A quantity that is compounded continuously follows the next equation:
[tex]A=Pe^{rt}[/tex]Where:
[tex]\begin{gathered} A=\text{ amount in time ''t''} \\ P=\text{ initial amount} \\ r=\text{ rate of interest in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Now, the interest rate in decimal notation is determined by dividing the percentage by 100:
[tex]r=\frac{4.75}{100}=0.0475[/tex]Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:
[tex]A=2P[/tex]Substituting in the formula we get:
[tex]2P=Pe^{rt}[/tex]Now, we can cancel out the "P":
[tex]2=e^{rt}[/tex]Now, we solve for "t". First, we take the natural logarithm to both sides:
[tex]ln2=lne^{rt}[/tex]Now, we use the following property of logarithms:
[tex]lnx{}^y=ylnx[/tex]Applying the property we get:
[tex]ln2=rtlne[/tex]We have that:
[tex]lne=1[/tex]Therefore:
[tex]ln2=rt[/tex]Now, we divide both sides by "r":
[tex]\frac{ln2}{r}=t[/tex]Now, we substitute the value of "r":
[tex]\frac{ln2}{0.0475}=t[/tex]Solving the operations:
[tex]14.593=t[/tex]Therefore, the right option is A.
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.
What is a rectangle?A rectangle is a type of parallelogram that has equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
The dimensions of the given rectangle is (650 - 2x) and x.
Then, the area of the given rectangle is A(x) = x(650 - 2x)
In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,
(660 - 2x) - 2x = 0
=> 4x = 660
=> x = 660 / 4
=> x = 115
Now, the maximum area is the value of A(x) at x = 115 as below,
= 115 × (650 - 2×115)
= 115 × 320
= 36800
The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.
Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width labeled in the figure is given as 115 meter.
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2(x2 - 4x) + 5(x + 1)x(2x + 1) - (4x - 5)(x² - 6x + 7) - (x² - 14x + 13)x(3x - 4) - 3(x² + 2) + 122x(x + 1) + x(x + 1)4(x+ - 1.5x) + 2(x? - 3)8x - 62x2 - 3x + 5Don
Starting with the first expression:
[tex]\begin{gathered} (x^2-6x+7)-(x^2-14x+13) \\ \Rightarrow x^2-6x+7+x^2+14x-13 \\ \text{collect like-terms} \\ x^2+x^2-6x+14x-13+7 \\ \Rightarrow2x^2+8x-6 \\ \\ \text{This is not the answer, as it is not the same with the two(2) expressions given in the solution} \end{gathered}[/tex]Simplifying the second expression:
[tex]\begin{gathered} 2(x^2-4x)+5(x+1) \\ \Rightarrow2x^2-8x+5x+5 \\ \Rightarrow2x^2-3x+5 \\ \\ \text{This expression is equal to the option B} \end{gathered}[/tex]Simplifying the third expression:
[tex]\begin{gathered} x(2x+1)-(4x-5)_{} \\ \Rightarrow2x^2+x-4x+5 \\ \Rightarrow2x^2-3x+5 \\ \\ \text{This expression is also equal to option B} \end{gathered}[/tex]Simplifying the fourth expression:
[tex]\begin{gathered} x(3x-4)-3(x^2+2)+12x \\ \Rightarrow3x^2-4x-3x^2-6+12x \\ \Rightarrow3x^2-3x^2-4x+12x-6 \\ \Rightarrow8x-6 \\ \\ \text{This is correct for option A} \end{gathered}[/tex]Simplifying the last expression:
[tex]\begin{gathered} x(x+1)+x(x+1)-4(x^2-1.5x)+2(x^2-3) \\ \Rightarrow x^2+x+x^2+x-4x^2+6x+2x^2-6 \\ \Rightarrow x^2+x^2-4x^2+2x^2+x+x+6x-6 \\ \Rightarrow8x-6 \\ \\ \text{This expression is also true for option A} \end{gathered}[/tex]Farmer Joogh wanted to sell some dubbles and gespils at the market.
