Comparing and Building Functions: Functions That Fit

Answer:

Air

Step-by-step explanation:

it's asking you to look at the chart and find which substance is densest by comparing it to how fast sound can move through it (the speed of sound in the substance). In my opinion copper is not the densest material because sound moves through it the fastest; which means the particles in copper are not as densely held together. Air however, shows that sound can only travel 330 meters per second which is incredibly slow compared to the other listed materials, so by that logic it must be the densest.  

The equation 3x² - 12x - 15 = 0 when solved by factoring has the solutions x = 5 and x = -1

The equation 3x² - 12x - 15 = 0, is a representation of the equation in the question.

The aforementioned problem is a quadratic equation, and factoring is one way to solve this kind of issue.

Divide 3 from the equation.

As a result, we have the following

x² - 4x - 5 = 0.

Expanding the equation, we get

x² + x - 5x - 5 = 0.

Factoring the equation, we get

x(x + 1) - 5(x + 1) = 0

The result is

(x - 5)(x + 1) = 0.

We can solve for x by getting

x = 5 and x = -1.

Thus, the equation's answers are 5 and -1.

And it means that there are actually two solutions to the equation.

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The weight of the baby elephant is less than 212.59 kilograms which can be calculated using inequality.

To solve this problem, we need to use the inequality and the given information to find the weight of the baby elephant and the adult elephant. We can write the inequality as follows:

27w + 400 < a

Where w is the weight of the baby elephant in kilograms, and a is the weight of the adult elephant in kilograms. We can rearrange this inequality to get:

w < (a - 400)/27

Now, we can plug in the given information to find the weight of the baby elephant and the adult elephant. For example, if the weight of the adult elephant is 6000 kilograms, we can plug this into the inequality and get:

w < (6000 - 400)/27

w < 212.59

Similarly, we can plug in different values for the weight of the adult elephant to find the weight of the baby elephant.

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Explanation:

There are 4 white marbles out of 4+10 = 14 total

4/14 = 2/7 is the probability of randomly picking a white marble.

(2/7)*(2/7) = 4/49 is the probability of picking two whites in a row, when the first marble is replaced.

Use a calculator to find that 4/49 = 0.0816 approximately.

That converts to 8.16% after moving the decimal point two spots to the right. This is equivalent to multiplying by 100.

The gradient of line A is 4/72% or 0.0555.The gradient of line B is -2/6 or -0.3333.

Value is the worth of something, or the amount of importance, good qualities, or benefits that something has. It is determined by the amount of effort, time, and resources that have been put into it. Value can also refer to a person's moral or ethical principles and standards. It is the measure of worth that someone places on something or someone. Ultimately, value is subjective, as it is based on individual opinion.

The gradients of lines A and B indicate the rate of change of the line in relation to the x-axis. The gradient of line A is positive, which indicates that the line is increasing as it moves along the x-axis. This means that the y-value of the line is increasing as the x-value increases. On the other hand, line B has a negative gradient, which means that the y-value of the line is decreasing as the x-value increases. This means that the line is decreasing as it moves along the x-axis. This is why the gradients of lines A and B are different.

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The scale factor of a dilation is the ratio between the lengths of corresponding sides of the original and dilated figures. If the length of the top side of the original figure is 5 units and the length of the top side of the dilated figure is 10 units, then the scale factor is 2.

The scale factor is a number that is used to compare two measurements of the same object or design. It is the ratio between the two measurements, and is used to determine the size difference between the two. Scale factors can be used to scale objects up or down in size.

In other words, the scale factor is the multiplier used to stretch or compress the original figure. In Patrick's case, the scale factor can be determined by comparing the lengths of the corresponding sides of the original and dilated figures. For example, if the length of the top side of the original figure is 5 units and the length of the top side of the dilated figure is 10 units, then the scale factor is 2.

Since the dilation is on a coordinate plane, Patrick can also find the scale factor by comparing the coordinates of the original figure and the dilated figure. For example, if the coordinates of one of the vertices of the original figure are (2, 4) and the coordinates of one of the corresponding vertices of the dilated figure are (4, 8), then the scale factor is 2.

The scale factor of the dilation in Patrick's science project is an important concept and can be found by comparing the lengths of the corresponding sides of the original and dilated figures or by comparing the coordinates of the original and dilated figures.

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The unit rate for inches per mile is 0.8 inches.

