Let f(x)=2(3)^x+1 +4. The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x). What is the equation of g(x)?
Answers
f(x)=2(3)^(x+1) +4.
g(x) = 2[2(3)^(x+1)] + 4 (do not mult. that 4 by 2).
= 4*3^(x+1) + 4 (answer)
the equation of g(x) after stretching the graph of f(x) vertically by a factor of 2. Therefore, the equation of g(x) is g(x) = 4(3)^x+1 + 8.
To stretch the graph of (f(x)) vertically by a factor of 2 to form the graph of ( g(x)), we need to multiply the entire function (f(x)) by 2.
Given:
[tex]\[ f(x) = 2(3)^{x+1} + 4 \][/tex]
To stretch the graph vertically by a factor of 2, we multiply the function by 2:
[tex]\[ g(x) = 2 \cdot f(x) \][/tex]
Substitute the expression for [tex]\( f(x) \):[/tex]
[tex]\[ g(x) = 2 \cdot [2(3)^{x+1} + 4] \][/tex]
Now, distribute the 2 inside the brackets:
[tex]\[ g(x) = 4(3)^{x+1} + 8 \][/tex]
This is the equation of [tex]\( g(x) \)[/tex] after stretching the graph of [tex]\( f(x) \)[/tex] vertically by a factor of 2.
Therefore, the equation of [tex]\( g(x) \) is \( g(x) = 4(3)^{x+1} + 8 \).[/tex]
Related Questions
Which is an equation in point-slope form of the line that passes through the points (4, 5) and (−3, −1) ?
Answers
A linear equation or function is always a representation of a straight line in the coordinate plane. The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
The equation of a straight line is given by, y = mx + c
Where m is the slope while c is the y-intercept.
The slope of line passing by two points (x₁, y₁) and (x₂, y₂)
Slope(m) = (y₂ - y₁)/(x₂ - x₁)
The slope of the line that passes through (4, 5) and (−3, −1) will be,
m = (-1 -5)/(-3-4)
m = -6/-7 = 6/7
So equation converts as, y = (6/7)x + c
Substitute, (4,5)
5 = (6/7)4 + c
c = 9/7
So, y = (6/7)x + 9/7 will be the equation.
Hence "The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7".
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What is the slope of this graph?
Answers
Answer: The slope (m) of the line using two points where the line goes through is:
m = - 4 (negative 4).
Solution:
m=(y2-y1) / (x2-x1)
Taking two points in the graph where the line goes through:
P1=(0,2)=(x1,y1)→x1=0, y1=2
P2=(1,-2)=(x2,y2)→x2=1, y2=-2
Replacing in the formula of the slope:
m=(-2-2) / (1-0)
m=(-4) / (1)
m=-4
Fill in the missing reasons in the Two-column proof below.
Given: m∠2 + m∠3 + m∠4 = 180°
Prove: m∠1= m∠3 + m∠4
Statement Reasons
a. m∠2 + m∠3 + m∠4 = 180° a.
b. m∠1 + m∠2 = 180° b.
c. m∠1 + m∠2 = m∠2 + m∠3 + m∠4 c.
d. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 -m∠2 d.
e. m∠1 = m∠3 + m∠4 e.
Answers
b. Supplementary angles form 180 degrees (The definition of supplementary angles is that two or more angles have a sum of 180 degrees. DC is a straight line and has a measure of 180 degrees)
c. Substitution (Given the two previous statements, they are each equal to 180 degrees. Since 180=180 then you can substitute the angles in the equation.)
d. Subtraction (m<2 is being subtracted)
e. Subtraction postulate (Since the same quantity was being subtracted from each side of the equation, they are still equal)
The area of a rectangle is 201.5 square inches. The length of the rectangle is 13 inches. What is the width of the rectangle?
Answers
area = length * width
We can solve the equation for width.
width = area/length
Divide the area by the length to find the width.
width = (201.5 in.^2)/(13 in.) = 15.5 in.
Answer: the width is 15.5 in.
Which expression uses the greatest common factor and the distributive property to rewrite the sum 75 + 45?
A. 45(30 + 1)
B. 15(5 + 3)
C. 15(3 + 7)
D. 5(70 + 40)
Answers
First let's find the greatest common factor.
75: 1, 3, 5, 15, 25, 75
45: 1, 3, 5, 9, 15, 45
Their GCF is 15.
To get 75, you multiply 15 by 5.
To get 45, you multiply 15 by 3.
Therefore, 15(5 + 3) = 75 + 45.
