James owns a restaurant and has 216 two-liter
bottles of soda to use for the soda machines, but wants to save space by pouring all the soda into one-gallon jugs. How many jugs does James need to hold all of the soda? Round your answer to three decimal
places, if necessary. Use 1 gal = 3. 785 L

The method we would be using here to prove the triangle's congruency is LA, the leg-acute theorem.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent or not. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form.

Here in the given figures, we can use the LA theorem also known as leg acute. It says that a right triangle is congruent if its leg and any acute angle are congruent with the corresponding leg and any acute angle of another right triangle.

The hypotenuse of the first triangle is corresponding to the hypotenuse of the second triangle.

The angle opposite to the right angle in both the triangles are corresponding to each other.

So as per the LA theorem we can prove that the triangle is congruent.

To know more about congruency, visit:

https://brainly.com/question/6976551

#SPJ1

In the given system of equations one taco costs $0.80 and one burrito costs $0.72.

An equation system is a finite collection of equations for which we searched for the common solutions. It is sometimes referred to as a set of simultaneous equations or an equation set. The classification of a system of equations is similar to that of a single equation. In modelling issues where the unknown values may be expressed in the form of variables, a system of equations finds use in everyday life.

Let us suppose the cost of one taco = x.

Let us suppose the cost of one burrito = y.

Then, for Emma we have:

3x + y = 3.65

For Cooper we have:

x + 2y = 3.30

Using elimination, multiply the first equation by 2 and subtract it from the second equation:

(2)(3x + y = 3.65)

6x + 2y = 7.30

x + 2y = 3.30

-5x = -4

x = 4/5

Substituting this value of x into either equation:

3(4/5) + y = 3.65

y = 2.15/3 ≈ 0.72

Therefore, one taco costs $0.80 and one burrito costs $0.72.

Learn more about system of equations here:

https://brainly.com/question/13760328

#SPJ1

Answer: 8377828766289

Step-by-step explanation:

Answer:

The sum is:

74569273469287465294875629837469523746539287465927346592873654987264982768

999999999999999999292929292929923798341038701384710348710387017

= 74569273469287465294875629837469523746539287465927346592873655087264969785

An 1 οr perhaps an even integer will be drawn back 75% οf the times frοm the set οf 1, 2, 3 and 4. Thus, Prοbability P(nοt even) is 75%.

Prοbability is the likelihοοd that sοmething will οccur οr the prοbability that sοmething will happen. Prοbability is the measure οf hοw prοbable it is that a cοin will land heads up after being tοssed intο the air.

As prοbabilistic arguments sοmetimes prοduce οutcοmes that appear cοntradictοry οr illοgical, prοbability is usually regarded as amοng the mοst challenging tοpics οf mathematics.

P(1) = 1/4(there is one card with a 1)

P(even) = 2/4 = 1/2 (there are 2 cards with even numbers out of 4)

Therefore,

P( 1 or even) =P(1) + P(even)

= 1/4 + 1/2

= 3/4

To express the answer as a percentage, we can multiply by 100:

P(1 or even) = 3/4 × 100%

=> 75%

To know more about probability visit:

brainly.com/question/30034780

#SPJ1

You pick a card at random. card 1, card 2 and card 3

What is P(not even)?

Write your answer as a fraction or percentage.

Answer: So that means the answer is $112.5

Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.

YES THIS IS RIGHT!!!!

The area of the parallelogram is 324 square yards.

What is a parallelogram ?

A parallelogram is a four-sided geometric shape that has two pairs of parallel sides. It isdefined by its four vertices, four sides, and two diagonals that intersect at their midpoint. The opposite sides of a parallelogram are congruent, and the opposite angles are also congruent. The adjacent angles are supplementary and add up to 180 degrees.

To find the area of a parallelogram, we need to multiply the length of the base by the height, which is the perpendicular distance from the base to the opposite side. This formula is similar to finding the area of a rectangle, where the base is one side of the rectangle and the height is the distance from that side to the opposite side.

