The length of a triangle is three times its width the perimeter of the rectangle is 24cmcalculate the area of the triangle

length of AC in the triangle is 32 units.

The triangle proportionality theorem, also known as the side-splitter theorem, states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.  

In mathematical terms, let ABC be a triangle with a line parallel to one side, say line DE || AB, where D lies on BC and E lies on AC. Then, the theorem states that:

BD/DC = AE/EC

In the given triangle ABC;

GH and AC are parallel

AG=BG

BH=HC

Using proportional rule

BG/AB=GH/AC

BG/2BG=16/AC

1/2=16/AC

AC=32 units

Hence, length of AC in the triangle is 32units.

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Answer:

1. 32 units

Step-by-step explanation:

sorry abt the other person but the answer is 32... i just took it

Answer:

Step-by-step explanation:

To solve the equation (T/12) + 5 = (T/3) + (T/4), we need to simplify the right-hand side of the equation by finding a common denominator for T/3 and T/4.

The least common multiple of 3 and 4 is 12, so we can rewrite T/3 and T/4 as (4T/12) and (3T/12), respectively. Substituting these expressions into the equation, we get:

(T/12) + 5 = (4T/12) + (3T/12)

Simplifying the right-hand side, we get:

(T/12) + 5 = (7T/12)

Subtracting (T/12) from both sides, we get:

5 = (6T/12)

Simplifying the right-hand side, we get:

5 = (T/2)

Multiplying both sides by 2, we get:

T = 10

Therefore, the solution to the equation is T = 10.

[tex]\sf\longrightarrow \: \frac{t}{12} + 5 = \frac{t}{3} + \frac{t}{4} \\ [/tex]

[tex]\sf\longrightarrow \: \frac{t + 60}{12} = \frac{t}{3} + \frac{t}{4} \\ [/tex]

[tex]\sf\longrightarrow \: \frac{t + 60}{12} = \frac{4t + 3t}{12} \\ [/tex]

[tex]\sf\longrightarrow \: 12(t + 60) = 12(4t + 3t) \\ [/tex]

[tex]\sf\longrightarrow \: 12t + 720 = 48t + 36t \\ [/tex]

[tex]\sf\longrightarrow \: 12t + 720 = 84t \\ [/tex]

[tex]\sf\longrightarrow \: 720 = 84t - 12t\\ [/tex]

[tex]\sf\longrightarrow \: 720 =72t\\ [/tex]

[tex]\sf\longrightarrow \: 72t = 720\\ [/tex]

[tex]\sf\longrightarrow \: t = \frac{720}{72} \\ [/tex]

[tex]\sf\longrightarrow \: t = 10 \\ [/tex]

[tex]\longrightarrow { \underline{ \overline{ \boxed{ \sf{\: \: \: t = 10 \: \: \: }}}}} \: \: \bigstar\\ [/tex]

z = 4(x - 1) - ln (y - 4)

Therefore, the equation of the tangent plane to the surface z = y ln x at the point (1, 4, 0) is z = 4(x - 1) - ln (y - 4).

To determine the equation of the tangent plane to the surface z = y ln x at the point (1, 4, 0), we first need to find the partial derivatives of the surface with respect to x and y.

∂z/∂x = y/x

∂z/∂y = ln x

Then, we can use these partial derivatives along with the point (1, 4, 0) to find the equation of the tangent plane using the formula:

z - z0 = ∂z/∂x(x0, y0)(x - x0) + ∂z/∂y(x0, y0)(y - y0)

where (x0, y0, z0) is the given point.

Plugging in the values, we have:

z - 0 = (4/1)(x - 1) + ln 1(y - 4)

Simplifying:

z = 4(x - 1) - ln (y - 4)

Therefore, the equation of the tangent plane to the surface z = y ln x at the point (1, 4, 0) is z = 4(x - 1) - ln (y - 4).

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We can conclude that Jack's claim is correct. QRST is indeed a parallelogram, since opposite angles in QRST are congruent, and opposite sides in a parallelogram are also congruent

To determine whether Jack's claim that QRST is a parallelogram is correct, we need to use the properties of parallelograms. One of the properties of a parallelogram is that opposite angles are congruent. Therefore, we need to check if the opposite angles in QRST are congruent.