B. 15(5 + 3)
The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)
What is distributive property?The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is
A(B + C) = AB + AC
This property is known by distributive law and applies to subtraction also.
Given; the distributive property to rewrite the sum 75 + 45
First find the greatest common factor.
75: 1, 3, 5, 15, 25, 75
45: 1, 3, 5, 9, 15, 45
Their GCF is 15.
To get 75, we will multiply 15 by 5.
To get 45, we will multiply 15 by 3.
Therefore, 15(5 + 3) = 75 + 45.
The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)
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list these number from greatest to least: 0.386, 0.3, 0.6833, 0.836
Answers
the correct order from greatest to least is:
0.863, 0.6833, 0.386, 0.3
What is 3x-6+1=-2x-5+5x
Answers
Carly can ride her bicycle 6000 meters in 15 minutes how far can she ride her bicycle in two minutes
Answers
A trough is 12 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 8 inches deep?
I have been getting 13/30, but apparently, that is wrong?
V=.5 * h * l * b
Because of similar triangles:
b = 5h (b/h = 5/1)
l = 12
V = .5 * h * 5h * 12
V = 30h^2
(dV/dt) = 60 h (dh/dt)
dV/dt = 13
h = .5 (because this is in feet)
13 = 60*.5(dh/dt)
13/30 = dh/dt
Answers
The rate at which the water level is rising when the water is 8 inches deep in the trough is 13/30 ft/min.
Explanation:To find how fast the water level rises when the water is 8 inches deep, we need to use the equation V = 30h^2, which represents the volume of the trough as a function of its height h. We are given that the trough is being filled at a rate of 13 ft^3/min, so we can set dV/dt (the rate of change of volume) equal to 13.
Substituting the given values into the equation dV/dt = 60h * dh/dt, we get 13 = 60 * h * dh/dt. Since h = 0.5 (in feet), we can solve for dh/dt which turns out to be 13/30 ft/min.
Therefore, the water level is rising at a rate of 13/30 ft/min when the water is 8 inches deep.
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Rebecca had 9/10 of a yard of ribbon. Then she gave 7/20 of a yard to a friend. How much does she have left? Explain your work
Answers
A yard is a unit of length. Hence, the Rebeccas have [tex]\frac{11}{20}[/tex] a yard of ribbon.
What is the yard?
A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.
Here, Rebecca had [tex]\frac{9}{10}[/tex] a yard of ribbon, and Rebecca gives [tex]\frac{7}{20}[/tex] of a yard of a friend.
Now, we have to subtract [tex]\frac{7}{20}[/tex] from the original [tex]\frac{9}{10}[/tex].
Since the denominator is the same as the rules of fractions.
Now, we multiply [tex]\frac{9}{10}[/tex] by [tex]\frac{2}{2}[/tex] so that the denominator [tex]10[/tex] and [tex]20[/tex] would be the same.
Therefore,
[tex]\frac{9}{10}[/tex]×[tex]\frac{2}{2}[/tex]=[tex]\frac{18}{20}[/tex].
Here, both the denominator are the same, we can subtract [tex]\frac{7}{20}[/tex] from the [tex]\frac{18}{20}[/tex].
[tex]\frac{18}{20}-\frac{7}{20}\\=\frac{11}{20}[/tex]
Hence, the Rebeccas have [tex]\frac{11}{20}[/tex] a yard of ribbon.
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Final answer:
Rebecca has 11/20 of a yard of ribbon left after subtracting the 7/20 yard she gave to a friend from her initial 9/10 yard of ribbon by converting both fractions to have a common denominator.
Explanation:
Rebecca started with 9/10 of a yard of ribbon and gave away 7/20 of a yard. To find out how much ribbon she has left, we need to subtract the amount she gave away from the amount she started with. This can be done following these steps:
Ensure that both fractions have a common denominator. The least common multiple of 10 and 20 is 20, so multiply the numerator and the denominator of the first fraction (9/10) by 2 to get the equivalent fraction with a denominator of 20, which gives us 18/20.
Now subtract the second fraction (7/20) from the first fraction (18/20) since they now have a common denominator. This gives us 18/20 - 7/20 = 11/20.
Therefore, Rebecca has 11/20 of a yard of ribbon left.
(PLEASE HELP ILL GIVE ALL THE COINS ICAN ASAP).In the situation, simple interest is calculated yearly. How much interest was earned? Drag and drop the answer into the box. Principal: $8000; Time: 4 years; Interest rate: 12%; Interest: ? $960 $3,840 $8,000 $11,840 $32,000
Answers
I=prt
I interest earned?
