The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right. What is the equation of the new function g(x) ?
Answers
Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right by h units, then
the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then
the new function g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then the new
function g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then the
new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)
vertically compressed by multiplying each of its y-coordinates by k.
* Lets solve the problem
∵ f(x) = sin(x)
∵ f(x) is stretching vertically by a factor of 4
∴ f(x) multiplied by 4
∵ f(x) is shifting 3 units to the right
∴ We will change x to (x - 3)
∵ The new function is g(x)
∴ g(x) = 4 sin(x - 3)
- The attached graph for more understand
f(x) is the red graph
g(x) is the blue graph
Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
The given function is:
f(x) = sin(x)
Stretching by a factor of 4:
A vertical stretch or compression of f(x) can be expressed as:
cf(x), where c is any constant
if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.
Since, given function is being stretched by a factor of 4, the transformed function will become:
4f(x)
Shifting by 3 units right:
A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:
f(x - 3)
Applying both the transformations to f(x), we get g(x) as:
g(x) = 4 f(x - 3)
g(x) = 4 sin(x - 3)
Related Questions
given : MN is an angle bisector of (angle)JMK
prove : m(angle)JMN=1/2m(angle)JMK
(i need all the reasons)
Answers
If the line MN is the angle bisector of ΔJMK, then it creates two angles of equal measure. Hence, m∠JMN is half of m∠JMK due to the property of an angle bisector.
Explanation:In the field of geometry, an angle bisector is a line or ray that divides an angle into two equal angles. This is given by the information provided that MN is an angle bisector of ΔJMK.
By definition, if MN is an angle bisector of ΔJMK, then it creates two angles, ∠JMN and ∠NMK, that are equal in measure. So, we have m∠JMN = m∠NMK. This is the definition of an angle bisector, which is the reason you are looking for.
Given this, if you want to find m∠JMN in terms of ∠JMK, keep in mind that MN bisects ∠JMK, creating the two equal angles we just mentioned. Therefore, m∠JMK = m∠JMN + m∠NMK. Since ∠JMN and ∠NMK are equal, m∠JMK = 2m∠JMN. Hence, m∠JMN = 1/2m∠JMK. This would be a consequence of the angle bisector property.
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The price of an item has been reduced by 85% . The original price was 20 . What is the price of the item now?
Answers
Reduced by 85%,
So, 100-85 = 15% of 20,
[tex] \frac{15}{100} \times 20 \\ = \frac{15}{5} \\ = 3[/tex]
Prove of item is now 3.
!! Hope It Helps !!
Final answer:
The new price of the item is $3 after the 85% reduction from the original price of $20.
Explanation:
To find the new price of the item after an 85% reduction, we start with the original price and calculate 85% of that price to know how much is being subtracted. The original price is $20. Now let's calculate 85% of 20 dollars:
0.85 (85%) × $20 = $17
This means an $17 reduction from the original price. We subtract this from the original price to find the new price:
$20 - $17 = $3
The new price of the item is $3 after a reduction of 85%.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Subract and simplify.
Answers
Answer: C
Step-by-step explanation:
[tex]\dfrac{x+1}{x-5} - \dfrac{x-2}{x+3}[/tex]
= [tex]\dfrac{x+1}{x-5}(\dfrac{x+3}{x+3}) - \dfrac{x-2}{x+3}(\dfrac{x-5}{x-5})[/tex]
= [tex]\dfrac{x^{2}+4x+3}{(x-5)(x+3)} - \dfrac{x^{2}-7x+10}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{x^{2}+4x+3-(x^{2}-7x+10)}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{11x-7}{(x-5)(x+3)}[/tex]
Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
Answers
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room.
Step-by-step explanation:
10 x 4 = 40$
Samuel earned $6.67 per hour.
Explanation:To calculate how much money Samuel earned per hour, we need to find the total number of hours he spent both mowing the lawn and cleaning his room.
Samuel spent 4 hours mowing the lawn and 2 hours cleaning his room, for a total of 6 hours.
He earned $40 for this time period.
To find how much he earned per hour, we divide the total amount earned by the total number of hours:
$40 divided by 6 hours = $6.67 per hour.
Therefore, Samuel earned $6.67 per hour.
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please help me with these please.