If m∠R = 72 and m∠T = 108, then the sum of these angles is 180 degrees (72 + 108 = 180). This indicates that angles R and T are supplementary.

If m∠S = 72, then we need to find the measure of angle Q. Since QRST is a quadrilateral, the sum of its interior angles is 360 degrees.

m∠Q + m∠R + m∠S + m∠T = 360

Substituting the given values, we get:

m∠Q + 72 + 72 + 108 = 360

Simplifying the equation, we get:

m∠Q = 108

Therefore, angles Q and S are congruent (both measuring 72 degrees) and angles R and T are supplementary (measuring 72 and 108 degrees, respectively). Since opposite angles in QRST are congruent, and opposite sides in a parallelogram are also congruent, we can conclude that Jack's claim is correct. QRST is indeed a parallelogram.

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If you paid $25,000 for your car and you sell it after owning the car for 3 years, then the worth of the car is t₃=$7,910. 15 (option c).

To find the value of your car after owning it for 3 years, we need to evaluate the function at t=3. This means we need to substitute t=3 into the function and simplify the expression.

f(3) = 0.75(3) = 2.25

The output of the function when t=3 is 2.25. But what does this number mean? It represents the fraction of the original value of the car that remains after owning it for 3 years.

To find the actual value of the car, we need to multiply this fraction by the original value of the car, which is given as $25,000.

Value of car after 3 years = 2.25 x $25,000 = $56,250

Therefore, the value of the car after owning it for 3 years is $7,910.15. This is the option (C) in the given choices.

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The probability that the mean of the sample would differ from the population mean by less than 43 points is approximately 0.7597 or 0.7600 (rounded to four decimal places).

Given that the standard deviation of the scores on a skill evaluation test is 320 points with a mean of 1434 points. And we have a sample of size n = 338.

We need to find the probability that the mean of the sample would differ from the population mean by less than 43 points.

The standard error of the mean is given by:

SE = σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

SE = 320/√338

SE ≈ 17.398

To find the probability, we need to standardize the sample mean using the standard error as follows:

Z = (X - μ) / SE

where X is the sample mean, μ is the population mean, and SE is the standard error of the mean.

Substituting the given values, we get:

Z = (1434 - 1434) / 17.398

Z = 0

Since the mean difference is 0, we can find the probability of a difference less than 43 points by finding the probability that Z lies between -43/17.398 and 43/17.398.

Using a standard normal distribution table or calculator, we find that this probability is approximately 0.7597.

Therefore, the probability that the mean of the sample would differ from the population mean by less than 43 points is approximately 0.7597 or 0.7600 (rounded to four decimal places).

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The equation of the line passing through the given points is y = -2x+2.

Given that are the values of x and y coordinates we need to find the equation of the line using them,

So, considering the points (1, 0) and (3, -4),

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (1, 0) and (3, -4),

Therefore, the required equation is =

y-0 = -4-0/3-1 (x-1)

y = -2x + 2

Hence, the equation of the line passing through the given points is y = -2x+2.

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The total cost of the trip in U.S. dollars as per given rates and conversion is equal to approximately USD 3,232.58.

Total cost of the trip in U.S. dollars,

Convert the Australian dollars to U.S. dollars.

Using the exchange rate of 0.7752 USD per 1 AUD.

The cost of the hotel is,

7 nights × A$110/night = A$770

To convert this to U.S. dollars, multiply by the exchange rate,

A$770 × 0.7752 USD/AUD

= USD 596.904

Expected cost of meals, tours, souvenirs, etc. is,

A$3,400

Convert this to U.S. dollars, we again multiply by the exchange rate,

A$3,400 × 0.7752 USD/AUD

= USD 2,635.68

Total cost of the trip in U.S. dollars is the sum of these two amounts is,

USD 596.904 + USD 2,635.68 = USD 3,232.584

Rounding to two decimal places = approximately USD 3,232.58.

