The discounted cost per person is, $24.50
And, The total cost for 20 people at the discounted price is, $2,205.
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;
A group of 20 people wants to go on the Caribbean cruise.
And, The cruise ship offers a discount of 10%, or 0.1 times the cost, for groups of more than 10 people.
Hence, The discounted cost per person is,
⇒ 1% of $2450
⇒ 1/100 × $2450
⇒ $24.50
And, The total cost for 20 people at the discounted price is,
⇒ $2450 - 10% of 2450
⇒ $2450 - 10/100 × 2450
⇒ $2450 - $245
⇒ $2,205
Thus, The discounted cost per person is, $24.50
And, The total cost for 20 people at the discounted price is, $2,205.
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Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of D′ if the preimage is rotated 90° counterclockwise.
D′(−2, −4)
D′(−2, 4)
D′(2, 4)
D′(4, −2)
The image vertices of D′ if the preimage is rotated 90° counterclockwise is: A. D′(−2, −4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:
(x, y) → (-y, x)
Ordered pair D = (-4, 2) → Ordered pair D' = (-2, -4)
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.Which is not a method by which minerals form
The option that is not a way by which minerals are being formed is decrystallization. That is option B
What are ways by which minerals are formed?Minerals are organic substances that are form through the following ways;
volcanic gases, sediment formation, oxidation, crystallization from magma, or deposition from a saline fluid,Decrystallization is not a way through which minerals are formed because it is just the break down of solid or crystal structures.
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Complete question:
Which of the following is not a method by which minerals form?. a. crystallization. b. decrystallization. c. water evaporation from a solution. d. cooling of magma or lava
An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping. describe how the linear function would change if the shipping charge applied to each sweatshirt.
The description is that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges
How to describe how the linear function would changeFrom the question, we have the following parameters that can be used in our computation:
The company charges $6.50 for each sweatshirt Flat fee of $3.99 for shippingUsing the above as a guide, we have the following:
Slope = 6.50
This means that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges
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32c as a percentage of R3. 80
Answer:
40%
Step-by-step explanation:
32 out of 80 as a percentage it is 40%
Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
How many grams of 25% sugar syrup did Samantha use?
Pls help :D Thxs
Samantha used 120 grams of 25% sugar syrup.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
Let Samantha used y grams of 25% sugar syrup.
Then, she used (120 - y) grams of 10% sugar syrup.
We know that the final concentration of sugar syrup is 15%, which means that 15% of the total 120 grams of the syrup is sugar.
This can be expressed as:
0.15 x (y + (120 - y)) = 0.15 x 120
Expanding and simplifying the equation, we get:
0.15y + 0.15 x 120 - 0.15y = 18
0.15 x 120 = 18
Solving for y, we get:
y = 120 x 18 / (0.15 x 120)
= 120 x 18 / 18
= 120.
Hence, Samantha used 120 grams of 25% sugar syrup.
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Answer:
work hard you can get it
Step-by-step explanation:
lol
a right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. what is the surface area in square centimeters if the height is 2 centimeters?
The surface area of the right triangular prism with legs of 5 centimeters and 12 centimeters, a hypotenuse of 13 centimeters, and a height of 2 centimeters is 108 square centimeters.
Surface area refers to the total area of the surface of a three-dimensional object. When it comes to a right triangular prism, the surface area includes the area of all six faces.
Let's call the height of the triangular prism "h" and label the legs of the triangle "a" and "b". Using these values, we can find the area of the base of the triangular prism. The area of a right triangle is equal to 1/2 times the product of the legs, so the area of the base is
=> (1/2) * a * b = (1/2) * 5 * 12 = 30 square centimeters.
Next, we need to find the surface area of each of the three lateral faces. Each of these faces is a rectangle, so we can find the area by multiplying the height of the prism by the length of one of the sides of the triangle base.
The length of one side of the triangle base is equal to the hypotenuse, which is 13 centimeters. So, the surface area of each of the three lateral faces is
=> h * 13 = 2 * 13 = 26 square centimeters.
Finally, we can find the total surface area by adding the surface area of the base and the surface area of the three lateral faces.
The surface area of the base is 30 square centimeters, and the surface area of each lateral face is 26 square centimeters, so the total surface area is
=> 30 + 3 * 26 = 30 + 78 = 108 square centimeters.