Answers
6. Answer: y = 5x - 11
Step-by-step explanation:
Parallel means "same slope". y = 5x - 2 is in the form y = mx + b,
so the slope (m) = 5
Next, input the point (x₁, y₁ = 2, -1) and slope (m = 5) into the Point-Slope formula:
y - y₁ = m(x - x₁)
y - (-1) = 5(x - 2)
y + 1 = 5x - 10
y = 5x - 11
*******************************************************************
7. Answer: [tex]\bold{y = \dfrac{1}{3}x + 4}[/tex]
Step-by-step explanation:
Perpendicular means "opposite reciprocal slope". y = -3x + 7 is in the form y = mx + b, so slope (m) = -3 ⇒ m⊥ = [tex]\frac{1}{3}[/tex]
Next, input the point (x₁, y₁ = 3, 5) and slope (m = [tex]\frac{1}{3}[/tex] ) into the Point-Slope formula:
y - y₁ = m(x - x₁)
[tex]y - 5=\dfrac{1}{3}(x - 3)[/tex]
[tex]y - 5 =\dfrac{1}{3}x - 1[/tex]
[tex]y=\dfrac{1}{3}x + 4[/tex]
Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away. She is _____ percent closer to the school.
Answers
Answer:
Tiffany is 34% closer to the school.
Step-by-step explanation:
Given the statement: Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away.
She lived away from the school = 15 km
as, she moved 9.9 km away.
Now, the distance closer to school from where she lived = 15 -9.9 = 5.1 km
To, find how much percent she is closer to school.
Percent states that a number or ratio expressed as a fraction of 100.
[tex]percent = \frac{5.1}{15} \times 100[/tex] = [tex]\frac{51 \times 100}{150} = \frac{51 \times 10}{15}[/tex]
Simplify:
percent closer to school = 34%
Therefore, she is 34% closer to the school.
PLEASE HELP A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled by this equation:an=500+(k-1)10 Use summation notation to model and evaluate the sales for the first ten years. Explain your steps.
Answers
Answer: 131,400$
Step-by-step explanation:
The sale for first month is $500.
The sale increases by $10 each month, as modelled by the equation:
a_k=500+(k-1)10
where, k = 1 (first month)
k = 2 (second month)
.... and so on.
we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)
Total sales = ∑ a_k
∑ a_k = ∑ (500+(k-1)10)
= 500k + ∑ (10k - 10)
= 500k + 10∑k - 10k
= 490k + 10∑k
= 490k + 10 {k*(k+1)/2}
= 490k + 5{k*(k+1)}
= 490k + 5k^2 + 5k
= 5k^2 + 495k
∴∑ a_k = 5k^2 + 495k
For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)
= 5*(120*120) + 495*120
= 72,000 + 59, 400
= 131,400$
Answer:
Distribute 10 to (k – 1) and simplify.
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used. The upper index is 10*12=120.
The values of the summations are 58,800 + 72,600. So, the total sales is $131,400.
Step-by-step explanation:
Sweet t saved 20% of the total cost of the green-eyed fleas new album let three be fleas on the earth .If the regular price is $30 how much did sweet t save?
Answers
Answer:
$6 Sweet t saved on green-eyed fleas new album .
Step-by-step explanation:
As given
Sweet t saved 20% of the total cost of the green-eyed fleas new album .
.If the regular price is $30.
20% is written in the decimal form.
[tex]= \frac{20}{100}[/tex]
= 0.20
Thus
Sweet t saved on green-eyed fleas new album = 0.20 × 30
= $6
Therefore $6 Sweet t saved on green-eyed fleas new album .
The function h=-16t^2 +1700 gives you the height h, of an object in feet, at t seconds. How long will it take the object to hit the ground ?Round to the nearest hundresth of a second?
Answers
Answer:
The object will hit the ground after 10.308 seconds.
Step-by-step explanation:
h(t) = -16t² + 1700
If you graphed this function, the object would be shown hitting the ground when it crosses the x-axis, in other words, when h = 0. So, to find the answer, just set h(t) equal to 0 and solve.
-16t² + 1700 = 0 Plug this into a calculator if you have one.
t = -10.308 and t = 10.308
Since time can't be negative, your answer will be the positive value, 10.308.
The object, described by the equation h(t) = -16t^2 + 1700, will hit the ground after around 10.308 seconds. This is determined by setting h(t) to 0, yielding a valid, positive solution.
