
Step-by-step explanation:
a) 3y-2x=5 to find the value of y let we replace x by 0
then solve it
Answer:
(a) y = 2/3x + 5/3
(b) y = 1/3
Step-by-step explanation:
(a) Make y the subject of 3y - 2x = 5
3y - 2x = 5
+ 2x + 2x ==> isolate the variable y, by adding 2x to both sides
3y = 2x + 5 ==> divide both sides by three
/3 /3
y = 2/3x + 5/3 ==> y now becomes the subject, or our final answer
(b) Using 3y - 2x = 5 or y = 2/3x + 5/3, find the value of y when x= -2
y = 2/3x + 5/3
y = 2/3(-2) + 5/3 ==> substitute -2 for x
y = -4/3 + 5/3 ==> add the fractions
y = 1/3 ==> the value of y, our final answer
OR
3y - 2x = 5
3y - 2(-2) = 5 ==> substitute -2 for x
3y - (-4) = 5
3y + 4 = 5 ==> --4 makes a +4, the subtract 4 (-4) from both sides
- 4 - 4
3y = 1 ==> divide both sides by 3
/3 /3
y = 1/3 ==> your final answer
Hope this helps!
Juwan and his friend Jamie are watching their favorite tech penny stocks in the stock market. The initial value of Jamie’s stock was $4.00, while Juwan’s stock’s initial value was $0.00. Because of some incredible turns in the market this morning, the stocks are now increasing in value. Every time Juwan’s stock rises by $4.00, Jamie’s stock increases by $3.00. If these stock gains remain constant throughout the day, perform the following:
a. Convert this scenario into two linear equations; show both the standard form and the slope-intercept form for both equations.
b. Explain how you decided to label the axes.
c. What are the realistic bounds for the domain and range of today’s stock gains? Explain your answer.
d. Does this scenario imply correlation or causation? Explain your answer.
Linear equations in slope intercept form for the given scenarios:
Juwan: y = 4x + 4
Jamie: y = 3x
Linear equations in standard form for the given scenarios:
Juwan: y - 4x = 4
Jamie: y - 3x = 0
Where, y = current stock value and x = number of times the stock value increased.
Domain: Set of natural number.
Range: Real number greater than or equal to 0.
This scenario is an example of causation.
What is standard form of line?The standard form of a line is Ax + By = C, where A and B are not both zero.
In the given scenario, we take
y = the present stock value of Jamie and Juwan.
x = number of times the stock value increased.
where, y depends upon x.
Juwan: y - 4x = 4
Jamie: y - 3x = 0
What is slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
Juwan: y = 4x + 4
Slope = 4
y - intercept = 4
Jamie: y = 3x
Slope = 3
y - intercept = 0
What is domain and range?The domain is the set of all the input values of a function and range is the possible output given by the function.
In this particular question, x is the number of times stock price increased. Thus, it can be 0, 1, 2, 3....set of natural number. y is the current stock price. The stock price was positive in the beginning and has been increasing since then, therefore y lies in the set of positive real number.
What is causation?Causation means that one variable causes another to change, which means one variable is dependent on the other. Here, the price of stock depends upon the number of times its value increased.
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Chrissy has some ribbon in her craft room. She has 3/8 yards of purple ribbon and 1 yard of green ribbon.
Chrissy has a total of 3 yards of ribbon.
How many yards of Chrissy's ribbon are neither purple nor green?
The number of Chrissy's ribbon which are neither purple nor green is 1 5/8 yards
How to calculate Chrissy's ribbon which are neither purple nor green?Purple ribbon = 3/8 yardsGreen ribbon = 1 yardTotal yards of ribbon = 3 yardsRibbon which is neither purple nor green = Total - (purple + green)
= 3 - (3/8 + 1)
= 3 - (1 3/8)
= 3 - 11/8
= (24-11) / 8
= 13/8
= 1 5/8 yards.
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Hello, the point (-2,k) lies on the line. Determine the value of k. please answer this. ty
Answer:
0
Step-by-step explanation:
This problem is impossible if the x value is -2. However, if the x value is 2, find where the line meets x=2 and record the y value.
a fair coin is flipped 11 times exactly 9 are tails
The probability of having tails is 9/11
Data;
N = 11tails = 9ProbabilityThis is the possibility of an event occurring. In a sample space of 11 coin flips, tails came up 9 times and head came up 3 times
Number of time head came up = [tex]11-9 = 3[/tex]
The probability of having tails is calculated as
[tex]p = \frac{9}{11}[/tex]
The probability of having head is calculated as
[tex]p = \frac{3}{11}[/tex]
The probability of having tails is 9/11
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. In Problem 2, how many lateral faces would there be if the base had
two sides of length 3 tnches and four sides of length 2 inches? Explain.
The number of lateral faces for a hexagonal prism or pyramid is 6.
What is a prism?A prism is a three dimensional figure consisting of pair of opposite bases and lateral faces which are parallelogram.