She expected to sell no more than 11 units. She planned to charge $7
per dubble and $4 per gespil. She expected to make no less than $56.
She expected to sell at least 3 gespils.
Write a system of statements, in standard form, modeling the
relationships between amount of dubbles (x) and amount of gespils
(Y)
The inequalities which represent relationships between the number of doubles (x) and amount of gospels (y) are x + y ≤ 11,7x + 4y ≥ 56 and y ≥ 3.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
No more than 11
x + y ≤ 11
Total earning ≥ $56
7x + 4y ≥ 56
At least 3 gospels
y ≥ 3
Hence "The inequalities which represent relationships between the number of doubles (x) and amount of gospels (y) are x + y ≤ 11,7x + 4y ≥ 56 and y ≥ 3".
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WILL GIVE BRAINIEST!!!!
The value of x for functions f(x)=(1+2x)/x and g(x)=2+x is 1 or -1
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
f(x)=(1+2x)/x
g(x)=2+x
f(x)=g(x)
Plug in values of f(x) and g(x)
(1+2x)/x=2+x
1+2x=x(2+x)
Apply distributive property on RHS
1+2x=2x+x²
1+2x-2x=x²
x²=1
x=±1
The value of x is 1 or -1.
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What is the area of the entire rectangle?
triangles?
square units
6.2 in.
8 in.
square units What is the area of one of t
Answer:
Step-by-step explanation:
Area of the triangle is:
A = 1/2 * (Base * Height)
A = 1/2 * (b * h)
A = 1/2 * (8 * 6.2)
A = 1/2 * 49.6
A = 24.8
Area of the rectangle is
A = Base * Height
A = b * h
A = 8 * 6.2
A = 49.6
Find slope for (19,-2),(-11,10)
Answer:
-2/5
Step-by-step Explanation:
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{10 - ( - 2)}{ - 11 - 19} [/tex]
[tex]m = \frac{12}{ - 30} [/tex]
[tex]m = - \frac{2}{5} [/tex]
Help me please and give me easy way how to solve
To solve for the value of x in the length of a rectangle:
[tex]\begin{gathered} \text{Length = (2x+1)cm} \\ \text{width = 12cm} \\ \text{Area is not less than 108cm}^2 \end{gathered}[/tex]Area of a rectangle = length x width , If the area of a rectangle is less than 108 thus the value is greater than 108cm²
[tex]\begin{gathered} \text{Area of a rectangle = length x width } \\ A=\text{ L X W} \\ A>\text{ L x W} \end{gathered}[/tex][tex]\begin{gathered} (2x+1\text{ x 12)>108} \\ 24x+12>108 \\ 24x>108-12 \\ 24x>96 \\ x>\frac{96}{24} \\ x>4 \end{gathered}[/tex]Hence the correct answer for the value of x > 4
The value of x is less than 4
What is an Area?
An object's Area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
According to the question,
Length = (2x+1) cm
Width = 12 cm
To solve , the Area of the rectangle = length x width i.e.
less than 108 cm^2
length x width = (2x+1) x 12 cm
Area < 108 cm^2
So,
(2x+1) x 12 < 108
2x+1 < 108/12
2x+1 < 9
2x < 8
x < 4
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The accompanying graph shows the heart rate, in the beats per minute, of a jogger during a 4 minute interval. What is the rage of the jogger's heart rate during this interval?
The range of the jogger's heart rate is defined by the interval from the minimum value to the maximum value, where we can have values in the y-axis.
Looking at the graph, the minimum heart rate is 60 bpm, and the maximum is 110 bpm, and we can have any value inside this interval.
So the range is:
[tex]\text{range}=\lbrack60,110\rbrack[/tex]it is one of the 4 answers
The rate of change at point A on the graph below for the y-axis in relation to the x-axis is -0.5.
What is the rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.
Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).
The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.
Other instances of changing rates are as follows: 40 more rats are added to the colony every week.
So, the rate of change is:
The point is given at 1.5 with respect to the y-axis.
And we can clearly see that it has been decreased to 1 with respect to the y-axis.