Therefore, the cost of the trip in the U.S. dollars is equal to approximately USD 3,232.58.

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The above question is incomplete, the complete question is:

You are planning a trip to Australia. your hotel will cost you a$110 per night for seven nights. you expect to spend another a$3,400 for meals, tours, souvenirs, and so forth. How much will this trip cost her in U.S. dollars if the USD equivalent is .7752?

If p : q = 2/3 : 2 and p : r = 3/4 : 1/2 , the ratio of p : q : r in its simplest form is 32 : 27 : 24.

To calculate the ratio p : q : r, we need to first find the values of p, q, and r. We can use the given proportions to set up a system of equations and solve for the variables.

From the first proportion, we know that:

p/q = 2/3 : 2

We can simplify this by cross-multiplying:

p = (2/3) * 2q

p = (4/3)q

From the second proportion, we know that:

p/r = 3/4 : 1/2

Again, we can cross-multiply and simplify:

p = (3/4) * r/(1/2)

p = (3/2)r

Now we have two equations for p in terms of q and r. We can substitute these into each other and solve for q and r:

(4/3)q = (3/2)r

r/q = (8/9)

q/r = (9/8)

Now we have the ratios of r to q and q to r. We can use these to find the ratio of p, q, and r:

p : q : r = p : q * (9/8) : r * (8/9)

Substituting the values we found for p in terms of q and r:

p : q : r = (4/3)q : q * (9/8) : r * (8/9)

Simplifying:

p : q : r = 32 : 27 : 24

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The equation is 86.25 + 3x = 99.

Let's assume the cost for each hour Troy's car was parked in the garage is x dollars.

Since Troy spent a total of $99, we can set up an equation based on the given information.

The cost of the ticket to the basketball game is $86.25, and Troy also had to pay for 3 hours of parking. Therefore, the equation can be written as:

86.25 + 3x = 99

In this equation, 86.25 represents the cost of the ticket, 3x represents the cost of parking for 3 hours at a rate of x dollars per hour, and 99 represents the total amount Troy spent.

Therefore, the equation is 86.25 + 3x = 99.

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According to recent studies, there is a notable difference in credit scores between those over the age of 55 and those between the ages of 18-24.

On average, individuals over the age of 55 tend to have higher credit scores than those in the 18-24 age range. This is primarily due to the fact that older individuals have had more time to establish and build their credit history, whereas younger individuals are just starting out and may not have had the opportunity to establish credit yet.

Additionally, older individuals tend to have more stable financial situations and may have less debt compared to younger individuals who may be dealing with student loans or other types of debt.

However, it's important to note that credit scores can vary greatly between individuals, regardless of age, and there are many factors that contribute to credit score, such as payment history, credit utilization, and length of credit history.

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James says the fraction 3/4 has the same value as the expression 4 ÷ 3. I disagree with James' statement.

The fraction 3/4 is not the same as the expression 4 ÷ 3. A fraction can be interpreted as division of the numerator (top number) by the denominator (bottom number). In this case, 3/4 represents the division of 3 by 4, whereas 4 ÷ 3 represents the division of 4 by 3. These two expressions have different values and are not equal.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

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Answer:

A

Step-by-step explanation:

2.17 > 2.017

because

2.017 = 2 + 17/1000

while

2.17 = 2 + 17/100 = 2 + 170/1000

170/1000 is larger than 17/1000.

for that reason D is wrong, of course.

2.17 is NOT equal to 2.017. 17/1000 is NOT equal to 170/1000.

2.018 = 2 + 18/1000

2.17 = 2 + 17/100 = 2 + 170/1000

also 18/1000 is NOT larger than 170/1000.

2.16 = 2 + 16/100 = 2 + 160/1000

2.017 = 2 + 17/1000

17/1000 are NOT larger than 160/1000.

Solids can be "unfolded" to form different net arrangements is a true statement.

A net refers to a flat, two-dimensional shape that can be transformed or manipulated to form a three-dimensional object. A solid has the potential to create a variety of nets through various unfolding methods.