Given that the base off the prism has two sides of length 3 inches and four sides of length 2 inches. Hence the base is hexagonal. The lateral faces would be 6.
The number of lateral faces for a hexagonal prism or pyramid is 6.
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Please just help. I’m stuck on math! Determining spinner probability Lol BUT please help! If you know how to do this
1. 2
2. 2
3. 4
4. 3 and 1
5. C
6. B
7. C and D
8. 3
9. 1 and 4
10. C
11. 2
12. D
You're Welcome✌! Brainliest would mean a lot.
PLS HELP ME I WILL MARK THE BRAINLIEST
Answer:
a. 314.2 in²
b. 36 m²
c. 60 m²
Step-by-step explanation:
The areas of these plane figures can be found by substituting the given dimensions into the area formula.
a.The area of a circle can be found from its diameter to be ...
A = (π/4)d²
A = (π/4)(20 in)² = 100π in² ≈ 314.2 in²
__
b.The area of a parallelogram can be found as ...
A = bh
A = (9 m)(4 m) = 36 m²
__
c.The area of a triangle can be found from ...
A = 1/2bh
A = 1/2(15 m)(8 m) = 60 m²
_____
Additional comment
A triangle with sides 17 and 15 and height 8 cannot be obtuse. It is a right triangle. (Those side lengths are a Pythagorean triple.)
Find the domain for the rational function f(x)=x+4/3x-5
Answer:
all real numbers
Step-by-step explanation:
the domain for normal linear and quadratic equations is always all real numbers
Factor completely 4xy−24y−x+6
An orange has a diameter of 3 in. and a grapefruit has a diameter of 4 in. What is the approximate difference in the volume of the two fruits?
A.
5 in.3
B.
7 in.3
C.
19 in.3
D.
29 in.3
The approximate difference of the volume of the two spherical fruits is: C. 19 in.³.
What is the Volume of a Sphere?Volume of sphere = 4/3πr³
The orange and the grapefruit are spherical in shape. Therefore:
Volume of orange = 4/3πr³ = 4/3π(1.5)³ = 14.14 in.³
Volume of grapefruit = 4/3πr³ = 4/3π(2)³ = 33.51 in.³
Difference in volume = 33.51 - 14.14 = 19.37
Therefore, the approximate difference of the volume of the two spherical fruits is: C. 19 in.³.
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Please help! I will mark brainliest
Answer: C
Step-by-step explanation:
Statement C is true
The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
Interquartile range = [tex]\underline{Q_{3} - Q_{1}}[/tex]
For bus drivers = 30 - 5 = 25 miles
For teachers = 25 - 5 = 30 miles
Distance of bus drivers = distance of teachers - 5 miles
10k^10/8k^4 simplify ???
help!!!
If f(x) = x2 – 2, then which of the following is the value of f(3)
(1) -11
(3) -8
(2) 7
(4) 4
Answer: 7
Step-by-step explanation:
This means we substitute x=3 into f(x).
f(3) = 3^2 - 2 = 7.
Can I pleae get some help i dont get it
Answer:
Step-by-step explanation:
Initial value ( y - value) for Function A is 12.
For B its 3(-1) + 2 = -1 so the answer is Function A.
Answer:
Find 'Function A's linear equation by using point-slope formula;
y - y1 = m(x - x1)Where y1 = your first y-coordinate in any pair, and x1 = your first x-coordinate in the following pair used for the y-coordinate, and lastly m = slope.
But, we do not have the slope so we use the formula to find the slope(rise/run) of any two random points;
y2(second y-coordinate) - y1(first y-coordinate)
______________________________________
x2(second x-coordinate) - x1(first x-coordinate)
We plug in these values using any two ordered pairs, so I'll just use (-1,12) and (0,8).
12 - 8 4
_____ = ______ = -4/1 or -4 is the slope, so now we utilize this slope into
-1 - 0 -1
our point slope formula:-
y - y1 = m(x - x1)
For this, we just use one arbitrary pair, I'll use (-1,12).
So,
y - 12 = -4(x - (-1))
simplify
y - 12 = -4x - 4
isolate y by adding 12 to both sides (inverse operation of subtraction is addition)
+12 +12
y = -4x + 8, is the function for A.
Now let's compare the y-intercepts of both of these functions because we want to see which one has the greatest initial value.
Function A: y = -4x + 8, 8 is the y-intercept in this case.
Function B: y = 3x + 2, 2 is the y-intercept in this case.
Compare;
8 > 2, therefore Function A has a greater initial value.
1 yards equals 3 feet in one mile equals 5280 feet how many yards are in 5 MI
Answer:
A conversion calculator gave me 8800
Math homework pls help!!