The length of road B is 9.6 inches on map.

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.

Road in inches = 1 1/5 = 6/5 inches

Road in miles = 1 1/2 miles =

Inches per mile = 6/5 / (3/2)

                         = 6/5 x 2/3

                         = 4/5

                         = 0.8 inches

If the road B is 12 miles long, on the map it would be;

= 0.8 x 12

= 9.6 inches

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15. The student got 18 questions correct.

16. The weight of vitamin C in that tablet is 14%.

17. The secretary's salary has been increased by 60%.

18. The typist's original typing speed was 21 words per minute.

19. The salesperson made $1,022.40 in commission.

20. The salesperson's monthly earnings will be $19,546.

15. On a 45 questions exam, a student gets 40%.

The number of correct questions that the student got is
= 40% × 45 questions

= 18 questions

16. A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C.

The percent of the weight of this tablet is vitamin C is
= 35mg/250mg × 100%

= 14%

17. Five years ago, a secretary made $11,200 annually. The secretary now makes $17,920 annually.

The percentage the secretary's salary has been increased by
= ($17,920/$11,200 × 100%) - 100%

= 160% - 100%

= 60%

18. A typist was able to increase his speed by 120% to 42 words per minute.

Her original typing speed was
= 42/120%  × 100%

= 42/1.2

= 21 words per minute

19. A salesperson makes a commission of 12% on the total amount of each sale. In one month, she makes a total of $8,520 in sales.

In that month, she made a commission of
= $8,520 × 12%

= $1,022.40

20. A salesperson receives a salary of $850 per month plus a commission of 82% of her sales. In a particular month, she sells $22,800 worth of merchandise.

Her monthly earnings will be
= $850 salary + 82% × $22,800

= $19,546

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Point D's coordinates are (-3, 3).

We may use the fact that the opposite sides of a parallelogram are parallel and the same length to get the coordinates of point D such that ABCD forms a parallelogram.

First, we may determine the segment AB's length and slope:

Length AB = sqrt((1 - (-1))² + (6 - (-2))²) = sqrt(64) = 8

Slope AB = (6 - (-2)) / (1 - (-1)) = 8/2 = 4

As AB and CD are parallel, CD's slope must likewise be 4.

Next, we may determine segment AB's midpoint, which will coincide with segment CD's midpoint:

Midpoint AB is equal to ((-1+1)/2, ((-2+6)/2)). (0,2)

Point D will therefore have the same coordinates as the point that is symmetric to point C around the centre of AB. The following is where to find this point:

Midpoint AB - C = (20-3, 22-1) = D = 2 * (-3, 3)

Hence, point D's coordinates are (-3, 3).

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The difference in area between a circle with a radius of 10cm and regular pentagon inscribed in it is  142cm².

The difference in area between a circle with a radius of 10cm and a regular pentagon inscribed in it can be found by first finding the area of the circle and then the area of the pentagon, and then subtracting the two values.

To find the area of the circle, we use the formula

A = πr²,

where r is the radius of the circle. In this case, r = 10cm, so the area of the circle is:

A = π(10cm)²
A = 100π cm²

To find the area of the regular pentagon, we can use the formula

A = (1/4)n*a² * cot(π/n),

where n is the number of sides of the polygon and a is the length of one side. Since the pentagon is inscribed in the circle, we can use the radius of the circle to find the length of one side of the pentagon.

The length of one side of the pentagon is:

a = 2r * sin(π/n)
a = 2(10cm) * sin(π/5)
a = 11.756cm

Now we can plug this value into the formula for the area of the pentagon:

A = (1/4)(5)(11.756cm)² * cot(π/5)
A = 172.047cm²

Finally, we can subtract the area of the pentagon from the area of the circle to find the difference in area:

Difference in area = 100π cm² - 172.047cm²
Difference in area = 314.159cm² - 172.047cm²
Difference in area = 142.112cm²

To the nearest whole, the difference in area between the circle and the pentagon is 142cm².

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Answer: I think the answer is B. 241.13

Step-by-step explanation:

Formula for the volume of a cube is length of an edge cubed.

[tex]6^3=216[/tex]

Formula for the volume of a cone is [tex]\pi r^2\frac{h}{3}[/tex]

Half of 4 is 2, so the equation will be [tex]\pi 2^2\frac{6}{3}=25.13[/tex]

Add them together to get the answer

[tex]216+25.13=241.13[/tex]

I might be wrong, because I haven't done this in a long time, but I tried to do as much as possible, so forgive me if this is wrong.