So, the rate of change:
1.0 - 1.5 - = -0.5
Therefore, the rate of change at point A on the graph below for the y-axis in relation to the x-axis is -0.5.
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Find the equation of the linear function represented by the table below in slope-intercept form.
pls help me
The equation of the linear function in slope intercept form is y = 2x -6
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope of the linear function using (0, -6)(1, -4).
m = -4 + 6 / 1 - 0
m = 2 / 1
m = 2
Therefore, the y-intercept of the linear function can be calculated using (0, -6) and the lope.
y = 2x + b
-6 = 2(0) + b
b = -6
Therefore, the equation of the line is y = 2x -6
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For the number line shown which statement is not true?
|d| <|c|
Ic
|c|>c
|d| = d
Answer:
The answer is C
Step-by-step explanation:
it's always the one in the lines at least that's what my math teacher told me he said it's really easy All you have to do is pick the ones with the lines there's more to it when you're doing homework but when there's just like a few questions it's way easier
Seeds cost for a farmer are 40$ per acre for corn and 30$ per acre for soybeans . How many acres of each crop should the farmer plant if she wants to spend no more than 2400 on seed? Express your answer as a liner inequality with appropriate nonnegative restrictions and draw its graph
Given that:
- The seeds cost is 40$ per acre for corn.
- The seeds cost is 30$ per acre for soybeans.
- The farmer wants to spend no more than $2400.
• Let be "x" the number of acres of seeds for corn and "y" the number of acres of seeds for soybeans.
You know that the total amount of money has to be less than or equal to $2400. Therefore, you can write the following Linear Inequality to represent that situation:
[tex]40x+30y\leq2400[/tex]You can rewrite it in another form by solving for "y":
[tex]\begin{gathered} 30y\leq-40x+2400 \\ \\ y\leq\frac{-40x}{30}+\frac{2400}{30} \end{gathered}[/tex][tex]y\leq-\frac{4}{3}x+80[/tex]Since the number of acres cannot be negative:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}[/tex]• You can identify that the boundary line is:
[tex]y=-\frac{4}{3}x+80[/tex]It is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can identify that the y-intercept is:
[tex]b=80[/tex]In order to find the x-intercept, substitute this value of "y" into the equation and solve for "x" (because the y-value is zero when the line intersects the x-axis):
[tex]y=0[/tex]Then, you get:
[tex]0=-\frac{4}{3}x+80[/tex][tex]\frac{(-80)(3)}{-4}=x[/tex][tex]x=60[/tex]You can identify that the symbol of the inequality is:
[tex]\leq[/tex]It indicates that the line must be solid and the shaded region must be below the boundary line.
Knowing all this information, you can graph the inequality on the Coordinate Plane (Remember that the values of the variables must be greater than or equal to zero. Then, you must shade with a different color the region in which "x" and "y" are greater than or equal to zero).
Hence, the answer is:
- Linear Inequality:
[tex]40x+30y\leq2400[/tex]- Nonnegative restrictions:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}[/tex]- Graph:
Bill is trying to plan a meal to meet specific nutritional goals. He wants to prepare a meal containing rice, tofu, and peanuts that will provide 283 grams of carbohydrates, 391 grams of fat, and 197 grams of protein. He knows that each cup of rice provides 50 grams of carbohydrates, 0 grams of fat, and 1 grams of protein. Each cup of tofu provides 4 grams of carbohydrates, 13 grams of fat, and 20 grams of protein. Finally, each cup of peanuts provides 35 grams of carbohydrates, 73 grams of fat, and 31 grams of protein. How many cups of rice, tofu, and peanuts should he eat?
♥Answer:
♥Bill needs to eat 5 Cups of rise, 1 cup of tofu and 4 cups of peanuts
♥Explanation:
♥Its simple calculations:
♥As Bill requirement is 350 grams of carbohydrates, 311 grams of Fats and 168 gram of proteins.
♥Each cup of rice provides 42 grams of carbohydrates, 0 grams of fat, and 1 gram of protein.