3) 18 mm
4mm
4) 11 in
19 in
5) 5 mi
11 m
Answer:
3= perimeter=44 area=73
4= perimeter=60 area=209
5= perimeter=32 area=55
Step-by-step explanation:
18x4=72
18+18+4+4=44
11+11+19+19=60
11x19=209
5x11=55
5+5+11+11=32
Find the distance between the points (-5,-3) and (0,9). Round your answer to one decimal place, if necessary.
Solve this system of equations by graphing. First graph the equations, and then type the solution. y=3x–2 y= – x+6 Click to select points on the graph. The solution is , .
Answer:
(2 , 4)
Step-by-step explanation:
set 3x-2 = -x + 6
4x = 8
x = 2
3(2) - 2 = 4
n expression is shown below. -x + 1 + 4x - 3
Answer:
3x - 2
Step-by-step explanation:
Collect like timers. -x + 4x = 3x and -3 + 1 = -2, 3x - 2
Hey there!
-x + 1 + 4x - 3
= -1x + 1 + 4x - 3
COMBINE the LIKE TERMS
= (-1x + 4x) + (1 - 3)
= -1x + 4x + 1 - 3
= 3x - 2
Therefore, your answer is: 3x - 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Please help asap i will give brainlist!!!!
Answer:
The answer is D
Step-by-step explanation:
This is because 5π is equal to 15.7
I’m stuck, HELP
3(6) + 4(2)^3 - 5
Answer:
45
Step-by-step explanation:
Lets split the problem then add/subtract at the end
3 x 6 = 18
Due to Order of operations we do 2^3 first then multipy by 4
so 2^3 = 8 Then we do 8 x 4 = 32
Now we add/subtract
18 + 32 - 5 = 45
45 is the answer
Answer:
45
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtration
[tex]3(6) + 4(2)^3 - 5 < ==multiply\ the\ exponents\ first\\\\18+4(8)-5 < ==multiply\ first\\\\18+32-5 < ==addition\ before\ subtraction\\\\50-5 < == subtract\\\\45 < == final\ answer[/tex]
Hope this helps!
The number 100 can be written as the sum of a 1-digit prime number and a 2-digit prime number. What is the product of these prime numbers?
Answer:
Answer: 3 + 97
Step-by-step explanation:
Just off the top of my head, I'm pretty sure that the answer you want is 3 and 97.
The single digit primes are 2 3 5 7
2 + 98 is what you are forced to use. 98 is not prime
3 + 97 is the answer I gave.
5 and 95 Ninety five is not prime (5 divides into it).
7 and 93 but 93 is not prime. 3 will divide into it.
Select the correct answer.
Function f is an increasing exponential function that is negative on the interval (-∞, 2) and positive on the interval (2, ∞). Which could be the graph of function f?
Answer:
A.
Step-by-step explanation:
The interval values given are the values of x.
We see that on Graph A, to the left of x = 2 the graph is below the x-axis ( negative values of f) and to the right the values of f are above the x-axis (positive f).
Answer:
A :)
Step-by-step explanation:
I just tokk the test!
the figure shows a solid cube with dimensions 24 cm by 15 CM by 16 cm. A cylinder with a base radius of 4 cm and height of 7 cm is removed from the cuboid. find the area that will be covered in paint? (surface area)
Answer:
=2,133 3/7cm^2
Step-by-step explanation:
sides
15x16=240
240x2
=480cm^2
24×16=384
384×2= 768cm^2
768+480
a=1248cm^2
24x15=360cm^2
22/7x4x4
=50 2/7cm^2
360- 50 2/7
=354 5/7cm^2
(354 5/7)2
b=709 3/7cm^2
22/7x8x7
=22x8
c=176cm^2
a+b+c
1248+709 3/7+ 176
=2,133 3/7cm^2
in a school of 330 students, 85 of them are in a drama club, 200 of them are in a sports team and 60 of them do both
find the probability that the student isn't in a sports or drama club
Answer:
105/330 = 21/66 = 7/22
7/22 is the answer I think
Step-by-step explanation:
n(U) = 330
n(A) = 85
n(B) = 200
n(A n B) = 60
Now,
n(A U B) = n(A) + n(B) - n(A n B)
or, n(A U B) = 85 + 200 - 60
or, n(A U B) = 285 - 60 = 225
Now,
n(A U B) compliment = n(U) - n(A U B)
n(A U B) compliment = 330 - 225
so, n(A U B) compliment = 105
Now,
probability = 105/330
What is the value of 350−30(−14+2.5)
Answer:
695
Step-by-step explanation:
So for thus, you need to follow PEMDAS
First, Parentheses
(-14 + 2.5) = -11.5
Skip E, there are no Exponents
Now for Multiplication
30 * (-11.5) = -345
Lastly, Subtraction
350 - -345
Becomes 350 + 345 = 695
Answer:
The answer is 695.
350-30(-14+2.5)=695.
Select all the numbers that round to 5.6
when rounded to the nearest tenth.
A. 5.058
B. 5.54
C. 5.56
D. 5.58
E. 5.590
Answer:
C, D, and E are the answers.