The provided equation h(t) = -16t^2 + 1700 describes the height (h) of an object as a function of time (t), taking into account gravitational acceleration. To determine when the object hits the ground, set h(t) to 0 and solve for t:
-16t^2 + 1700 = 0
Solving this equation using the quadratic formula or factoring yields two solutions: t = -10.308 and t = 10.308. However, time cannot be negative in this context, so the only valid solution is t = 10.308.
Consequently, the object will hit the ground after approximately 10.308 seconds. This conclusion is reached by identifying the point where the height function intersects the x-axis, representing ground level. The positive value for t ensures a meaningful interpretation in the temporal context, indicating the time elapsed until the object reaches the ground.
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Which expression are a factor of 36abc-9bcd+24abc
Answers
3bc ( 20a - 3d )
An expression which factorises 36abc - 9bcd + 24abc is:
3bc ( 20a - 3d )
STEP-BY-STEP EXPLANATION:
= 36abc - 9bcd + 24abc
= 60abc - 9bcd
= 3bc ( 20a - 3d )
An extra large pizza has 12 slices. If there are four people at they table and they each get two slices, how many slices are left?
Answers
Answer:
there should be 4 slices left
Hope This Helped
Step-by-step explanation:
Answer:
The most accurate answer is:
*4*
I hope I helped you!
Step-by-step explanation:
Alright, lets examine the problem; *12* slices of pizza are given. We also have *4* guests at the table, and each are given *2* slices. Lets use subtraction to solve: 12 - 2 - 2 - 2 - 2- the *2*'s equal the amount of pizzas given, and the *12* represents our amount of slices of pizza. We also gave 4 people 2 slices, which is why we have *4* *2*'s
[SOLVE]
12 - 2 - 2 - 2 - 2 = 4
It's 1:00 p.M. And I've driven 120 miles. At 3:00 p.M. I will have driven 208 miles. What is my speed?
Answers
From 1 pm to 3 pm is 2 hours.
208 miles - 120 mile = 88 miles
You drove 88 miles in 2 hours.
Speed = miles driven / time driven:
88 / 2 = 44 miles per hour
Answer:
44 miles/hour
Step-by-step explanation: since speed = distance/time
= 88miles/2hours
=44miles/hour
People need to develop a financial plan to accomplish their retirement goals. True False
Answers
Answer:
True
Step-by-step explanation:
The reason I say this is because of the fact you can't go into retirement without knowing how much your going to get. You need to create a financial plan stating how much you will get and how much you have saved prior to this occurence.
Hope This Helps :)
Answer: True
Step-by-step explanation: People need to develop a plan to overcome the effects of taxation, inflation, and purchasing power risk. In addition, people need to coordinate their company benefits with a personalized financial plan. Because there are many complexities in dealing with the stock market and real estate, you need to have a properly constructed financial plan.
Use your knowledge of insulators and conductors to explain why
cooking pots are usually made of metal with some sort of plastic
handle
Answers
Cooking pots are made of metal because metals are good conductors of heat. Plastic is an insulator that is slow at conducting heat. That is why an insulator is used so that we don't burn ourselves.
The cooking pots are good conductor of electricity and sort of plastic
handle are insulator for safety purpose.
Conductors are materials that permit electrons to flow freely from particle to particle. Conductors allow for charge transfer through the free movement of electrons. Conductors are good conduction of electricity.Insulators are materials that does not allow the free flow of electrons from atom to atom and molecule to molecule.Insulator are bad conductor of electricity.Learn more:
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PLEASE HELP ASAP 25 POINTS
Answers
Answer:
the answer is d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
To see if it is a solution substitute x in and see if it works for y
a. y>= x +2
-4 >= -2+2
-y> = 0 No
b y <= x+2
-4<=-2+2
-4 <0 True
keep going
y<= x-3
-4 <= -2-3
-4<=-5
No
c y> x+2
-4 >-2+2
-4 > 0
True
y< x-3
-4 <-2-3
-4 <-5
NO
d y <= x+2
-4 <= -2+2
-4<=0
True
-4 >= -2-3
-4>=-5
This is the solution
Enter the equations of the asymptotes for the function
Answers
Answer:
x = 7 and y = 2
Step-by-step explanation:
the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote
solve x - 7 = 0 ⇒ x = 7 is the asymptote
horizontal asymptotes occur as
[tex]lim( x → ± ∞), f(x) → c ( where c is a constant )
divide terms on numerator/ denominator by x
f(x) = (3/x/x/x -7/x ) + 2
as x → ± ∞, f(x) → 0 / 1 - 0 + 2 = 2
y = 2 is the asymptote
Answer: Vertical asymptote is x = 7
Horizontal asymptote is y = 2
Step-by-step explanation:
The vertical asymptote is the restriction on the domain (x-value). Since the denominator cannot be zero ⇒ x - 7 ≠ 0 ⇒ x ≠ 7 so the vertical asymptote is at x = 7.