♥Each cup of tofu provides 4 grams of carbohydrates, 11 grams of fat, and 23 grams of protein.
♥Each cup of peanuts provides 34 grams of carbohydrates, 75 grams of fat, and 35 grams of protein.
♥If he eats 5 cups of rise than he gets 42 × 5 = 210 grams of carbohydrates. similarly he gets 0 × 5 = 0 grams of fats and 1 × 5 = 5 grams of proteins.
♥If he eats 1 cup of tofu than he gets 4 × 1 = 4 grams of carbohydrates. similarly he gets 11 × 1 = 11 grams of fats and 23 × 1 = 23 grams of proteins, and If he eats 4 cups of peanuts than he gets 34 × 4 = 136 grams of carbohydrates. Similarly he gets 75 × 4 = 300 grams of fats and 35 × 4 = 140 grams of proteins.
♥GRAND TOTAL BECOMES
♥CARBOHYDRATES: 210+4+136=350 grams
♥FATS: 0+11+300= 311 grams
♥PROTEINS:5+23+140=168 grams♥
Graph the equation on a coordinate grid:y=-1/2x
In this case you have a linear equation of the form:
y=mx+b
To graph a line we only need to specify two points of the line and then join them.
b the intercept is zero in this case, and the slope of your line is -1/2. Since the intercept is zero, this means that the line crosses the origin, so the point (0,0) is included in the line, to find other poin of the line we just have to replace a value of x and calculate the value of y, for example let's take x equals 2.
[tex]y(2)=-\frac{1}{2}2=-\frac{2}{2}=-1[/tex]Now, we know that the line crosses the points (0,0) and (2,-1), let's graph them.
find the area of the equilateral triangle. round to the nearest tenth
the The area of the triangle is 35.1
We can get the height of the triangle using Pythagorean theorem
a^2+b^2=c^2
the height is 7.8
the area of the triangle is 1/2 * base * height
1/2 * 9 *7.8 = 35.1
Kenya is driving on the highway at a speed of 75 mph. She sees an accident about 500 feet ahead and must come to a complete stop. How far will Kenya travel before coming to a complete stop? Answer to the nearest hundredth of a foot. (Use rule of thumb for reaction time: 1 foot traveled for each mile per hour of speed.)
The distance Kenya travels before coming to a complete stop found by writing equations is 425 feet
What is an equation?An equation is a mathematical statement that connects two expressions with an equal sign
The speed at which Kenya is driving = 75 mph
The distance between Kenya and the accident = 500 feet
The rule of thumb for the reaction distance = 1 ft per mile per hour of speed
The rule of thumb expressed as an equation is therefore;
Distance traveled during the reaction time = 1 × v
Where;
v = The speed of driving
The distance Kenya traveled before reacting is therefore;
r = 1 ft/mph × 75 mph = 75 feet
The distance Kenya traveled before stopping is therefore;
500 feet - 75 feet = 425 feet
500 feet – 75 feet = 425 feet
The distance Kenya travels before coming to a complete stop is 425 feet’
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slove 2/3 + 5/6 in its simplest term
We solve as follows:
[tex]\frac{2}{3}+\frac{5}{6}=\frac{3}{2}[/tex]Simplify the following complex rational expression completely. Detailed Step By Step
Given:
[tex]\frac{\frac{1}{7}+\frac{1}{x}}{\frac{x}{7}-\frac{7}{x}}[/tex]Let us write the numerator as a single fraction, as well as the denominator. This can be written as:
[tex]\frac{\frac{x+7}{7x}}{\frac{x^2-49}{7x}}[/tex]Division by a fraction may become a mu
[tex]\begin{gathered} \frac{x+7}{7x}\times\frac{7x}{x^2-49} \\ \\ =\frac{x+7}{7x}\times\frac{7x}{(x+7)(x-7)} \\ \\ =\frac{1}{x-7} \end{gathered}[/tex]Write an equation in Standard Form that passes through the point (-8, 7) and has a slope of -3.
