What happens when the function f(x)=cos(x) is transformed by the rule g(x)=f(1/2x)?
A: f(x) is stretched away from the y-axis by a factor of 2.
B: f(x) is compressed toward the y-axis by a factor of 1/2.
C: f(x) is compressed toward the x-axis by a factor of 1/2.
Answers
Answer:
A: f(x) is stretched away from the y-axis by a factor of 2
Step-by-step explanation:
Parent function:
[tex]f(x)=\cos(x)[/tex]
Given transformation:
[tex]g(x)=f\left(\dfrac{1}{2}x\right)=\cos \left(\dfrac{1}{2}x\right)[/tex]
Translation:
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis by a factor of} \: \dfrac{1}{a}[/tex]
Therefore, f(x) is stretched parallel to the x-axis (horizontally) by a factor of 2:
[tex]a=\dfrac{1}{2} \implies \dfrac{1}{a}=\dfrac{1}{\frac{1}{2}}=2[/tex]
Related Questions
What is the measure of the major arc?
135⁰
S
L
OA. 250°
OB. 135°
C. 225°
OD. 215°
Answers
Answer:
C. 225°.
Step-by-step explanation:
1) according to the condition minor arc is 135°;
2) the measure of the major arc can be calculated as
360°-135°=225°.
Find dy/dx any one
x=acost , y=asint
Answers
Answer:
[tex]x=a \cos t \implies \dfrac{dx}{dt}=-a \sin t[/tex]
[tex]y= a \sin t \implies \dfrac{dy}{dt}=a \cos t[/tex]
Using the chain rule:
[tex]\begin{aligned}\implies \dfrac{dy}{dx} & =\dfrac{dy}{dt} \times \dfrac{dt}{dx}\\\\& = a \cos t \times \dfrac{1}{-a \sin t}\\\\& = \dfrac{a \cos t}{-a \sin t}\\\\& = - \dfrac{\cos t}{\sin t}\\\\& = - \cot t\end{aligned}[/tex]
Jose is 35 years old, and makes $40,000 per year. If he dies, how much would
the beneficiaries of his life insurance policy receive if they can get by on 75% of
his income?
Answers
The amount that the beneficiaries of his life insurance would receive would be $30000.
How to solve for the amount that would be receivedThe total amount of insurance is 40000
percentage needed by beneficiaries on this amount = 75%
Hence 75% * 40000
= $30000
Therefore it can be concluded that the amount that the beneficiaries would require on 75% is $30000.
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Solve for X.
21
14
X
42
x = [?]
Enter the number that belongs in the green box.
Answers
Answer:
x = 28
Step-by-step explanation:
By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28
Try This Q 1. Write the expressions for each of the following using brackets. (a) Four multiplied by the sum of nine and two. (b) Divide the difference of eighteen and six by four. (c) Forty five divided by three times the sum of three and two. 2. Write three different situations for (5+8) x 6. (One such situation is: Sohani and Reeta work for 6 days; Sohani works 5 hours a day and Reeta 8 hours a day. How many hours do both of them work in a week?) 3. Write five situations for the following where brackets would be necessary. (a) 7(8-3) (b) (7+2) (10-3)
Answers
Answer:
Step-by-step explanation:
Writing expressionsa) Sum of nine and two ⇒ 9 + 2
Four multiplied by (9+2) :
4* (9+2)
[tex]b) \dfrac{(18-6)}{4}[/tex]
[tex]c) \dfrac{45}{3*(3+2)}[/tex]
2) a) Multiply the sum of five and eight by 6
b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?
3) a) 7*(8-3)
Multiply the difference of eight and three by 7.
Writing One Variable Algebraic
Expressions
Leslie buys a new pair of sneakers for $43 and several
pairs of laces, I, that cost $6 each. Write an algebraic
expression to represent the total amount she will spend.