The horizontal asymptote (H.A.) is the restriction on the range (y-value). There are three rules that determine the horizontal value which compare the degree of the numerator (n) with the degree of the denominator (m):
If n > m , then there is no H.A. (use long division to find the slant asymptote) If n = m , then the H.A. is the coefficient of n ÷ coefficient of mIf n < m, then the H.A. is y = 0In the given problem, n = 0 and m = 1 ⇒ n < m ⇒ H.A. is y = 0
Since there is a vertical shift of +2 units, the H.A. is y = 0 + 2 ⇒ y = 2
A parabola has x-int of (-8,0) and (4,0) and a minimum value of -9 in intercept form
Answers
Answer:
The function is 1/4x^2 + x - 8
Step-by-step explanation:
In Factor form the function is
a(x + 8)(x - 4) where a is a constant to be found.
= a( x^2 + 4x - 32) Note the coefficient of x is positive because the function has a minimum value.
The line of symmetry is x = (-8+4)/2 = -2.
So the minimum value will be the value of f(x) when x = -2, so we have the equation
a(-2+8)(-2-4) = -9
-36a = -9
a = 1/4.
Which of the following is a trinomial with a constant term?
A. x3 + 12x2 + x
B. y - 426
C. -x + 42
D. x + 7y + 6
E. x7 - 6
F. y13
Answers
Choice A is a trinomial, but it doesn't have a constant term
Choice D is the only other trinomial. This has a constant term, which is 6. The constant is the term without any variables attached to it.
Answer: Choice D
Answer: D. [tex]x+7y+6[/tex]
Step-by-step explanation:
We know that a trinomial is a polynomial with three terms.
From all the given options, only option A. [tex]x^3+12x^2+x[/tex] and option D. [tex]x+7y+6[/tex] are trinomials having three terms .
But option A [tex]x^3+12x^2+x[/tex] does not have any constant term .
On the other hand option D. [tex]x+7y+6[/tex] has a constant term of 6.
Therefore, the option D. [tex]x+7y+6[/tex] represents a trinomial with a constant term.
Simplify. -6i(5+3i) Enter your answer in standard form, in the box
Answers
Answer:
Pretty sure the answer is 18-30i
Step-by-step explanation:
-30i - 18i^2
-30i - 18 x (-1)
-30i +18
The expression -6i(5+3i) simplifies to 18 - 30i in standard form of a complex number.
Explanation:The problem asks us to simplify the expression -6i(5+3i). To simplify this, we multiply the complex number (-6i) with the complex number in the parenthesis. This results in (-6i * 5) + (-6i * 3i) which transforms into -30i - 18i^2. Since i^2 is -1, we can simplify further to -30i + 18. So the simplified form in standard form is 18 - 30i.
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which of the following names a diameter of circle A?
Answers
Answer:
BC
Step-by-step explanation:
The diameter is the distance across the circle, going through the center
BC or CB is the diameter
An account earns 1.5% interest compounded annually. The balance after 2 years is $8241.80. What is the principal?
Answers
I am not sure what did the problem mean by the principal but I guess It could be the valie invested initially
so,P=$8000
Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly get in return?
Answers
To get this answer, start by adding 16.79 and 28.49. The answer you should get is 45.28. Next, subtract 45.28 from 50 and your total should be 6.72. Hope this helped!
Write the linear equation in slope-intercept form: 5x - y = -17
a: y = -5x + 17
b: x = -1/5y - 17/5
c: y = 5x - 17
d: -5x - 17
Answers
In order to express the equation 5x - y = -17 in slope-intercept form (y = mx + b), we need to solve for y. After rearranging, it turns out the correct equation in slope-intercept form is y = 5x + 17.