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Find the equation of the line shown
Answer:
using the equation of the straight line we solve
Gary takes a suitcase and backpack on an airplane. The suitcase weighs 4 times as much as the backpack. The suitcase and the backpack together weigh 40 lb. HURRY!!! PLS :( Thank You, too!
suppose is an matrix that can be obtained from using the row operations (in the given order) what is ?
we add row 1 to row 3 to get the final matrix = [3, 0, 3; 1, 1, 1; 0, 0, 0]. Thus, the new matrix is obtained by applying the given row operations in the given order.
Let A be a given matrix.
Row Operation 1: Exchange row 1 and row 2.
Row Operation 2: Multiply row 1 by 3.
Row Operation 3: Add row 1 to row 3.
Then,
= [ 3, 0, 3; 1, 1, 1; 0, 0, 0 ]
We can obtain the matrix by applying the row operations in the given order. First, we exchange row 1 and row 2 to obtain the matrix [1, 1, 1; 3, 0, 3; 0, 0, 0]. Then we multiply row 1 by 3 to get [3, 0, 3; 1, 1, 1; 0, 0, 0]. Finally, we add row 1 to row 3 to get the final matrix = [3, 0, 3; 1, 1, 1; 0, 0, 0]. Thus, the new matrix is obtained by applying the given row operations in the given order.
The complete question is :
Suppose [tex]$\begin{bmatrix}4 & -2 & 3 \\2 & 3 & 1 \\5 & 1 & -2\end{bmatrix}$[/tex] is an matrix that can be obtained from [tex]$\begin{bmatrix}1 & 2 & 3 \\3 & 2 & 1 \\2 & 5 & -2\end{bmatrix}$[/tex]using the row operations (in the given order) [tex]$R_1 \leftrightarrow R_2, R_2 - 3R_1, R_3 - 5R_1$[/tex]
What is [tex]$\begin{bmatrix}1 & 2 & 3 \\3 & 2 & 1 \\2 & 5 & -2\end{bmatrix}$[/tex]?
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What is the measure of angle X?
Enter your answer as a decimal in the box. Round only your answer to the nearest hundredth.
m∠X= °
Using a trigonometric relation we will see that the value of x is 81.2°
What is the measure of angle X?We can see that we have a right triangle, and the angle x is the one that is on the top vertex.
We can use any trigonometric relation to find the value of x, for example we can use:
sin(x) = (opposite cathetus)/(hypotenuse)
Where we can see that:
opposite cathetus = 84
hypotenuse = 85
Then we will get:
sin(x) = 84/85
x = Asin(84/85) = 81.2°
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Look at the digram.
If AB BC and AB = 18 inches, AE = 5 inches, and CE = 6 inches, what is the length of AD?
A. 1.5 inches
B. 2.5 inches
C. 6.5 inches
D. 7.5 inches
Length of AD is, 2.5 inches
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Values are,
AB = 18 inches,
AE = 5 inches,
CE = 6 inches,
Let the length of ED = x
Now, By the figure,
⇒ ΔABD ≈ ΔECD
Hence, By definition of proportional we get;
⇒ AB / AD = EC / ED
⇒ AB / (AE + ED) = EC / ED
⇒ 18 / (5 + x) = 6 / x
⇒ 3x = 5 + x
⇒ 3x - x =5
⇒ 2x = 5
⇒ x = 2.5 inches
Thus, Length of AD is, 2.5 inches
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A farmer takes 250 chickens to be sold at a market. In the first hour he sells 8% of his chickens. In the second hour he sells 10% of those that were left. What percentage of the original number did he manage to sell in the two hours?
Answer:
17.2%
Step-by-step explanation:
In the first hour:
The farmer sells 8% of the total chickens:
[tex]= \frac{8}{100}[/tex]×[tex]250[/tex]
= 20 chickens
Therefore, the number of chickens left are:
= (250 - 20) chickens
= 230 chickens
In the second hour:
The farmer sells 10% of the chickens left:
= [tex]\frac{10}{100}[/tex]×[tex]230[/tex]
= 23 chicken
∴ The total number of chickens sold in the two hours = (20 + 23) chickens
= 43 chickens
43 has to be expressed as a percentage of the original number (i.e. 250)
Percentage = [tex]\frac{Number Of Chickens Sold}{Total Number Of Chickens}[/tex]×[tex]100[/tex]%
= [tex]\frac{43}{250}[/tex]×[tex]100[/tex]%
= 17.2%
Match the square root expression with it's correct simplified radical.