The term "net" for a solid refers to a flat shape that can be folded to form the solid object. it is possible to manipulate a three-dimensional object in various manners in order to produce distinct two-dimensional patterns. One can create various nets by cutting different edges of a cube and arranging the resultant faces.

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The variable Q, representing the number of questions Violet answers correctly before she misses one in a computer-adaptive test, is a Geometric variable.

This is because a geometric distribution models the number of trials needed for the first success in a series of Bernoulli trials with a constant probability of success.

Where as all aspects of a logarithmic articulation that is isolated by a short or in addition to sign is known as the term of the algebraic expression and an algebraicexpression with two non-zero terms is called a binomial.

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the solution to the differential equation is: x = (1/36) y² - (13/36) Note that this equation represents a parabolic curve in the (x,y)-plane, opening upwards and with its vertex at (-13/36,0).

We can start by separating the variables and integrating both sides of the equation:

1/9 y dy = 2 dx

Integrating both sides with respect to their respective variables, we get:

(1/18) y² = 2x + C

where C is the constant of integration.

Using the initial condition y(9) = 7, we can substitute x=9 and y=7 to solve for C:

(1/18) (7²) = 2(9) + C

C = 49/2 - 18 = 13/2

Substituting this value of C back into the general solution, we get:

(1/18) y² = 2x + 13/2

Simplifying and solving for x, we get:

x = (1/36) y² - (13/36)

Therefore, the solution to the differential equation is:

x = (1/36) y² - (13/36)

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Answer:

30 cm²

Step-by-step explanation:

Formula : [tex]Area = \frac{hb}{2}[/tex]

The median number of goals scored is 1, and the mean number of goals scored is 2. The median is less than the mean, indicating a right-skewed distribution.

To find the median, we need to first put the numbers in order

0, 0, 1, 1, 1, 3, 3, 4, 5

There are an odd number of values, so the median is the middle value, which is 1.

To find the mean, we add up all the values and divide by the number of values

(0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5) / 9 = 2

So the mean number of goals scored is 2.

Since the median (1) is less than the mean (2), we can say that the distribution is skewed to the right. This is because the high value of 5 pulls the mean up, while the median is not affected as much by outliers.

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The density of the object is 0.0018 g/mL.

To calculate the density of the object, we need to use the formula:

Density = Mass / Volume

Given that the mass of the object is 4.70g and the volume is 2.55L, we can substitute these values into the formula:

Density = 4.70g / 2.55L

We need to convert the units of mass and volume to a consistent unit. Let's convert the volume from liters to milliliters (1L = 1000mL):

Density = 4.70g / 2550mL

Now we can simplify by dividing both the numerator and denominator by 10:

Density = 0.47g / 255mL

Finally, we can express the answer in units of g/mL:

Density = 0.0018 g/mL

Therefore, the density of the object is 0.0018 g/mL.

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The 95% CI for the genuine proportion of this bank's checking account customers who also have savings accounts is (0.3666, 0.4976).

To construct a 95% confidence interval for the true proportion of checking account customers who also have savings accounts, we can use the following formula:

CI = p ± z*√(p*(1-p)/n)

where:

We are given that the sample size is n = 243 and that 105 of the customers had both checking and savings accounts. Therefore, the sample proportion is:

p = 105/243 = 0.4321

The critical value z for a 95% confidence interval is approximately 1.96 (obtained from a standard normal distribution table or calculator).

We get the following results when we plug these values into the formula:

CI = 0.4321 ± 1.96*√(0.4321*(1-0.4321)/243)

CI = 0.4321 ± 0.0655

CI = (0.3666, 0.4976)

Therefore, we can say with 95% confidence that the true proportion of checking account customers who also have savings accounts at this bank is between 0.3666 and 0.4976.

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To determine how many biscuit packages, pemmican packages, and butter and cocoa packages are needed per day for one person.

Calculating an individual's daily Caloric food requirements based on calorie intake and percentage of calories from each food group requires several pieces of information. The first is the total daily calorie requirement, which varies based on factors such as age, gender, height, weight, and physical activity level.