Calculating the area of the given parallelogram :

The area of a parallelogram is  A = bh, where b is the base and h is the height.

Given the height of the parallelogram is 12 yards and the base is 27 yards. Using the formula for the area of a parallelogram, we can calculate the area as follows:

A = bh

A = 27 yards × 12 yards

A = 324 square yards

Therefore, the area of the parallelogram is 324 square yards.

To know more about parallelogram visit :

brainly.com/question/29147156

#SPJ1

3. The statement is true,  the correlation coefficient is close to -1. 4. temperature for a city with a latitude of 48 is 43. 5. The statement is false. 6. cannot make a reasonable estimate

Equations can be used to model real-world situations and solve problems in many fields, including science, engineering, finance, and more. They are an essential tool in mathematics and are used extensively in algebra, calculus, and other advanced branches of math.

Equations can involve various mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and others.

Question 3:

The statement is true. We can check this by calculating the correlation coefficient between the latitude and temperature data points, which should be close to -1. The calculated line of best fit is also consistent with the given data.

Question 4:

To estimate the temperature for a city with a latitude of 48, we can use the equation of the line of best fit:

y = -1.07x + 92.87

Substituting x = 48, we get:

y = -1.07(48) + 92.87

y = 42.79

Rounding to the nearest whole number, the estimated temperature for a city with a latitude of 48 is 43.

Question 5:

The statement is false. We can check this by calculating the correlation coefficient between the passengers and suitcases data points, which should be close to 1. The given line of best fit has a negative slope, which is inconsistent with the positive correlation between the variables.

Question 6:

To estimate the number of suitcases for a flight carrying 250 people, we can use the equation of the line of best fit:

y = -1.98x + 7.97

Substituting x = 250, we get:

y = -1.98(250) + 7.97

y = -485.03

However, it does not make sense for the number of suitcases to be negative. Therefore, we cannot make a reasonable estimate for the number of suitcases on a flight carrying 250 people using this line of best fit.

To know more about correlation visit:

https://brainly.com/question/15269042

#SPJ1

Yes, every odd integer can be written as the difference of two squares.

To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.

To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.

To know more about squares click on below link:

https://brainly.com/question/13747846#

#SPJ11

Answer:

4 apples

Step-by-step explanation:

We know

John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.

How many apples does he have now​?

3 - 2 + 4 - 1 = 4 apples

So, he has 4 apples now.

Answer:

4 apples

Step-by-step explanation:

We know that John had 3 apples

but then he had dropped 2 of them

he then found 4

then he gave 1 to his friend

3-2=1

1+4=5

5-1=4

The answer is 4

Hope this helps!

The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.

As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.

We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:

Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:

Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)

Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)

(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)

Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)

(b), we can use the just-proven formula:

A = ln(1, 2,...) + ln + ln (89)

= ln(j=1 to 89) prod

sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).

To know more about hypothesis visit:-

https://brainly.com/question/29519577

#SPJ1

It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

First, we need to convert the dimensions of the tank from inches to feet:

68 inches diameter = 68/12 feet = 5.67 feet diameter

24 feet long = 24 feet long

Next, we can calculate the volume of the tank in cubic feet:

Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:

To find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:

Finally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:

Therefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

Learn more about feet here : brainly.com/question/29793314

#SPJ1

Answer:

16 feet

Step-by-step explanation:

Area of triangle = 1/2(a x b)

A = 1/2(6.4 x 5)

A = 32/2

A = 16 feet

The equation for the ellipse is: [tex]$\frac{x^2}{37}[/tex] + [tex]$\frac{y^2}{25}[/tex] [tex]= 1$$[/tex]

The standard equation for an ellipse centered at the origin is:

[tex]$\frac{x^2}{a^2}[/tex] + [tex]$\frac{y^2}{b^2}[/tex] [tex]= 1$$[/tex]

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex.