To find out how many of each product Derrick can buy, we can use algebra. Let's call the number of headphones x and the number of cell phone cases y. We can set up an equation to represent the situation:

26x + 14y = 150

Now we can solve for one of the variables in terms of the other. Let's solve for y:

14y = 150 - 26x

y = (150 - 26x)/14

Now we can plug in different values for x and see what values of y will result in a total cost of at least $150. For example, if x = 1, then y = (150 - 26)/14 = 8.86. This means that Derrick could buy 1 pair of headphones and 8 cell phone cases for a total cost of $150.

Similarly, if x = 2, then y = (150 - 52)/14 = 7. This means that Derrick could buy 2 pairs of headphones and 7 cell phone cases for a total cost of $150.

We can continue plugging in different values for x until we find a combination of products that will cost at least $150. Alternatively, we could use a graphing calculator or an online graphing tool to graph the equation and find the intersection points with the line y = 150. These intersection points will represent the combinations of products that will cost at least $150.

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If you travel 200 miles in four hours, then your average speed for the trip is 50 miles per hour. This is calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).

So, if you travel 200 miles in four hours, your average speed is 50 mi/h.

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In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.

Descriptive analytics is a method used to collect, analyze and summarize data. In the case of the aerospace industry, descriptive analytics can be used to track the response and resolution of technical support calls. This helps to provide insights into the quality of service and make decisions about future changes to optimize the process.

In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.

By analyzing this data, the producer can gain insights into the most common types of technical support issues, the average response and resolution times, and any trends or patterns in the data. This information can then be used to improve the technical support process, identify areas for improvement, and develop strategies to prevent future technical support issues.

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The mean number of days to fix defects is 3.2 days.

The random variable in this case is the number of days it takes to fix defects in a pair of eyeglasses. Therefore, the correct answer is:
rv X = the number of days to fix defects

The corresponding histogram for this frequency table would be right-skewed. This is because there is a higher probability of it taking fewer days to fix the defects, with the probability decreasing as the number of days increases.

To find the mean number of days to fix defects, we need to multiply each number of days by its corresponding probability and then sum the results. The formula for this is:

mean = ∑(x * P(x))

Where x is the number of days and P(x) is the probability of it taking that number of days.

Using the data from the table, we can calculate the mean as follows:

mean = (1 * 0.1) + (2 * 0.2) + (3 * 0.3) + (4 * 0.25) + (5 * 0.1) + (6 * 0.05)

mean = 0.1 + 0.4 + 0.9 + 1 + 0.5 + 0.3

mean = 3.2

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The first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.

A system of equations can be classified as consistent, dependent, or inconsistent. A consistent system has at least one solution. A dependent system has infinitely many solutions, and an inconsistent system has no solution.

The first system of equations, y=-x+1 and y=-x, is inconsistent. This is because there is no value of x that can make both equations true at the same time. The graphs of these equations would be parallel lines that never intersect, meaning there is no solution.

The second system of equations, y=x+2 and y=x, is consistent and dependent. This is because there are infinitely many solutions that make both equations true. The graphs of these equations would be the same line, meaning every point on the line is a solution.

The third system of equations, y=x and y=2x, is consistent and independent. This is because there is only one solution that makes both equations true. The graphs of these equations would be two lines that intersect at one point, meaning there is only one solution.

In summary, the first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.

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As the variance/mean ratio is significantly greater than 1, the population is found to be a clumped distribution.

A clumped distribution, also known as an aggregated distribution, is a pattern of dispersion or arrangement of individuals within a population where they are found in groups or clusters. This means that individuals within a population are more likely to be found in certain areas, while other areas may have few or no individuals.

From the table in the attached image, it can be seen that

the variance= sum of (x -  0.6)^2/ sum of frequency

= 362.88/288

= 1.26

Variance/mean = 1.26/0.6 = 2.1 which is greater than 1

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Based on the given information, the sample space for the event can be represented using a tree diagram, where the first level consists of the three pants (black, blue, and tan) and the second level consists of the five shirts (white, black, green, blue, and red). Each branch represents a possible combination of a pair of pants and a shirt.

To find the total number of outcomes in the sample space, we can simply multiply the number of options for pants (3) by the number of options for shirts (5), giving us a total of 15 possible outcomes.