Answers
Answer:
y = 6l + 43
Step-by-step explanation:
y=mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The y intercept is when x = 0, so the initial cost before buying the laces, which was the cost of the sneakers
b = 43
The slope is you purchase one pair of laces, it increases by 6 each time
m = 6
The y coordinate will represent the total cost spent
y
The x coordinate will represent the total number of laces purchase and we are told that the variable is l
x = l
combine:
y = 6l + 43
HELP ASAP Calculate the residuals for your scatterplot in step 2d.
Create a residual plot for your data. graph is below
Answers
The residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7
How to determine the residuals?The regression equation is given as:
y = 0.141x + 0.842
Next, we calculate the predicted values (y) at the corresponding x values.
So, we have:
y = 0.141 * 13.8 + 0.842 = 2.78
y = 0.141 * 18 + 0.842 = 3.38
y = 0.141 * 16.7 + 0.842 = 3.20
y = 0.141 * 18 + 0.842 = 3.38
y = 0.141 * 0.7 + 0.842 = 0.94
y = 0.141 * 21.9 + 0.842 = 3.93
y = 0.141 * 15.5 + 0.842 = 3.03
y = 0.141 * 9.2 + 0.842 = 2.14
y = 0.141 * 19.5 + 0.842 = 3.59
y = 0.141 * 16.7 + 0.842 = 3.20
The residuals are then calculated using:
Residual = Actual value - Predicted value
So, we have:
Residual = 1.42 - 2.78 = -1.36
Residual = 3.7 - 3.38 = 0.32
Residual = 3.21 - 3.20 = 0.01
Residual = 4 - 3.38 = 0.62
Residual = 1.11 - 0.94 = 0.17
Residual = 3.69 - 3.93 = -0.24
Residual = 3.92 - 3.03 = 0.89
Residual = 2.23 - 2.14 = 0.09
Residual = 3.77 - 3.59 = 0.18
Residual = 2.5 - 3.20 = -0.7
Hence, the residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7
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Which of the following functions has a maximum y-value of 2?
y = 2(x + 1)² +3
y = 3(x + 1)² +2
O y=-3(x + 1)² + 2
Oy=-(x - 2)² + 3
Answers
Answer:
-3(x+1)² + 2
Step-by-step explanation:
-3(x+1)² + 2 because the +2 indicates the y value of the turning point and the turning point is a maximum meaning the coefficient must be negative leaving this answer
chuck is making a map of his neighborhood. each grid unit represents one city block. He uses the following coordinates, with north being the direction of the positive y axis
Answers
8. A farmer needs to fertilize his field before planting again. Fertilizer is sold at $54.00 for a 100lbs bag and 1 bag should be used for every 1000 square feet. The farmer's field is 250 feet long and 150 feet wide. a) What is the area of the field? Ans: b) What will it cost the farmer to fertilize his field? Ans:
Answers
Answer:
a) 37 500 ft²b) $2 052Step-by-step explanation:
a)
the area of the field :
= 250 × 150
= 37 500 ft²
……………………
b)
→ the number of bags needed :
37 500 ÷ 1 000
= 37.5
Then he needs 38 bag
→ The cost :
= 38 × 54.00
= 2 052
Using data from 1996 to 1998, the annual number of cars sold at a certain dealership can be modeled by the formula y = 4x + 2. Where y is the number of cars in thousands sold x years after 1996. According to this form line in which years will be the number of car sold exceed 46,000
Answers
The year, where the number of cars sold exceed 46,000 is 13496
How to determine the year?The equation of the function is given as:
y = 4x + 2
When the sales exceed 46000;
It means that y > 46000
So, we have:
4x + 2 > 46000
Subtract 2 from both sides
4x > 45998
Divide both sides by 4
x > 11499.5
The year is then calculated as:
Year = 1996 + x
So, we have:
Year > 1996 + 11499.5
Evaluate
Year > 13495.5
Approximate
y > 13496
Hence; the year, where the number of cars sold exceed 46,000 is 13496
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A parking garage in Raleigh, NC charges $5 for the first hour and $2.50 for each additional hour or part of an hour. Your receipt reads $20. How many hours did you park in the garage?