The square root expression with it's correct simplified radical can be matched as follow:
√45 = 3√5
√200 = 10√2
√80 = 4√5
√24 = 2√6
How to match the square root expression with it's correct simplified radical?
A simplified radical is a radical expression in which the radicand (the expression inside the square root symbol) has been simplified as much as possible. For example, the simplified form of √8 is 2√2.
√45 = √(9*5) = √9 * √5 = 3 * √5 = 3√5
√200 = √(100*2) = √100 * √2 = 10 * √2 = 10√2
√80 = √(16*5) = √16 * √5 = 4 * √5 = 4√5
√24 = √(4*6) = √4 * √6 = 2 * √6 = 2√6
Thus, match the square root expression with it's correct simplified radical accordingly.
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1/5 divided by 3/5 it wont say the answer
Answer:Exact Form:
1/3
Decimal Form:
0.33333333333
Step-by-step explanation:
Answer:
1/3 or 0.333333333333333333333333333333333333
Step-by-step explanation:
1/5 / 3/5
Dividing can be done by multiplying the number by its reciprocal (flipped).
So, 3/5 has a reciprocal of 5/3
1/5*5/3 = 5/15
5/15 = 1/3 or 0.33333(repeated forever)
Question's attached below.
Thanks! :)
Answer:
$ 4564.32
Step-by-step explanation:
APR=2%, monthly interest rate, i=2%/12=0.02/12
Monthly payment, A=250
After 18 monnth, n=18 months,
the balance. Pis therefore
P = A((1+i)^n-1)/i
=250((1+0.02/12)^18-1)/(0.02/12)
=$ 4564.32
what is the area of rectangle with length is 4/7 and width is 3/5
Answer: 12/35 units sqr
Step-by-step explanation: Multiply both values to find area and put proper units.
Answer:
Step-by-step explanation:
The area of a rectangle is given by the formula: area = length x width.
For a rectangle with length 4/7 and width 3/5, the area can be calculated as follows:
area = 4/7 x 3/5
= 12/35
So, the area of the rectangle with length 4/7 and width 3/5 is 12/35 square units.
the population of all standardized exam scores has a mean of 500 and a standard deviation of 100. twenty-five students in a professor's class take the exam, and their average score is 525. what is the z statistic that is associated with the class's average?
The z statistic that is associated with the class's average is 1.25.
In the given question the population of all standardized ex scores has a mean of 500 and a standard deviation of 100 . Twenty-five students in a professor's class take the ex , and their average score is 525.
We have to find z statistic that is associated with the class's average.
n = 25
μ = 500
σ = 100
[tex]\bar X[/tex] = 525
Then ,
z statistic = [tex]\frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt n} }[/tex]
putting the value in the formula:
z statistic = (525-500)/(100/\sqrt 25)
z statistic = (25)/(100/5)
z statistic = (25)/(20)
z statistic = 1.25
Therefore,
The z statistic that is associated with the class's average is 1.25.
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find the value of x , please show how you did it
The value of x in the figure is 15 degrees
How to find the value of xThe value of x in the figure is solved using the concept of sum of exterior angles in a polygon
The sum of exterior angles in a polygon is 360
7x + 83 + 33 + 6x + 49 = 360
collecting like terms
7x + 6x = 360 - 83 - 33 - 49
13x = 195
isolating x
x = 15 degrees
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PLS ASAP!! WILL GIVE BRAINLEST
The sides and angle of the right triangle are as follows:
b = 57.2 unitsc = 57.4 unitsB = 85 degreesHow to find the side and angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of the triangle can be found using trigonometric ratios as follows:
Hence,
tan 5 = opposite / adjacent
tan 5 = 5 / b
b = 5 / tan 5
b = 57.1506949525
Hence,
b = 57.2 units
sin 5 = opposite / hypotenuse
sin 5 = 5 / c
c = 5 / sin 5
c = 57.3685943662
c = 57.4 units
B = 180 - 90 - 5
B = 85 degrees
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Can someone please help me with this question. If you do, you’ll be rewarded with brainliest and extra points!
Answer:
EG/HJ=GF/JI or EG/HJ=FE/IH
Step-by-step explanation:
Given
AngleF=AngleI
AngleE=AngleH
Therefore triangles EGF AND HJI are similar by Angle-Angle Similarity Theorem
So
EG/HJ=GF/JI=FE/IH as they are the corresponding sides of a similar triangle
the sum of a five-term arithmetic sequence is 100. if all terms are positive integers, what is the smallest possible value for a term?
The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".
The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100
Simplifying the expression, we get:
5a + 10d = 100
Dividing both sides by 5, we get:
a + 2d = 20
Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:
1 + 2 * 1 = 3
Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.
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Mr. Ford wants to better understand the value of used cars over time. He reviewed some
used-car ads and recorded the relationship between age and price in a table. Finally, he
calculated a line of best fit.
Used cars
Age in years (x) 3 6 4
2
6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:
They likely had an average price around $22,000 when new.
They typically lose $2,200 of value per year.
At 5 years old, they had an average value of around $11,000.
You can estimate that the used cars Mr. Ford reviewed were worth roughly $2,200 less now than when they were new, had an average price of around $22,000 when new, and typically lose $2,200 of value per year. (option 1, 2, 3)
To calculate this, you can substitute the x-values from the table into the equation and solve for y. For example, when x is 3,
y = -2,200(3) + 22,000 = $15,000which is the price of the car when it was 3 years old. This same formula can be used to calculate the price of the car at other age values and shows that the car loses an average of $2,200 of value per year. At 5 years old, the equation would be
y = -2,200(5) + 22,000 = $11,000which is the average value of the used car at that age.
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Complete Question:
Mr. Ford wants to better understand the value of used cars over time. He reviewed some used-car ads and recorded the relationship between age and price in a table. Finally, he calculated a line of best fit. Used cars Age in years (x) 3 6 4 2 6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:They likely had an average price of around $22,000 when new.They typically lose $2,200 of value per year.At 5 years old, they had an average value of around $11,000.The bottom of a circular swimming pool with a radius of 30ft, was painted blue. How many square feet of the pool was painted blue?
Answer:
2826 sqft
Step-by-step explanation:
π r² = 900π =2826
A rocket is launched in the air. Its height in feet is given by h(t)= -16t^2+88t where t represents the time in seconds after launch. How long is the rocket in the air?
Answer: ___ seconds
For the given height function h(t)= -16t²+88t the rocket is in the air for 5.5 seconds.
Height of the launched rocket is equal to :
h(t)= -16t²+88t
Time is represented by 't' in seconds after launch
'h' represents the height of the rocket.
For how long time rocket is in the air :
h(t) = 0
⇒ -16t²+88t = 0
⇒ t ( -16t+88 ) = 0
⇒ t = 0 or ( -16t+88 ) = 0
value of time 't' cannot be equal to zero.
This implies ( -16t+88 ) = 0
⇒16t = 88
⇒ t = 88 / 16
⇒ t = 5.5 seconds
Therefore, the time for which rocket is in the air as per given height function is equal to 5.5 seconds.
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At a university, the student body is made up of approximately 12000 students. Of that total, there are approximately 3500 graduate students and 8500 undergraduate students. Which of the following fractions represents the ratio of undergraduate students to graduate students?
Step-by-step explanation:
Seeing the question, I assume there are answer choices, but I'll give all possible answers below.
A ratio is pretty much a fraction, that's about it. It's asking the ratio of undergraduate to graduate, which creates
[tex] \frac{undergraduate}{graduate} [/tex]
Now we plug in those numbers in the correct spots
[tex] \frac{8500}{3500} [/tex]
Now to simplify. Since both of these numbers end in 0, there a little truck you can do to automatically make it smaller, and that's getting rid of all the 0s on the end. That makes it...
[tex] \frac{85}{35} [/tex]
To continue simplifying
[tex] \frac{8500}{3500} = \frac{85}{35} = \frac{17}{7} [/tex]
if x,y,z are different and =mod x x^2 1+x^3
y y^2 1+y^3 = 0 then show than 1+xyz=0
z z^2 1+z^3
Given that x, y, z are different and satisfy the equations:
x^3 + x^2 - x = 0
y^3 + y^2 - y = 0
z^3 + z^2 - z = 0
We can multiply the first equation by y, the second by z, and the third by x to obtain:
x^3y + x^2y - xy = 0
y^3z + y^2z - yz = 0
z^3x + z^2x - zx = 0
Adding these three equations together, we get:
x^3y + x^2y - xy + y^3z + y^2z - yz + z^3x + z^2x - zx = 0
Expanding and simplifying, we find that:
x^2y + xy^2 + y^2z + yz^2 + z^2x + zx^2 - xy - yz - zx = 0
Now, we use the fact that x, y, and z are roots of the equations given above to simplify the expression further:
x^2 - x + y^2 - y + z^2 - z = 0
We can also write this as:
(x - 1)(x + 1) + (y - 1)(y + 1) + (z - 1)(z + 1) = 0
This expression can be factorized as:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
Since x, y, and z are all different, we have that:
(x - 1)(x + 1) ≠ 0
(y - 1)(y + 1) ≠ 0
(z - 1)(z + 1) ≠ 0
Therefore, we have:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = (x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
So, we can conclude that:
xyz = -1
And,
1 + xyz = 0
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Write an exponential decay function to model each situation. Then estimate the value of x for the given value of f(x)
initial value: 100
decay factor: .95
f(x)=60
Answer:
f(x) = 100(0.95^x)x ≈ 9.959 for f(x) = 60Step-by-step explanation:
You want the value of x that makes f(x) = 60, when f(x) is the exponential function with an initial value of 100 and a decay factor of 0.95.
Exponential functionThe form of an exponential function is ...
f(x) = (initial value) · (decay factor)^x
ApplicationFor the given initial value and decay factor, the function is ...
f(x) = 100 (0.95^x)
Solving for x, we find ...
f(x)/100 = 0.95^x
log(f(x)/100) = x·log(0.95)
x = log(f(x)/100)/log(0.95)
For f(x) = 60, the value of x is about ...
x = log(60/100)/log(0.95) ≈ 9.959
The value of x is about 9.959.
Given: KLMN is a trapezoid, KL=MN,
m∠1=m∠2,
LM:KN = 8/9, PKLMN=132
Find The length of midsegment
KLMN is a trapezoid where KL=MN and m∠1=m∠2 . It is also given that LM:KN = 8/9 and PKLMN=132.The midsegment is 34 units long.
The trapezoidal shape KLMN, where KL = MN.
m∠1=m∠2
Moreover, LM/KN = 8/9
Additionally, KLMN's perimeter is 132 units.
The midsegment's size (KM).
We can see that in the above case, KM is a transversal in relation to the parallel lines LM and KN. which implies,
∠KML=∠MKN
∠1=∠2
Two base angles are clearly equal. So, KLM and KMN are isosceles triangles.
Using the side ratios of two triangles as an example,
= KL: LM: MN: KN
= 8 : 8 : 8 : 9
The ratio units add out to 8 + 8 + 8 + 9 = 33. Consequently, each ratio's value is,
=[tex]\frac{perimeter}{33} \\\\\frac{132}{33} \\\\=4[/tex]
The segment LM's length is thus,
LM=8×4=32
Additionally, section KN's length is
KN=9×4=36
Taking the average of LM and KN as, one can then determine the length of the midsegment KM.
[tex]KM=\frac{LM+KN}{2} \\\\\\KM=\frac{32+36}{2}[/tex]
KE=34
As a result, the midsegment is 34 units long.
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PLEASE PLEASE HELP!!!
Solve √3x + 4 - 2 = 3
a. x = -1
b. x = 7
c. x ≈ 9.7
d. no solution
If the graph of f(x) = 9* is shifted 2 units to the right, then what would be the equation of the new graph?
The equation of the new graph is f(x) = 9^(x - 2)
What would be the equation of the new graph?From the question, we have the following parameters that can be used in our computation:
f(x) = 9^x
Also, we have
shifted 2 units to the right,
This is represented as
(x, y) = (x - 2, y)
Substitute the known values in the above equation, so, we have the following representation
f(x) = 9^(x - 2)
Hence, the function is f(x) = 9^(x - 2)
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