P principle 8000
R interest rate 0.12
T time 4 years
So
I=8,000×0.12×4
I=3,840....the answer
Hope it helps!
Answer:jgxgiddgidx
Step-by-step explanation:Hgxhfzjgxgdjgjggjdjgjgcy
Thomas earns $2100 per month and then got a 15 raise .how much will Thomas make per month after his raise
Answers
2100×0.15=315
now that's the actual increase in pay
so what he actually gets it 2100+315=2415 dollars per month more than previous month's
Final answer:
Thomas will earn $2415 per month after a 15% raise on his current salary of $2100, which results in a raise amount of $315.
Explanation:
Thomas currently earns $2100, and with a 15% raise, we need to calculate the increase in his monthly pay. To find the amount of the raise, we calculate 15% of his current earnings. That is, we multiply his earnings by the raise percentage expressed in decimal form: $2100 × 0.15 = $315.
After finding the raise amount, we add it to his current salary to find his new monthly earnings. $2100 + $315 = $2415 per month. Therefore, after a 15% raise, Thomas will make $2415 per month.
The sum of three consecutive numbers in 132. What is the smallest of the three numbers?
Answers
The lines x= 1/4y + a and y=1/4x +b intersect at the point (1,2). What is a+b?
Answers
x=1/4y + a
(1)=1/4(2) + a
1=1/2+a
1/2=a
y=1/4x+b
2=1/4(1) +b
b= 7/4
Solve a+b:
a+b=?
(2/4)+(7/4)= 9/4= 2.25
The values of a and b are 1/2 and 7/4 respectively. The sum of a and b is 9/4.
Explanation:To find the values of a and b, we need to solve the system of equations formed by the given lines. Let's start by substituting the given coordinates (1, 2) into the equations:
x = (1/4)y + a -> 1 = (1/4)(2) + a -> 1 = 1/2 + a -> a = 1 - 1/2 = 1/2
y = (1/4)x + b -> 2 = (1/4)(1) + b -> 2 = 1/4 + b -> b = 2 - 1/4 = 7/4
Therefore, a = 1/2 and b = 7/4. To find the sum of a and b, we add them: a + b = 1/2 + 7/4 = 2/4 + 7/4 = 9/4
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Am I doing this right?
16,14=4
15,35=5
24,32=4
27,63=9
20,80=20
18,38=2
14,49=7
66,99=33
9,35=1
6,24,42=6
30,50,70=10
32,48,96=12
10w,5w=5
16xy,24xy=8
21ab,35a=7
10jk,15k=5
3mn,9mn,12mn=3
6xy,9x,3y=3
Answers
Factors of 24 are 1,2,3,4,6,(8),12,24;Factors of 32 are 1,2,4,(8),16,32
32,48,96 = 16
Factors of 32: 1,2,4,8,(16),32
Factors of 48: 1,2,3,4,6,8,12,(16),24,48
Factors of 96: 1,2,3,4,6,7,12,(16),24,32,48,96
10w = 2 * 5 * w
5w = 5 * 1 w
GCF = 5w
16xy = 2 * 8 * x * y
24xy = 3 * 8 * x * y
GCF = 8xy
21ab = 3 * 7 * a * b
35a = 5 * 7 * a
GCF = 7a
10jk = 2 * 5 * j * k
15k = 3 * 5 * k
GCF = 5k
3mn = 3 * m * n
9mn = 3 * 3 * m * n
12mn = 3 *4 * m * n
GCF= 3mn
Julia plays volleyball and finished the regular season with 25 digs. The graph relates her total number of digs for the season to the number of games played in the post-season tournament. Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair. What is the equation in standard form that represents the relationship shown in the graph? y=3x+25 y−37=3(x−4) 3x+y=25 −3x+y=25 y=−3x+25
Answers
Answer:
As given : Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair.
As the ray passes through (0,25) and (4,37) and (8,49).
Equation of line passing through (a, b) and (p,q) is given by:
→ [tex]\frac{y-b}{x-a}=\frac{q-b}{p-a}[/tex]
→Equation of line passing through (0,25) and (4,37) is :
[tex]\frac{y-25}{x-0}=\frac{37-25}{4-0}=3\\\\y -25=3x\\y =3x + 25[/tex]
As , y= 3 x + 25, also passes through (8,49) also.
Equation of line is : y = 3 x + 25 or in Standard form : - 3 x + y = 25
Option (D) is the standard form of line which is : - 3 x + y = 25
The mean of 100 scores is 84. If each score is increased by 2 then what is the new mean?