Answers
In an examination, Musa got 7 marks
more than Emmanuel. If Emmanuel
had 25 marks and Faith had 1/4 of
Musa's mark more than Emmanuel's
mark, what is the score of Faith
Answers
Answer:
Let Musa's mark be = m
Emmanuel's mark be = e
Faith's mark be = f
m = e + 7
e = 25
m = 25 + 7 = 32
f = 1/4 m + e
f = (1/4 × 32) + 25
f = 8 + 25
f = 33
Ice cream shop is open within the month of june,july and august The shop served 100 fewer customers than they did in july They served twice as many customers in august as they did in june In total they served 400 customers over these three months
Answers
The number of customers served in the ice cream shop in June, July and August are 125, 25 and 250 customers respectively
How to write and solve equation?let
June = xJuly = x - 100August = 2xTotal customers = 400Total = June + July + August
400 = x + (x- 100) + 2x
400 = x + x - 100 + 2x
400 = 4x - 100
400 + 100 = 4x
500 = 4x
x = 500/4
x = 125
So,
June = x
= 125 customers
July = x - 100
125 - 100
= 25 customers
August = 2x
= 2(125)
= 250 customers
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The weight of 1 cm³ of
water is exactly I g.
A small desk top fish
tank is pictured below.
How much does the
water in the tank weigh
in kilograms?
HELP
Answers
Answer:
10,800 kilograms
Step-by-step explanation:
(24 x 30) x 15 = 10,800
or (24 x 15) x 30
You have 6 toppings to choose from for your pizza. I How many ways
can you choose 2 different toppings?
Answers
Answer:
3 ways
Step-by-step explanation:
2×3=6. That is how you do it
The Maxair amusement park ride consists of a circular ring that holds 50 riders. Suppose that the center of the ride is at the origin and that one of the riders on the circular ring is at (16, 15.1). If one unit on the coordinate plane equals 1 foot, give an approximation of the circumference of the ride to the nearest foot.
Answers
The approximation of the circumference of the ride is 138 feet to the nearest foot
How to determine the circumference?The given parameters are:
Center (a,b) = (0,0) i.e. the originA circular ring, (x,y) = (16,15.1)The radius is calculated using:
[tex]r = \sqrt{(x - a)^2 + (y -b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(16 - 0)^2 + (15.1 -0)^2}[/tex]
Evaluate
r = √484.01
Evaluate the square root
r = 22.0
The circumference is calculated using
C = 2πr
So, we have:
C = 2π * 22.0
Evaluate
C = 138
Hence, the approximation of the circumference of the ride to the nearest foot is 138 feet
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Which points are solutions to the system of inequalities shown below? Check all that apply.
y > x
y > 2
x > 4
A.(6, 4)
B.(9, -2)
C.(4, 2)
D.(9, 10)
E.(8, 1)
F.(5, 6)
Answers
Answer: D and F
Step-by-step explanation:
For the first inequality, we know that y>x, so this eliminates options A, B, C, and E. This means we only need to check D and F.
Both D and F have a y coordinate greater than 2 and an x coordinate greater than 4, so they are both correct.
what fraction is equivalent to 5?
Answers
Answer:
5/1
Step-by-step explanation:
Help with my study guide only answer topic 7 problem A
Answers
sin P = 24/26
cos P = 10/26
tan P = 24/10
sin Q = 10/26
cos Q = 24/26
tan Q = 10/24
you have the first part right. using Soh Cah Toa is the best way to find the trig function when given a labeled triangle.
remember the hypotenuse is the longest side and always across from the 90 degree angle.
# 18 I can solve problems involving e and In.
0.0.15t
3. The expression 1 e models the balance, in thousands of dollars, where t represents
time in years after the account was opened.
a. What does the 0.015 represent in this context?
b. Write an expression and for the number of years after which there will be $8,000 in the
account and simplify.
4. Explain why In 16 is greater than 2 but less than 3.
Answers
The expression is assumed here as it's unclear looking
If it's P=(P_o)ln0.015t then the below solution of Part B is correct else they may vary.
#a
0.015 represents rate of change with respect to t.#b
As per our assumed equation
It's.
8000=(P_o)ln0.015^tSimplify
tln0.015=8000/P_oInitial amount of account is not given so you have to solve the above equation after putting known P_o
#3
ln16ln4²2ln42(1.38)2.76(Approx)Hence it's less than 3 and greater than 2
If £2000 is placed into a bank account that pays 3% compound interest per year
how much will be in the account after 2 years?
Answers
Interest is 3%, so new percentage value is 100% + 3% = 103%
Change to decimal 103/100 = 1.03 (this is your multiplier)
For 2 years 1.03^2 So £2000 x 1.03^2 = £2121,8
Final answer= £2121,7
Answer:
£ 2121.8
Step-by-step explanation:
The formula to find the compound interest is :
[tex]A=P(1+\frac{R}{100} )^n[/tex]
Here,
A = Amount ⇒ ?
P ⇒ Principal ⇒ £2000
R ⇒ Interest rate ⇒ 3%
n ⇒ Time ⇒ 2 years
Let us find now.
[tex]A=P(1+\frac{R}{100} )^n[/tex]
[tex]A=2000(1+\frac{3}{100} )^2[/tex]
[tex]A=2000(1+0.03 )^2[/tex]
[tex]A=2000(1.03 )^2[/tex]
[tex]A=2000*1.0609[/tex]
[tex]A=2121.8[/tex]
Therefore, there will be £ 2121.8 in the bank account after 2 years.
Can someone help me with. This please
Answers
Answer:
wouldn't be 4.5 or something close too that maybe 5 or 5.5
Step-by-step explanation:
I got you I think
Evaluate the following for the given value. -2mn + n - 3m for m = -3 and n = -2
Answers
Hey there !
Answer:
-5 is the answerStep-by-step explanation:
In this question we are given with an expression that is -2mn + n - 3m , value of m as -3 , value of n as -2 . And we are asked to evaluate the expression .
Solution : -
For solving such types of expression in which we are provided with values of variables we need to substitute value of variable ( in given equation m and n ) and solve them .
Expression :
[tex] \longmapsto \: \qquad \: \rm{- 2mn + n - 3mn}[/tex]
Substituting value of m and n :
[tex] \longmapsto \: \qquad \: - 2( - 3)( - 2) + ( - 2) - 3( - 3)[/tex]
Simplifying it :
[tex]\longmapsto \: \qquad \: - 2(6) - 2 + 9[/tex]
Multiplying -2 and 6 :
[tex]\longmapsto \: \qquad \: - 12 - 2 + 9[/tex]
Adding -12 and -2 :
[tex]\longmapsto \: \qquad \: - 14 + 9[/tex]
Solving -14 and 9 :
[tex]\longmapsto \: \qquad \: \underline{ \blue{\boxed{\frak{- 5}}}} \quad \bigstar[/tex]
Henceforth , ❝ -5 ❞ is the answer .#Keep LearningHi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to evaluate the expression
[tex]\star~\mathrm{-2mn+n-3m}~\star[/tex]
for
[tex]\star~\mathrm{m=-3}~\star[/tex]
[tex]\star~\mathrm{n=-2}~\star[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Substitute the values of m and n into the expression.So, let's compute...
//\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\
Evaluating the expression
Since the value of m is -3, we should substitute -3 for m:
[tex]\star~\mathrm{-2(-3)n+n-3(-3)}[/tex]
Since the value of n is -2, we should substitute -2 for n:
[tex]\star~\mathrm{-2(-3)(-2)+(-2)-3(-3)}[/tex]
Simplify!
[tex]\star\mathrm{6(-2)-2+9}[/tex]
Simplify more!
[tex]\star\mathrm{-12-2+9}[/tex]
[tex]\star~\mathrm{-14+9}[/tex]
[tex]\boxed{\mathrm{-5}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
- 3.4 The rectangular box has the length of 8x² and the breadth of 6x² - 4x
3.4.1 What is the area of the box? to
Answers
The formula for calculating the area of a rectangle is expressed as A = lw. The area of the box is 48x^4 - 32x^3 cubic units
Area of a rectangleThe formula for calculating the area of a rectangle is expressed as:
A = lw
Given the following parameters
length l = 8x² breadth w = 6x² - 4xDetermine the area
Area = (8x²)6x² - 4x
Area of the box = 48x^4 - 32x^3
Hence the area of the box is 48x^4 - 32x^3 cubic units
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Find ac when a = 2 and c = 9?
Answers
Answer:
ac = 18
Keys:
[tex]\sf Given\\a = 2\\c = 9\\ac = a \cdot c[/tex]
Step-by-step explanation:
[tex]\sf a(2) \cdot c(9) = 18[/tex]
Answer:
The answer would be 18.
Step-by-step explanation:
ac is equal to a multiplied y c. Since we know that a is equal to 2 and c is equal to 9, we know we have to set up the equation 2(9). (Note: The parentheses around the 9 means you multiply by that number). 2 times 9 is equal to 18, getting you your answer. I hope this helps! :)
Which graph represents the function f (x) = StartFraction 2 x minus 1 Over x minus 1 EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 3 and 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 3, 4, and 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 4 and 1.
Answers
The correct description of the graph:
"One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4."
Which graph is the graph of the given functions?
Here we have the function:
[tex]f(x) = \frac{2x - 1}{x - 1}[/tex]
The graph of this function can be seen below:
Then we can see that a curve opens up on quadrant 1, and down on quadrants 2 and 3 (it pass throw quadrant 1 for a little bit).
Then the correct option is:
"One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4."
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Answer:
Graph D
Step-by-step explanation:
You are a for-hire motor carrier. Subpart A requires you to maintain a minimum level of financial
responsibility when transporting any quantity of what type of material in intrastate commerce?
A. All hazardous material
B. Class 7 material
C. Division 1.2 explosive material
D. Nonbulk oil
E. Nonbulk hazardous materials
Answers
You have to maintain a minimum level of financial responsibility when transporting any type of hazardous material in intrastate commerce Option A is correct.
What is Interstate commerce?Interstate commerce refers to any transaction or movement of goods, services, or money over state lines.
You operate a motor carrier for hire. When shipping any quantity of hazardous material in intrastate trade, A mandates that you maintain a minimum degree of financial accountability.
Hence option A is correct.
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Answer: A is correct
Step-by-step explanation:
Please help
Solve for r.
-8
= 4
T+6
=
Answers
Answer:
-8
Step-by-step explanation:
Solving for r means that we need to isolate r from the expression.
[tex] \frac{ - 8}{r + 6} = 4[/tex]
Multiply both sides by (r +6) to 'get rid' of the fraction:
-8= 4(r +6)
Expand:
-8= 4r +4(6)
-8= 4r +24
Minus 24 on both sides:
4r= -8 -24
4r= -32
Divide both sides by 4:
r= -32 ÷4
r= -8
Additional:
For a similar question on solving for a variable:
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r = -8
Step-by-step explanation:
-8/(r + 6) = 4
-8 = 4(r + 6)
-8 = 4r + 24
-32 = 4r
-8 = r
T
Radius i den store sirkelen er r.
Vis at summen av arealet til de fire hvite feltene kan skrives A = r²(2 – 2 ).
Løs oppgaven her.
Answers
Thank you :)
[tex]\pink{ \rule{1pt}{90000000pt}}\color{blue}{ \rule{1pt}{90000000pt}}\color{yellow}{ \rule{1pt}{90000000pt}}\purple{ \rule{1pt}{90000000pt}} \green{\rule{1pt}{90000000pt}}
[/tex]