Answer:
3x+y=-17
Step-by-step explanation:
Standard form is written as: Ax+By=C where the slope is always -A/B
-A/B = -3/1
A= 3 and B=1
3x+y=C
Plug in point to solve for C
3(-8)+7=C
-24+7=C
-17=C
3x+y=-17
A spinner is divided into five colored sections that are not of equal size: red, blue,green, yellow, and purple. The spinner is spun several times, and the results arerecorded below:Spinner ResultsColor Frequency718RedBlueGreenYellowPurple569Based on these results, express the probability that the next spin will land on green asa decimal to the nearest hundredth.
Answer:
0.11
Explanation:
First, find the total of the color frequency:
[tex]\begin{gathered} \text{Total}=7+18+5+6+9 \\ =45 \end{gathered}[/tex]The Frequency with which it lands on Green = 5
Therefore, the probability that the next spin will land on the green:
[tex]\begin{gathered} =\frac{5}{45} \\ \approx0.11 \end{gathered}[/tex]The required probability is 0.11 (to the nearest hundredth).
Find the 52nd term. 22, 30, 38, 46,…
Given a series.
22, 30, 38, 46,…
use the formula,
a+(n-1)d,
a= 22
n=52
d=8.
subsitute in the formula,
22+(52+1)8
=22+424
=446
You decide to invest $10,000 in an account where the interest compounds annually. Create an exponential function to represent how much money you will have after 20 years if the money grows at a rate of 7.5 percent
Apply the compound interest formula:
• A= P (1 + r/n)^nt
Where:
A = future value
P = Principal investment = $10,000
r = interest rate in decimal form = 7.5 /100 = 0.075
n= number of compounding periods per unit t = 1 (anually)
t= years = 20
Replacing:
A = 10,000 ( 1+ 0.075 )^20
A survey estimates the current average cost of college to be $34,179.
(a) If the average cost of college increased by 7.4% each year, what will be the average cost of college 15 years from now?
(b) If a savings plan offers a rate of 5.4% compounded continuously, how much should be put in the plan now to pay for 1 year of college 15 years from now?
(Round to the nearest cent as needed)
What is the solution of x^2+3x-28
Let's solve for x by factoring this quadratic equation.
We first need to determine which two numbers multiply to -28 (c) but add to 3 (b).
The two numbers that multiply to -28 and add to 3 are 7 and -4.
Therefore, we can factor this equation like so:
[tex](x+7)(x-4)[/tex]Now, we can set this equation to 0 and solve for x.
[tex](x+7)(x-4)=0[/tex]If we look at each factor individually, we can determine the values of x:
[tex](x+7)=0[/tex]Subtract 7 from both sides of the equation.
[tex]x=-7[/tex]Now, let's look at the other factor:
[tex](x-4)=0[/tex]Add 3 to both sides of the equation.
[tex]x=4[/tex]The solution of x^2 + 3x - 28 is x = -7, x = 4.
Mr. Lambert borrows $900 from a credit union to buy a new laptop. The credit union charges 6.5 % simple interest per year. How much interest will he owe if it takes him 18 months to repay the loan? Round to the nearest cent.
$87.75
Step-by-step explanation:
900×6.5%×18months
=58.5×1.5years
=87.75
what property of parallel lines is illustrated by where the snow has collected?
Okay, here we have this:
Considering that when two parallel lines are intersected by a transversal, corresponding angles have the same measure. In this case
What is the formula for figuring out how far the students walked?
37.
Add all the distances .
3/4 + 1/2 + 2/3 + 3/4 = 8/3 miles
To add fractions you need equal bottom numbers
find the LCM ( Least common multiple of the denominators )
4 , 2 , 3 , 4 = LCM = 12
Multiply each fraction by the same numerator and denominator, to obtain 12 as a bottom number
(3/4 * 3/3) + (1/2 * 6/6) + (2/3 * 4/4) + (3/4 * 3/3)
9/12 + 6/12 + 8/12 + 9/12
Now that all fractions have the same denominator ( bottom number) you can add them.