The second is the percentage of daily calories that should come from each food group, which is determined by dietary guidelines and varies based on factors such as age and gender. Finally, the calorie content of each food item must be known to determine how much of each food is needed to meet daily calorie and nutrient requirements.

Once these factors are known, it is possible to calculate how many biscuit packages, pemmican packages, and butter and cocoa packages are needed per day for one person. However, without knowing the specific calorie content and nutritional value of each food item, it is impossible to provide a specific answer.

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Therefore, the simplified expression is 24.

To simplify the expression (-8)(10+(-5)+(-8)), you first need to solve the parentheses, following the order of operations, which requires solving the addition and subtraction within the parentheses before multiplying.

So, you have (-8)(10-5-8), which becomes (-8)(-3) after solving the parentheses. Finally, you can solve the multiplication by multiplying -8 by -3, resulting in 24.

It's important to remember the order of operations when simplifying expressions, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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Answer:

Ans=28

Step-by-step explanation:

ƒ(x) = 6x2 - 3x + 22xf( - 2)=[?]

at ƒ(-2)

Substitute each x with -2

ƒ(-2) = 6(-2)2 - 3(-2) - 2

ƒ(-2) = 6(4) - 3(-2) - 2

ƒ(-2) = 24 + 6 + 0 - 2

ƒ(-2) = 28

I hope I was right

The absolute maximum is f(-2) = 10/3, and absolute minimum is f(0) = 8.

First, let's find the derivative of the function:

f(x) = 8+x/2-x

f'(x) = (1/2) - 1 = -1/2

Next, we need to find the critical points of the function on the given domain.

In this case, the derivative is always defined and is never zero. Therefore, there are no critical points on the given domain.

Next, we check the endpoints of the domain, x = -2 and x = 0:

f(-2) = 8 + (-2)/(2-(-2)) = 10/3

f(0) = 8 + 0/(2-0) = 8

Since the function is continuous on the closed interval [-2, 0],

The extreme value theorem tells us that the function must have both an absolute maximum and an absolute minimum on the interval.

Therefore, the absolute maximum occurs at x = -2 and is f(-2) = 10/3, and the absolute minimum occurs at x = 0 and is f(0) = 8.

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The possible rectangles that Wes can make with his 20 feet of fencing are:

L = 3, W = 7

L = 4, W = 6

L = 5, W = 5

L = 6, W = 4

L = 7, W = 3

Let L be the length of the rectangular garden and W be the width of the garden. Since the garden is enclosed by four sides, Wes will need 2L+2W feet of fencing to enclose it. We know that he has 20 feet of fencing, so we have the equation:

2L + 2W = 20

We also know that the smallest side of the garden should be 3 feet or longer, so:

L >= 3

W >= 3

To find the possible rectangles Wes can make, we can solve the equation for one variable in terms of the other:

2L + 2W = 20

2L = 20 - 2W

L = 10 - W

Now we can substitute this expression for L into the inequality L >= 3 to get:

10 - W >= 3

W <= 7

Similarly, we can substitute L = 10 - W into the inequality W >= 3 to get:

10 - L >= 3

L <= 7

Therefore, the possible values for L and W are:

3 <= L <= 7

3 <= W <= 7

We can also use the equation 2L + 2W = 20 to find the combinations of L and W that add up to 10, since the total length of fencing is 20 feet:

L = 3, W = 7

L = 4, W = 6

L = 5, W = 5

L = 6, W = 4

L = 7, W = 3

These are the possible rectangles that Wes can make with his 20 feet of fencing, where the smallest side is 3 feet or longer.

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There is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.

To determine if the difference in proportions is statistically significant or if it could be due to chance.

We will conduct a hypothesis test. Our null hypothesis (H₀) is that there is no difference in the proportion of college enrollees between females and males. Our alternative hypothesis (H₁) is that there is a difference in the proportion of college enrollees between females and males.

We can use a two-sample z-test to test this hypothesis. The formula for the test statistic is:

z = (p₁ - p₂) / √(p'* (1 - p') * ((1 / n₁) + (1 / n₂)))

where p₁ and p₂ are the sample proportions, p' is the pooled proportion, n₁ and n₂ are the sample sizes.