For Natalie selecting a pair of pants and shirt that are the same color, the favourable outcomes would be the combinations where the pants and shirt are either both black or both blue. These can be listed as:

Black pants and black shirt

Blue pants and blue shirt

For Natalie selecting a black shirt, the favourable outcomes would be the combinations where the shirt is black. These can be listed as:

Black pants and black shirt

Blue pants and black shirt

Tan pants and black shirt

For Natalie selecting a blue article of clothing, the favourable outcomes would be the combinations where either the pants or the shirt (or both) are blue. These can be listed as:

Black pants and blue shirt

Blue pants and white shirt

Blue pants and black shirt

Blue pants and green shirt

Blue pants and blue shirt

Tan pants and blue shirt

The two binomials that Camden must have multiplied and got the product of 49x^(2)-100 are (7x+10) and (7x-10).

To find the two binomials that Camden must have multiplied to get the product of 49x^(2)-100, we can use the process of factoring. Factoring is the process of breaking down a larger expression into two or more smaller expressions that can be multiplied together to get the original expression.

One way to factor the expression 49x^(2)-100 is to look for two binomials that have a difference of squares. A difference of squares is an expression of the form a^(2)-b^(2), which can be factored into (a+b)(a-b).

In this case, we can see that 49x^(2) is a perfect square, as it is equal to (7x)^(2), and 100 is also a perfect square, as it is equal to 10^(2). Therefore, we can factor the expression 49x^(2)-100 into (7x+10)(7x-10).

So, the two binomials that Camden must have multiplied are (7x+10) and (7x-10).

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603 white-tailed deer are expected to live in the rectangular area. To find the total number of white-tailed deer in the rectangular area, we need to find the area of the rectangle first. The area of a rectangle is given by the formula:

Area = length × width

In this case, the length is 2.25 miles and the width is 6.7 miles. So, the area of the rectangle is:

Area = 2.25 × 6.7

Area = 15.075 square miles

According to the given information, there are about 40 white-tailed deer per square mile in each of 35 Texas counties. We need to find how many white-tailed deer are expected to live in a rectangular area that measures 2.25 miles by 6.7 miles.

Now, we can find the total number of white-tailed deer in the rectangular area by multiplying the area by the number of deer per square mile:

Total number of deer = 15.075 × 40

Total number of deer = 603

Therefore, there are expected to be 603 white-tailed deer in the rectangular area.

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Answer:

Step-by-step explanation:

OK so im not that smart im only in 8th grade but i think the answers either A or B. hope i kind of helped you and good luck and have a nice day.

(i) The area of the path is 120x - 4x² square meters.

(ii) The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² is (900 - 120x + 4x²) × 40

To find the area of the path and the remaining portion of the garden, we need to first find the dimensions of the inner square after the path has been constructed.

Let the width of the path be "x" meters. Then the dimensions of the inner square garden will be (30-2x) meters on each side.

(i) The area of the path can be found by subtracting the area of the inner square from the area of the outer square.

Area of outer square = 30 × 30 = 900 sq.m.

Area of inner square = (30-2x) × (30-2x) = 900 - 120x + 4x² sq.m.

Area of path = Area of outer square - Area of inner square

= 120x - 4x² sq.m.

(ii) The remaining portion of the garden is the area of the inner square.

Area of remaining portion = (30-2x) × (30-2x) sq.m.

= 900 - 120x + 4x² sq.m.

The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² can be found by multiplying the area of the remaining portion by the rate.

Cost of planting grass = Area of remaining portion × Rate

= (900 - 120x + 4x²) × 40

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As per the given distance, the maximum height reached by the football is 15.4 yards.

To find the maximum height reached by the football, we need to find the vertex of the parabolic path. The vertex of a parabola represents the highest point on the path. In this equation, the vertex can be found by using the formula:

x = -b / 2a

where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

By comparing the given equation with the standard form of the quadratic equation (y = ax² + bx + c), we can find that a = -0.035 and b = 1.4.

Substituting these values in the formula, we get:

x = -1.4 / 2(-0.035)

x = 20

This means that the maximum height is reached when the football has traveled a distance of 20 yards. To find the maximum height, we need to substitute this value of x back into the original equation:

y = -0.035(20)² + 1.4(20) + 1

y = 15.4

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Complete Question:

A punter kicked a 41-yard punt. The path of the football can be modeled by y=-0.035x² + 1.4x + 1 where x is the distance in yards the football is kicked and y is the height in yards the football kicked.

what is the maximum height reached by the football?

The inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:

[tex]$$s \geq \frac{525}{p}$$[/tex]

In business and finance, profit refers to the monetary gain earned by a business or individual after subtracting the expenses from the total revenue. In other words, profit is the difference between the amount of money earned from selling goods or services and the total cost of producing or delivering those goods or services. Profit is often used as a key performance indicator (KPI) to measure the financial success of a business or individual.

Let's assume that the cost of making one t-shirt is c and Lee sells each t-shirt for p.

To make at least $400 profit, Lee's revenue from sales p must be greater than or equal to the sum of the startup costs $125 and the desired profit $400:

[tex]$$p\times s \geq 125+400$$[/tex]

We can simplify this inequality to:

[tex]$$p\times s \geq 525$$[/tex]

Therefore, the inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:

[tex]$$s \geq \frac{525}{p}$$[/tex]

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Step-by-step explanation:

When 508,000,000 is written in scientific notation, it will be represented as:

5.08 x 10^8

Therefore, the value of the exponent is 8.

The inequality that represents the set of solutions above the straight line is: x-3y<5

What is a linear inequality?

A linear inequality is an inequality in which one side is a linear expression in one or more variables, and the other side is a constant, or another linear expression. The solution set of a linear inequality is a region in the coordinate plane that satisfies the inequality.

Calculate the inequality to represent the set of solution by shaded region:

A linear inequality can be represented by a shaded region on the coordinate plane. The boundary of the region is a straight line, and the shaded region represents all the points in the plane that satisfy the inequality. In this case, the line that intersects the x-axis at (5,0) and the y-axis at (0, -5/3) represents the boundary of the region.

To find the inequality that represents the set of solutions above the line, we first need to find the equation of the line. We can use the point-slope form of the equation of a line, which relates the slope of the line and a point on the line to the equation of the line.

We know that the line passes through the points (5,0) and (0, -5/3), so we can calculate the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two points through which the line passes.

m = (-5/3 - 0) / (0 - 5) = 1/3

Now we can use the point-slope form of the equation of the line to write the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is one of the two points through which the line passes.

Using the point (5,0) as (x1, y1), we get:

y - 0 = (1/3)(x - 5)

y = (1/3)x - 5/3

3y = x - 5

To represent the set of solutions above the line, we need to use the greater than symbol. So the inequality that represents the set of solutions above the straight line is:

x-3y<5

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The equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.

To find the equation of a line with the given properties, we need to use the concept of parallel lines and the point-slope form of a linear equation.

Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line ( y=-6x+4 ), which is -6.

Next, we can use the point-slope form of a linear equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the given point (3, 5) and the slope -6, we get:

y - 5 = -6(x - 3)

Simplifying the equation, we get:

y - 5 = -6x + 18

y = -6x + 23

Finally, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the new line is y = -6x + 23.

Therefore, the equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.

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The total excise tax per pack is $2.15.

The total excise tax is the sum of the federal excise tax and the state excise tax.

Excise tax is the tax that is levied at the moment of manufacture of a good or service. Excise tax is usually levied on alcoholic or tobacco products.

Total excise tax = federal excise tax + state excise tax

$3,80 + $17.70 = $21.50

The total excise tax per pack can be known by dividing the total excise tax by the total number of packs.

Total excise tax per pack = $21.50 / 10 = $2.15

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Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \]

To find the expression for \( f(x) \), we need to use the fact that the zeros of a polynomial are the values of \( x \) that make the polynomial equal to zero. This means that if \( -1, 4, \) and \( 3+2i \) are zeros of \( f(x) \), then the factors of \( f(x) \) are \[ (x+1)(x-4)(x-(3+2i))(x-(3-2i)) \] Now, we can simplify the last two factors by multiplying them together: \[ (x-3-2i)(x-3+2i) = (x-3)^2 - (2i)^2 = x^2 - 6x + 9 - 4i^2 = x^2 - 6x + 9 + 4 = x^2 - 6x + 13 \] So, the expression for \( f(x) \) is \[ f(x) = (x+1)(x-4)(x^2 - 6x + 13) \] Now, we can use the fact that \( f(1) = -144 \) to find the value of the leading coefficient of \( f(x) \). Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \] This is the final answer.

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