Add the numerators ( top numbers ) and put 12 as a denominator.
(9 + 6 + 8 + 9 ) / 12 = 32/12
Simplify ( divide both numbers by 4 )
32/12 = 8/3
Please help me with this problem I keep getting this wrong an my son is not understanding clearly.Use the parabola tool to graph the quadratic function. f(x)=3x^2 + 6x − 24 Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The general vertex-equation of a parabola has the following form:
[tex]f(x)=a\cdot(x-h)^2+k.[/tex]Where:
• a is a multiplicative factor,
,• (h, k) are the coordinates of the vertex of the parabola.
In this exercise we have the following equation:
[tex]f(x)=3\cdot x^2+6x-24.[/tex]Vertex of the parabola
To find the vertex of the parabola, we will complete squares to take the equation f(x) to the general form as in the equation above.
i. We factorize the equation of f(x) in the following way:
[tex]f(x)=3\cdot(x^2+2x)-24.[/tex]ii. Now, we rewrite the term inside the parenthesis as:
[tex]\begin{gathered} f(x)=3\cdot(x^2+2\cdot1\cdot x)-24 \\ =3\cdot((x^2+2\cdot1\cdot x+1)-1)-24 \\ =3\cdot(x^2+2x+1)-3-24 \\ =3\cdot(x^2+2x+1)-27. \end{gathered}[/tex]iii. Now, we see that the term in parenthesis can be rewritten as a square:
[tex]f(x)=3\cdot(x+1)^2-27.[/tex]iv. Finally, we rewrite the term inside and outside the parenthesis as:
[tex]f(x)=3\cdot(x-(-1))^2+(-27).[/tex]In the last step, we rewrite the term inside the parenthesis to have the same shape as in the general expression.
Comparing the equation that we have obtained and the general one, we see that the coordinates of the vertex are:
[tex](h,k)=(-1,-27).[/tex]Second point
We find a second point by evaluating the function f(x) in x = 1, we get:
[tex]f(1)=3\cdot1^2+6\cdot1-24=3+6-24=-15.[/tex]The coordinates of the second point are (1, -15).
Graph
We have the following points of the parabola:
[tex]\begin{gathered} \text{ Vertex }=(-1,-27), \\ \text{ Second point }=(1,-15). \end{gathered}[/tex]Using these points and taking into account that the axis of symmetry is x = -1 (because the x-coordinate of the vertex is -1), we get the following graph:
AnswerCoordinates of the vertex: (-1, -27)
Coordinates of the second point: (1, -15)
Consider the function f(x)=2(3)x.
What are the coordinates of the y-intercept of the function?
The coordinates of the y-intercept of the function is (0, 2)
How to determine the coordinates of the y-intercept?The equation of the function is given as
f(x) = 2(3)x
The equation is an exponential function
So, we need to represent it properly
The equation of the function is:
f(x) = 2(3)ˣ
Next, we set the x-coordinate to 0
So, we calculate the y-intercept
f(0) = 2(3)⁰
Evaluate the equation
f(0) = 2
This means that the y-intercept of the function is (0, 2)
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Answer the question for me please and explain how you got the answer
Given:
a.) y = 2.5 when x = 9
Let's find the constant of variation (k).
For us to be able to determine which of the given choices is the answer, let's plugin x = 2.5 and y = 9 in each of them to see if it will make the equation correct.
CHOICE A: k = 22.5 ; y = 22.5x
2.5 = 22.5(9)
2.5 ≠ 202.5 (False)
Choice A is not the answer
CHOICE B: k = 3.6 ; xy = 3.6
(2.5)(9) = 3.6
22.5 ≠ 3.6 (False)
Choice B is not the answer
CHOICE C: k = 3.6 ; y = 3.6/x
2.5 = 3.6/9
2.5 ≠ 0.4 (False)
Choice C is not the answer
CHOICE D: k = 22.5 ; xy = 22.5
(2.5)(9) = 22.5
22.5 = 22.5 (True)
Choice D is the answer
Therefore, the answer is CHOICE D.