Answers
84x100=8400
100 scores that you're adding two onto
100x2=200
8400+200=8600
8600/100= 86
To find the new mean after increasing each score by 2, we add 2 to the original mean of 84 to get a new mean of 86
The question concerns the calculation of the new mean when each score in a set is increased by a consistent amount. Given that the mean of 100 scores is 84, if we increase each score by 2, the new mean is also increased by 2. This is because the mean is the sum of all values divided by the number of values. Adding 2 to each score adds 200 to the total sum (since there are 100 scores), but the number of values remains the same. Thus, the new mean is 84 + 2, which equals 86
The difference between three-fifths of a number and 7 is -36
Answers
(3/5)x - 7 = -36
Add 7 to both sides: (3/5)x = -29
Then x = -29 div. by (3/5).
-29 -29 5 -145
x = - -------- = ------- * ----- = --------
3 1 3 3
---
5
The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
Let's say that number is x.
Three-fifth of x ⇒ (3/5)x
The difference of (3/5)x and 7 will be,
(3/5)x - 7 = -36
Add 7 on both sides
(3/5)x = -29
Multiply 5/3 on both sides
x = -29(5/3)
x = -145/3
Hence "The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3".
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what is the difference between 5 and 2/5
Answers
2/5 is a fraction
The Hamptons family has a fish tank holding 10,450 ml of water.The water is leaking at a rate of 270 ml per minute.
Part A: Define the input and output in the given scenario.
Part B: Write a function to model this situation.
Part C: How many liters of water will be left in the tank after 10 minutes.?
Answers
B: f(x)=10450-270x
C: f(10)=10450-270(10)=7750 ml of water
We can give a letter 't' for the time, the input, and f(t) for the output
----------------------------------------------------------------------------------------------------------------
The original amount of water in the tank is 10450, so this will be the fixed constant.
The amount of water lost per minute is 270 so this will be the term that varies depends on the variable of time, we write this as 270t
The function is given f(t) = 10450 - 270t
--------------------------------------------------------------------------------------------------------------
Given, t = 10
f(10) = 10450 - 270(10)
f(10) = 7750 ml
Answer This Problem,Please! :D
Type the integer that makes the following subtraction sentence true:
*blank*– 5 = -6
Answers
x - 5 = -6
x - 5 + 5 = -6 + 5
x = -1
-1 - 5 = -6
The highest elevation in Africa is in Kilimanjaro which is 19,334 feet above sea level. The lowest elevation in Africa is at Lake castle which is 509 feet below sea level. What is the difference in elevation between the two locations
Answers
every day, mike gets paid from his job. on monday, he gets 19 cents; on tuesday, he gets 14 cents; on wednesday, he gets 20 cents; on thursday, he gets 15 cents; and so on. how much money will he have by the 4th day?
Answers
PLEASE HELP I NEED THE ANSWER A.S.A.P!!!!!!!!! 20 POINTS!!!!!!!!!!!!!!!
When solving an equation using the distributive property that involves distributing fractions usually the first step is to multiply by the LCD to eliminate the fraction in order to simplify computation. Is it necessary to do this solve 1/2 (4x+6) = 1/3 (9x-24)? Why or why not?
Answers
Answer:
need points ty
Step-by-step explanation:
The length of a rectangle is 4 more than twice the width. If the length is 62, find the width.
Answers
58 / 2 = 29
The width is 29.
What is 24 divided by 1272
Answers
Rounded to the nearest hundredth: 0.02
In the story Charlotte's Web, How does the goose react to her big news?
A. She threatens the rat
B. She bows shamelessly
C. She trembles with fear
or D. She sits still and talks less
Answers
If the equatorial diameter of the sun is 1.39 million km how many kilometers is the sun's radius
Answers
2x+3y+7=3 in standard form
Answers
2x + 3y + 7 - 7 = 3 - 7
2x + 3y = -4
Simplify:
4p + 12 – 3q – 4p – 18 + 6q
A. 8p + 3q – 6
B. 8p – 3q + 6
C. 3q + 6
D. 3q – 6
Answers
4p + 12 - 3q - 4p - 18 + 6q
Combine like terms
4p - 4p + 12 - 18 - 3q + 6q
= -6 + 3q
The correct answer is option D
The simplifying value of the expression is,
⇒ 3q - 6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4p + 12 - 3q - 4p - 18 + 6q
Now,
Simplify the expression as;
⇒ 4p + 12 - 3q - 4p - 18 + 6q
⇒ 4p - 4p - 3q + 6q + 12 - 18
⇒ 0 + 3q - 6
⇒ 3q - 6
Thus, The simplifying value of the expression is,
⇒ 3q - 6
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