Explanation:To write the equation 5x - y = -17 in slope-intercept form, we first need to solve the equation for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.
Let's rearrange the given equation: Start by adding 'y' to both sides to get 5x = y - 17. Add 17 to both sides, you will get y = 5x + 17. So, the correct answer is: y = 5x + 17. This aligns with option c.
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Comparing this with the answer choices, the correct option is c: y = 5x - 17.
To write the linear equation 5x - y = -17 in slope-intercept form, you must solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equation:
Add y to both sides to isolate the y-variable on one side: 5x - y + y = -17 + y, which simplifies to 5x = y - 17.Now, subtract 17 from both sides to solve for y: y - 17 = 5x - 17.The equation in slope-intercept form is y = 5x - 17.Comparing this with the answer choices, the correct option is c: y = 5x - 17.
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answers
Jack can run a mile in 9, 1/3 minutes. How long will it take for him to run 3, 1/2 miles? What is the answer
Answers
Answer:
32, 2/3 minutes.
Step-by-step explanation:
Divide the original mile time by two to get what half a mile would be. Multiply the original mile time by 3, since he is running 3 miles. Add 4 and 2/3, half of a mile time, to that and you're left with 32 minutes and 40 seconds.
You are in charge of buying the hamburgers and chicken for a party. The hamburgers cost $2 per pound and the chicken is $3 per pound, You have $60 to spend.
Answers
You can buy 15 hamburgers, and 10 chickens if you spend $30 on each.
$30 divided by $2 = 15 Hamburgers
$30 divides by $3 = 10 Chickens
30 + 30 = 60
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Alison and Justins father donated $3 every lap they swam in a swim-a-thon.Alison swam 21 laps and justin swam 15 laps.Use the distributive property tp find out the amount of money their father donated/
Answers
Answer:
The total amount of money Alison and Justins father donated be $108 .
Step-by-step explanation:
Distributive property.
Let a, b and c be any real numbers.
Thus
a.( b + c ) = a.b + a.c
This is distributive property.
As given
Alison and Justins father donated $3 every lap they swam in a swim-a-thon.
Alison swam 21 laps and justin swam 15 laps.
Total amount of money Alison and Justins father donated = Cost of each lap (Number of laps of Alison father + Number of laps of Justins father )
As
Cost of each lap = $3
Number of laps of Alison father = 21 laps
Number of laps of Justins father = 15 laps
Putting in the above
Total amount of money Alison and Justins father donated = 3(21 + 15)
= 3 × 21 + 3 × 15
= 63 + 45
= $ 108
Therefore the total amount of money Alison and Justins father donated be $108 .
HEEEEEEEEEELLLLLLPPPPPPPPPPPPPPPPP ME !
Answers
Answer:
B.) 72
Step-by-step explanation:
Because when there is one cup there are 8 fluid ounces, when there are 9 cups there are 9 times more fluid ounces.
Hello :3
To get your answer we would need to multiply.
So, if there's 8 fl. oz. in 1 cup then we need to multiply 8 by 4.
8 x 4 = 32
Your answer would be 32 fl. oz.
Hope This Helps!
Cupkake~
Algebra 1 A Semester Exam
30. Write y=-3/4x-6 in standard form using integers. (1 point)
Answers
3x+4y= -24
Final answer:
To convert y = -3/4x - 6 to standard form with integers, multiply by 4 to remove the fraction and then arrange the equation as 3x + 4y = -24.
Explanation:
To write the equation y = -3/4x - 6 in standard form using integers, we need to rearrange the terms so that the x and y terms are on the left side of the equation and the constant is on the right side. Moreover, in standard form, the coefficients should be integers. The standard form is typically expressed as Ax + By = C.
Starting with the given equation:
y = -3/4x - 6
Multiply each term by 4 to remove the fraction:
4y = -3x - 24
Now, we need to move the x term to the left side of the equation:
3x + 4y = -24
This is the standard form of the equation, and all the coefficients are integers.
Carlos bought a snowboard for $24.99 and ice skates for $19.19 how much money did he spend all together
Answers
Answer: Carlos would owe in fact (Not including sales taxes) $44.18 (forty-four dollars and eighteen cents)
Step-by-step explanation: