Answers
Given:
The graph of a triangle ABC.
A line is parallel to AC and passes through the point D.
To find:
The point at which the intersection of this parallel line be with the line BC.
Solution:
From the given figure it is clear that A(1,7), B(9,7), C(9,1) and D(5,7).
Slope of AC is
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope=\dfrac{1-7}{9-1}[/tex]
[tex]Slope=\dfrac{-6}{8}[/tex]
[tex]Slope=\dfrac{-3}{4}[/tex]
Slope of parallel lines are same. So, the slope of parallel line is also [tex]-\dfrac{3}{4}[/tex].
The parallel line passes through D(5,7) with slope [tex]-\dfrac{3}{4}[/tex]. So, the equation of the line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-7=-\dfrac{3}{4}(x-5)[/tex]
[tex]y=-\dfrac{3}{4}(x)+\dfrac{15}{4}+7[/tex]
[tex]y=-\dfrac{3}{4}(x)+\dfrac{28+15}{4}[/tex]
[tex]y=-\dfrac{3}{4}(x)+\dfrac{43}{4}[/tex] ...(i)
From the given graph it is clear that the line BC is a vertical line. So, the x-coordinates of all the points lie on BC are the same, i.e., 9.
Putting x=9, we get
[tex]y=-\dfrac{3}{4}(9)+\dfrac{43}{4}[/tex]
[tex]y=\dfrac{-27}{4}+\dfrac{43}{4}[/tex]
[tex]y=\dfrac{16}{4}[/tex]
[tex]y=4[/tex]
Therefore, the point at which the intersection of this parallel line be with the line BC is (9,4).
Related Questions
Help Quickly! Which line in the graph contains the point (4,3) and has a slope of 2/5?
*Giving Brainlyest if correct*
A. line r
B. line p
C. line s
D. line t
Answers
increase a gross by 10%
Answers
The results of increasing a gross by 10% is 158.4.
What is percentage?Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.
In mathematics, gross is written in figures as 144
increase a gross by 10%
= 144 + (10% × 144)
= 144 + (0.1 × 144)
= 144 + 14.4
= 158.4
Hence, 158.4 is the 10% increase in gross.
Complete question:
Calculate the increase in a gross by 10%.
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At the beginning of the week, James has 8 quarts of milk. At the end of the week there are 412 cups of milk left.
How many cups of milk did James drink during the week?
Answers
James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week
To determine how many cups of milk James drank during the week, we need to find the difference between the initial amount of milk and the amount of milk left at the end of the week. The initial amount of milk: 8 quarts = [tex]$8 \times 4 = 32$[/tex] cupsThe remaining amount of milk: [tex]$4 \frac{1}{2}$[/tex] cupsTo find the amount of milk James drank, we subtract the remaining amount from the initial amount: [tex]$32 \text{ cups} - 4 \frac{1}{2} \text{ cups} = 27 \frac{1}{2}$[/tex] cupsThe concept used in this problem is subtraction. By subtracting the amount of milk left at the end of the week from the initial amount of milk, we can determine how much milk James consumed during the week. The difference between these two values represents the amount of milk that James drank.Therefore, James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week.
NOTE: The given question has wrong information. The correct question is:
"At the beginning of the week, James has 8 quarts of milk. At the end of the week, there are [tex]$4 \frac{1}{2}$[/tex] cups of milk left. How many cups of milk did James drink during the week?"
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Find the 5th term in the expansion of (3x + 1)7 in simplest form.
Answers
The 5th term in the expansion of [tex](3x + 1)^7[/tex] would be [tex]945x^3[/tex].
Binomial expansionTo find the 5th term in the expansion of [tex](3x + 1)^7[/tex], we use the binomial theorem formula:
[tex](a + b)^n = nC0 a^n b^0 + nC1 a^(n-1) b^1 + nC2 a^(n-2) b^2 + ... + nCn-1 a^1 b^(n-1) + nCn a^0 b^n[/tex]
where nCk represents the binomial coefficient, given by the formula:
nCk = n! / (k!(n-k)!)
In this case, a = 3x and b = 1, so we have:
[tex](3x + 1)^7 = 7C0 (3x)^7 1^0 + 7C1 (3x)^6 1^1 + 7C2 (3x)^5 1^2 + 7C3 (3x)^4 1^3 + 7C4 (3x)^3 1^4 + 7C5 (3x)^2 1^5 + 7C6 (3x)^1 1^6 + 7C7 (3x)^0 1^7[/tex]
To find the 5th term, we need to look at the term with k = 4, which is:
[tex]7C4 (3x)^3 1^4[/tex] = [tex]35 (3x)^3[/tex]
= [tex]35 (3x)^3[/tex]
= [tex]35 (27x^3)[/tex]
Therefore, the 5th term in the expansion of [tex](3x + 1)^7[/tex] is [tex]945x^3[/tex].
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There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answers
Answer:
The ratio is 3:7
Step-by-step explanation:
You add 104+78
The un-simplified ratio is 78:182
hope this helps!!
rate this if it does!
HELP PLEASE ASAP PHOTO INCLUDED
Answers
The volume of water that the pool can hold is 150.72 cubic centimeters.
How to find the volume of the pool?Remember that the volume of a cylinder of radius R and height H is:
V = pi*R²*H
Where pi = 3.14
For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft
Replacing that in the volume formula we will get:
V = 3.14*(4cm)²*3cm
V = 150.72 cubic centimeters.
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x + 2y = 2 y = −2x − 2
Answers
The solution of the system of equations is (-2, 2).
How to solve the system of equations?Here we want to find the solution of the system of equations:
x + 2y = 2
y = -2x- 2
To solve this, we can replace the second equation into the first one, then we will get:
x + 2*(-2x - 2) = 2
Now we can solve that for x:
x - 4x - 4 = 2
-3x = 2 + 4
-3x = 6
x = 6/-3 = -2
Thus, the value of y is:
y = -2*-2 - 2
y = 4 - 2 = 2
The solution of the system is (-2, 2)
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Complete question:
"Which is the solution of the system of equations?
x + 2y = 2
y = -2x- 2"
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answers
Answer: where is the answer choices
Step-by-step explanation:
Suppose you pick 4 cards randomly from a well shuffled standard deck of 52 playing cards. The probability that you draw the 2,4,6, and 8 of spades in that order is
Answers
The probability of drawing the 2, 4, 6, and 8 of spades in that specific order is 0.0002.
What is the probability?The probability of drawing a specific card without replacement from a well-shuffled deck is 1/52 for the first card, 1/51 for the second card, 1/50 for the third card, and 1/49 for the fourth card.
We wish to draw the specific cards (2, 4, 6, and 8 of spades) in that specific order.
The probability will be:
Probability = (1/52) * (1/51) * (1/50) * (1/49)
probability = 0.0002.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The proof of ΔRUV ≅ ΔSUT is shown below.
Given that:
RSTV is a rectangle and U is the midpoint of VT.
Here, We have to Prove:
⇒ ΔRUV ≅ ΔSUT
Now, We can prove as;
Statement Reason
1) RSTV is a rectangle Given
2) Angle V and T are Because every angle in a rectangle is 90
right triangle.
3) ∠V ≅ ∠T Because both are right angle.
4) U is the midpoint of VT. Given
5) VU = UT By midpoint theorem.
6) VR ≅ TS Opposite sides of rectangle.
7) ΔRUV ≅ ΔSUT By SAS congruency theorem.
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The distribution for the life of refrigerators is approximately normal with a mean of 14 years and a standard deviation of 2.5 years. What percentage of refrigerators have lives between 11 years and 18 years?
Answers
The percentage of refrigerators that have lives between 11 years and 18 years is approximately 83.01%.
The values of 11 years and 18 years using the given mean and standard deviation, and then find the area under the standard normal curve between those two standardized values.
First, we standardize the value of 11 years:
z1 = (11 - 14) / 2.5 = -1.2
Next, we standardize the value of 18 years:
z2 = (18 - 14) / 2.5 = 1.6
Now we need to find the area under the standard normal curve between these two standardized values.
We can use a standard normal table or calculator to find this area.
Using a standard normal table, we can find the area between z = -1.2 and z = 1.6 by finding the area to the left of z = 1.6 and subtracting the area to the left of z = -1.2:
Area = P(-1.2 < z < 1.6) = P(z < 1.6) - P(z < -1.2)
Looking up these values in the standard normal table, we find:
P(z < 1.6) = 0.9452
P(z < -1.2) = 0.1151
Substituting these values, we get:
Area = 0.9452 - 0.1151 = 0.8301
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Please urgent help I can’t figure this out thank you guys for always helping
Answers
Answer:
Domain: {-24, -12, -8, 9, 14, 50}
Range: {23, 69, 83, 92, 97, 32}
Step-by-step explanation:
The domain of a function is the set of all possible input values (usually x) for which the function is defined. The range of a function is the set of all possible output values (usually y, which is synonymous with f(x)) that the function can produce.For a function like f(x), each coordinate is in the form (x, f(x)) aka (x, y)
Since our x-coordinates are -24, -12, -8, 9, 14, and 50, the domain of f(x) is {-24, -12, -8, 9, 14, 50}
Since our f(x) or y-coordinates are 23, 69, 83, 92, 97, and 32, the range is {23, 69, 83, 92, 97, 32}
Find the greatest common factor of 21x^4 and 49x^3
Answers
The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to 7x³.
To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.
To find the factors, we can break each term down into its prime factors:
21x⁴ = 3 * 7 * x * x * x * x
49x³ = 7 * 7 * x * x * x
The common factors are 7 and x³. To find the GCF, we multiply these common factors together:
GCF = 7 * x³
GCF = 7x³
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The side of a square is measured to be 16 ft with a possible error of ±0.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your answer.
Answers
The estimated error in the calculated area is approximately 3.2ft²
How did we estimate the error?To estimate the error in the calculated area of a square, use linear approximation or differentials.
The area of a square is given by the formula A = s², where s represents the length of a side.
Calculate the area of the square using the given side length of 16 ft:
A = (16 ft)²
A = 256 ft²
Now, let's consider the possible error in the side length, which is ±0.1 ft. Treat this error as a change in the side length (Δs) and use linear approximation or differentials to estimate the corresponding change in the area (ΔA).
Using linear approximation, express the change in the area as:
ΔA ≈ 2s Δs
Substituting the values:
ΔA ≈ 2(16 ft)(0.1 ft)
ΔA ≈ 3.2 ft²
Therefore, the estimated error in the calculated area is approximately 3.2ft².
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LUUK al uit grapii velow.
Part B
-4
Part A
-3-2
Part C
3
2
-2
-3
Part D
Which part of the graph best represents the solution set to the system of
inequalities y ≥x+1 and y + x>-1? (5 points)
Answers
The solution set of given inequalities are represented by Part A.
The given inequalities are
⇒ y ≥ x + 1 and y + x > -1
Hence, The related equations of both inequalities are
y = x + 1
Put x=0, to find the y-intercept and put y=0, to find x intercept.
y = 0 + 1
y = 1
And, 0 = x + 1
x = - 1
Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).
Similarly, for the second related equation
y + x = - 1
y + 0 = - 1
y = - 1
0 + x = - 1
x = - 1
Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).
Now, join the x and y-intercepts of both lines to draw the line.
Now check the given inequalities by (0,0).
0 ≥ 0 + 1
0 ≥ 1
It is a false statement, therefore the shaded region is in the opposite side of origin.
0 + 0 ≥ - 1
0 ≥ - 1
It is a true statement, therefore the shaded region is about the origin.
Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.
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make a table for each equation using the following numbers as : x -2,-1,0,1
y=3x-2
Answers
The equation y = 3x - 2. can be placed in table as shown below. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.
In this table, each row represents a pair of values (x, y) that satisfy the equation y = 3x - 2. For example, when x is -2, y is calculated as 3(-2) - 2 = -8. Similarly, for the other values of x, the corresponding values of y are calculated accordingly.
Here's a table showing the values of x and the corresponding values of y for the equation y = 3x - 2:
x y
-2 -8
-1 -5
0 -2
1 1
To fill in the table, substitute each value of x into the equation and calculate the corresponding value of y. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.
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Extract the common factor from
(1) 2.x-2.y
(2) 5.x.x.x+5.3.x.y
Answers
Answer:
(1) 2x - 2y = 2(x - y)
(2) 5x^3 + 15xy = 5x(x^2 - 3y)
Find your answer on above picture ihope it will help you thank you.
please help me important question in image
Answers
Segment BF is 36 will be the accurate statement.
Similarity theorem of triangleA triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.
From the given triangle, the following expression is true:
EC/FC = AC/BF+FC
Substitute the given parameters into the formula to have:
20/30 = 24+20/BF+30
20/30 = 44/BF+30
2/3 = 44/BF + 30
2(BF+30) = 132
2BF + 60 = 132
2BF = 132 - 60
2BF = 72
BF = 36
Hence the correct statement will be that segment BF is 36
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Does the data follow a normal distribution? Why or why not?
Answers
What the meaning of statement this?
Answers
The statement means that an n-ary operation on set X takes n inputs and produces a single output, with the operation defined by the function f:[tex]X^n[/tex] -> X.
The statement "An n-ary operation on x is functions f:X^n -> X" can be understood as follows:
In mathematics, an n-ary operation refers to an operation that takes n inputs and produces a single output. In this case, the operation is defined on a set X, and the inputs are elements from X. The result of the operation is also an element from X.
The symbol "f" represents the function that performs the n-ary operation. The function f takes n arguments, which are elements from the set X. The notation [tex]X^n[/tex] indicates the Cartesian product of X with itself n times, meaning that the inputs are taken from X and repeated n times as ordered tuples. The arrow "->" signifies that the function f maps the n-tuple of inputs to a single element in X.
To put it simply, the statement is describing a mathematical operation that takes n elements from a set X and combines them in some way to produce a single element, where the combination is determined by the function f. This function f can be defined explicitly based on the specific operation being considered.
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Nancy flew home from vacation with a heavy bag. With the first airline she flew, Nancy had to pay $20 to check her bag, plus $5 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Nancy had to pay $4 per pound that her bag was over the weight limit, in addition to the checked bag fee of $25. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag? Write a system of equations, graph them, and type the solution.
Answers
Nancy's bag was 0.2kg over the weight limit.
What weight in which Nancy's bag exceeded limit?Let's denote the weight limit as x.
The total cost for the first airline can be expressed as:
Cost1 = 20x + 5
The total cost for the second airline is given by:
Cost2 = 25x + 4
As fees were same with both airlines, we will set up equation to find the weight difference:
20x + 5 = 25x + 4
20x-25x = 4-5
-5x = -1
x = -1/-5
x = 0.2kg
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Question 14 of 15
Which number line shows the solutions to x+8 > 15?
Answers
A number line that shows the solutions to x+8 > 15 include the following: B. number line B.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Based on the information provided above, we have the following equation (inequality);
x + 8 > 15
By subtracting 8 from both sides of the equation (inequality), we have;
x + 8 - 8 > 15 - 8
x > 7
This ultimately implies that, the inequality must be shaded to the right with an open dot because the inequality symbol is greater than (>).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
the box plot below represents some data set. what percentage of the data values are greater than 130
Answers
The percentage of the data values that are greater than 130 is 25%
What percentage of data values are greater than 130From the question, we have the following parameters that can be used in our computation:
The box plot
From the box plot, the five-number summary are
40, 70, 110, 130, and 150
In the above five-number summary, we have
Third quartile = 130
This means that the percentage of the data values that are greater than 130 is 25%
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A school class went on a field trip to see a magician perform there were 17 females 20 males in the class the magicians randomly selected a volunteer from the audience in which had 52 females and 68 males given that the randomly selected audience member is a student from the class which equation can be used to find the probability p that the perdimos also a female?please help does anyone know the answer
2
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Answers
The probability p that the perdimos is also a female is 17/120
What is Conditional Probability?Conditional Probability is the possibility or likelihood of an event or outcome happening, based on the existence of a previous event or outcome.
How to determine this
When there were 17 females in class
And 20 male in class
When randomly selected, the female are 52
And males are 68
To calculate the selected volunteer is a student of the class.
= 20 + 17/52 + 68
= 37/120
To calculate the probability that the selected student is female.
= 17/52 + 68
= 17/120
= 0.14
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A thermometer reading 10°C is brought into a room with a constant temperature of 36°C. if the thermometer reads 14°C after 2 minutes, what will it read after beint left in the room for 4 minutes? and for 9 minutes?
Answers
Answer:
4 minutes: 17.4 °C9 minutes: 23.7 °CStep-by-step explanation:
You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.
Newton's law of coolingNewton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...
T = 36 -26·(22/26)^(t/2)
At times of t=4 and t=9, the temperature readings will be ...
4 minutes: 36 -26(11/13)^(4/2) ≈ 17.4 °C9 minutes: 36 -26(11/13)^(9/2) ≈ 23.7 °C__
Additional comment
The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.
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find the surface area of a regular hexagonal pyramid with the base edges of 10 and a slant height of 9 inches.
Answers
The surface area of the regular hexagonal pyramid is equal to 529.8 in² to the nearest tenth.
How to calculate for the surface area of the regular hexagonal pyramidArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of nonagon × (n)number of side
apothem = s/[2tan(180/n)]
apothem = 10in[2tan(180/6)]
apothem = 5√3in
perimeter = 6 sides × 10in = 60 in²
Area of the bottom hexagon = 1/2 × 5√3 × 60 in²
Area of the bottom hexagon = 259.8075 in²
Area of one triangle side face = 1/2 × 10in × 9in = 45 in²
Area of 6 triangle side faces = 6 × 45 in² = 270 in²
Surface area of the regular pyramid = 259.8075 in² + 270 in²
Surface area of the regular pyramid = 529.8 in²
Therefore, the surface area of the regular hexagonal pyramid is equal to 529.8 in²
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Find the quotient and express the answer in scientific notation. 302 ÷ (9.1 x 10^4 )
Answers
The quotient of 302 ÷ (9.1 x [tex]10^4)[/tex] in scientific notation is approximately 3.31868131868 x [tex]10^1[/tex]
How to find the quotientDividing 302 by 9.1 gives:
302 ÷ 9.1 ≈ 33.1868131868
Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:
33.1868131868 ≈ 3.31868131868 x[tex]10^1[/tex]
Therefore, the quotient of 302 ÷ (9.1 x [tex]10^4[/tex]) in scientific notation is approximately 3.31868131868 x[tex]10^1[/tex]
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Identify the part, percent and base.
$37.60 interest earned on a $460 investment at 8%.
Part:
Percent:
Base:
Answers
The given information is,$37.60 interest earned on a $460 investment at 8%.
Part:The amount of interest earned is called the part. Here, the amount of interest earned is $37.60. Hence the part is $37.60.
Percent:The rate per 100 units of the base is called the percent. Here, the percent rate is 8%.
Base:The original amount invested or borrowed is called the base. Here, the original investment amount is $460. Hence the base is $460.
Thus,
Part: $37.60
Percent: 8%
Base: $460.
Part: The part is the interest earned, which is $37.60.
Percent: The percent is 8%, which represents the annual interest rate.
Base: The base is the amount of the investment, which is $460.
You are holding a kite string in your hand and your hand is 3 feet above the ground. The kite is 225 feet above the ground and the angle of elevation from your hand to the kite is 42°. How long is the kite string?
Answers
The kite string is 331.77 feet long.
How to find how long the kite string is?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for labeling. Where l represents the length of kite string.
h = 225 - 3 = 222 ft
Using trig. ratio:
sin 42° = 222/l
l = 222 / sin 42°
l = 331.77 feet
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Need help, show work please
Answers
Using the first two points we can get an exponential model:
[tex]y = (225/23)*(23/15)^x[/tex]
How to find the exponential equation?
The general exponential equation can be written as:
[tex]y = A*(b)^x[/tex]
We can replace any two values of the table to get the system of eqautions:
[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]
Taking the quotient between the second and the first equation we get:
[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]
Replacing that on the first equation we will get:
[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]
Then an exponential model is:
[tex]y = (225/23)*(23/15)^x[/tex]
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