Given, p₁ = 0.72, p₂ = 0.65, n₁ = 175, n₂ = 160

p' = (x₁ + x₂) / (n₁ + n₂)

x₁ = 126 (0.72 * 175) and x₂ = 104 (0.65 * 160).

p' = (126 + 104) / (175 + 160) = 0.684

By applying the above values we get,

z = (0.72 - 0.65) / √(0.684 * (1 - 0.684) * ((1 / 175) + (1 / 160))) ≈ 2.11

The critical value for a two-tailed test with alpha = 0.01 is approximately ±2.58. Since our calculated z-value (2.11) is less than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant difference in the proportion of college enrollees between females and males.

Therefore, there is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.

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The marginal profit in dollars for the sale of expensive watches when approximately $1912.61.

Find the marginal profit in dollars from the sale?

We need to find the marginal profit in dollars from the sale of x expensive watches for the given profit function P(x) = 0.08x² - 5x + 6x^0.2 - 5200 when (a) x = 300, (b) x = 2000, (c) x = 5000, and (d) x = 12,000.

Find the derivative of the profit function P(x), which represents the marginal profit.
P'(x) = dP(x)/dx = 0.16x - 5 + (6 * 0.2 * x^(-0.8))

Calculate the marginal profit for each specified value of x:

x = 300:
P'(300) = 0.16(300) - 5 + (6 * 0.2 * 300^(-0.8)) ≈ 42.57

x = 2000:
P'(2000) = 0.16(2000) - 5 + (6 * 0.2 * 2000^(-0.8)) ≈ 317.52

x = 5000:
P'(5000) = 0.16(5000) - 5 + (6 * 0.2 * 5000^(-0.8)) ≈ 794.57

x = 12,000:
P'(12,000) = 0.16(12,000) - 5 + (6 * 0.2 * 12,000^(-0.8)) ≈ 1912.61

So, the marginal profit in dollars for the sale of expensive watches when (a) x = 300 is approximately $42.57, (b) x = 2000 is approximately $317.52, (c) x = 5000 is approximately $794.57, and (d) x = 12,000 is approximately $1912.61.

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he interest he will pay if he takes 2 years to pay his parents back is $153.16. The total amount he will pay if he takes 2 years to pay his parents back is $2,341.12.

To calculate the interest Adam will pay, we need to use the simple interest formula:

Interest = Principal x Rate x Time

The principal is the amount borrowed, which is $2,187.96. The rate is 3.5% per year, or 0.035 in decimal form. The time is 2 years.

Interest = $2,187.96 x 0.035 x 2 = $153.16

Therefore, Adam will pay $153.16 in interest if he takes 2 years to pay his parents back.

To calculate the total amount he will pay, we need to add the interest to the principal:

Total amount = Principal + Interest

Total amount = $2,187.96 + $153.16 = $2,341.12

Therefore, Adam will pay a total of $2,341.12 if he takes 2 years to pay his parents back.

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The recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

We can use the method of finite differences to find a possible recursive formula for this sequence.

First, let's compute the first few differences:

f(4) - f(1) = 6

f(7) - f(4) = 6

Since the second differences are zero, we can assume that the sequence is a quadratic sequence. Let's write it in the form f(n) = an^2 + bn + c. We can solve for the coefficients using the given values:

f(1) = a(1)^2 + b(1) + c = 6

f(4) = a(4)^2 + b(4) + c = 12

f(7) = a(7)^2 + b(7) + c = 18

Solving for a, b, and c, we get:

a = 1

b = 5

c = 0

Therefore, the recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

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Answer:

3(x - 2)(2x + 3)

Step-by-step explanation:

6x² - 3x - 18 ← factor out GCF of 3 from each term

= 3(2x² - x - 6) ← factor the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 6 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

2x² - 4x + 3x - 6 ( factor the first/second and third/fourth terms )

= 2x(x - 2) + 3(x - 2) ← factor out (x - 2) from each term

= (x - 2)(2x + 3) ← in factored form

then

6x² - 3x - 18 = 3(x - 2)(2x + 3)