In this case, the vertices are located at [tex]$(\pm\sqrt{37}, 0)$[/tex], which means [tex]$a=\sqrt{37}$[/tex]. The distance between the foci is [tex]$2c=2\sqrt{12}=2\sqrt{3\times 4}=2\sqrt{3}\times 2=4\sqrt{3}$[/tex], which means [tex]$c=2\sqrt{3}$[/tex].

The value of b can be found using the relationship between a, b, and c in an ellipse:

[tex]$$a^2 = b^2 + c^2$$[/tex]

Substituting the values we know, we get:

[tex]$$37 = b^2 + (2\sqrt{3})^2$$[/tex]

Simplifying:

[tex]$$37 = b^2 + 12$$[/tex]

[tex]$$b^2 = 37 - 12 = 25$$[/tex]

Taking the square root of both sides, we get:

[tex]$$b = \pm 5$$[/tex]

Since the co-vertices are located at [tex]$(0,\pm b)$[/tex], we can see that [tex]$b=5$[/tex] (and not -5, since the ellipse is centered at the origin).

Therefore, the equation for the ellipse is:

[tex]$\frac{x^2}{37}[/tex] + [tex]$\frac{y^2}{25}[/tex] [tex]$ = 1$$[/tex]

To learn more about standard equations:

https://brainly.com/question/2892729

#SPJ4

We have to find the minimum number, k, of z in (a, b) such that g'(z) = 0. The function g is continuous on the interval [a, b] and is differentiable on (a, b). Suppose that g(x) = 0 for 4 distinct values of x in (a, b).

Let x1, x2, x3, and x4 be the four distinct values of x such that g(x) = 0.Now consider the following cases:Case 1: All four x1, x2, x3, x4 are local extrema of g(x).If this is the case, then g′(x1)=g′(x2)=g′(x3)=g′(x4)=0. Therefore, the minimum number, k, of z in (a, b) such that g′(z) = 0 is 4.Case 2:

There are less than four local extrema of g(x).In this case, by Rolle's Theorem, there exists at least one point z in (a, b) such that g′(z)=0. Since there are less than four local extrema of g(x), this point z is not equal to any of x1, x2, x3, and x4. Therefore, the minimum number, k, of z in (a, b) such that g′(z) = 0 is 1.In conclusion, the minimum number, k, of z in (a, b) such that g′(z) = 0 is either 1 or 4 depending on whether there are less than four local extrema of g(x) or all four x1, x2, x3, and x4 are local extrema of g(x).

Learn more about distinct values:

https://brainly.com/question/30042754

#SPJ11

The monthly profit, P(x), of a pizza parlor is given by the function P(x) = 5.75x - 1,200, where x is the number of pizzas sold, given revenue and expense functions.

The monthly profit, P(x), is the difference between the revenue and the expenses, so:

P(x) = R(x) - E(x)

From the given information:

R(x) = 12.5x (revenue per pizza is $12.5, and x is the number of pizzas sold)

E(x) = 1,200 + 6.75x (expenses, which include the monthly rent of $1,200 and the production cost of $6.75 per pizza, multiplied by the number of pizzas sold)

Substituting the values of R(x) and E(x) into the equation for P(x):

P(x) = 12.5x - (1,200 + 6.75x)

Simplifying the equation:

P(x) = 5.75x - 1,200

Therefore, the function representing the monthly profit, P(x), is P(x) = 5.75x - 1,200.

To know more about Profit:

https://brainly.com/question/1291585

#SPJ4

Answer:

P(x)= 5.75x -1,200

Step-by-step explanation:

Plato/Edmentum

After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.

Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.

The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.

If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.

The number of generations (n) in seven hours is calculated as:

n = t/g

n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations

The number of cells in the cream pie after 7 hours is calculated as :

N = N₀ × 2ⁿ

N = 6 cells × 2⁷

N = 768 cells

Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.

Learn more about Number of generations here:

https://brainly.com/question/17045618

#SPJ11

Work Shown:

x = previous total weight

2% of x = 0.02x = amount of weight lost

x - 0.02x = 0.98x = current total weight

0.98x = 1519

x = 1519/0.98

x = 1550 pounds

Check:

2% of 1550 = 0.02*1550 = 31

The group collectively lost 31 pounds.

1550-31 = 1519

The answer is confirmed.

Note that 98% of 1550 = 0.98*1550 = 1519

Answer:

2)She could either divide by 3 or distribute 3 into the parenthesis

Answer: Total number of males= C

Step-by-step explanation:

The normal distribution that best approximates X is N(42, 21).

In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).

In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)

Learn more about Normal distribution

brainly.com/question/29509087

#SPJ11

Answer: -109

Step-by-step explanation:

Concept : First take note of what operations are in play and how they relate to y. In this case, -10 is being multiplied to y and then 19 is subtracted from the product of -10 and y.

Steps:

Plug 9 in for y (parentheses just mean multiply):

-10(9)-19

Simplify using correct order of operations:

-90-19

-109

Hope this helps :)

the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".

How to solve and what is subtraction?

To write the subtraction problem "-3 - 4" as an addition problem using negative numbers, we can rewrite it as follows:

-3 - 4 = -3 + (-4)

So, the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".

Subtraction is a fundamental arithmetic operation used to find the difference between two values or quantities. It involves taking away a certain amount from a starting value, resulting in a lower value.

The starting value is called the minuend, the amount being subtracted is called the subtrahend, and the result is called the difference. Subtraction is commonly used in everyday life, such as in calculating change when making a purchase or determining how much time has elapsed between two events. It is also an important concept in more advanced mathematical topics such as algebra and calculus.

To know more about Subtraction related questions, visit:

https://brainly.com/question/2346316

#SPJ1

The chance that a randomly selected individual found to have a positive result actually has the disease is called the Positive Predictive Value (PPV). What is the chance that a randomly selected individual found to have a positive result actually has the disease?

The probability that a randomly chosen individual with a positive test result really has the disease is referred to as the Positive Predictive Value (PPV). It reflects how well the test can detect disease in those who have it. In statistics, the PPV is calculated as follows:

PPV = True Positives / (True Positives + False Positives) x 100

In addition, the PPV is influenced by a variety of factors, including the disease's prevalence, the sensitivity and specificity of the test, and the prevalence of the disease in the population.

To learn more about Positive Predictive value refer :

https://brainly.com/question/30709682

#SPJ11

In both cases, the slope (m) is the coefficient of the x-variable, and the y-intercept (b) is the constant. In the first equation, the slope (m) is 2, and the y-intercept (b) is -3. In the second equation, the slope (m) is 3, and the y-intercept (b) is 6.

Graph is a data structure that consists of nodes (vertices) and edges (connections between nodes). Graphs are used to represent networks, such as social networks, transportation networks, and communication networks. Graphs provide a way to visualize relationships between data points and can be used to discover patterns in data and make predictions. Graphs are a powerful tool in data science and can be used to analyze complex systems.

This is happening because the equations represent the linear relationships between the variables of the graphs. The first equation is in slope-intercept form, and can be used to calculate the y-value of a given x-value. The equation for the second graph is also in slope-intercept form, and can be used to calculate the y-value of a given x-value.

In both cases, the slope (m) is the coefficient of the x-variable, and the y-intercept (b) is the constant. In the first equation, the slope (m) is 2, and the y-intercept (b) is -3. In the second equation, the slope (m) is 3, and the y-intercept (b) is 6.

These equations represent the linear relationships between the variables of the graphs. The slope of the line is the rate of change between the x- and y-values, while the y-intercept is the starting point of the line. By using the equations, we can calculate the y-value of any given x-value on the graph, and thus accurately represent the linear relationships between the variables.

The diagram is given below.

To know more about graph click-
https://brainly.com/question/19040584
#SPJ1

Complete questions as follows-

Answer: In 2030, the population will be 16,800 and in 2040 the population will be 18,816.

Step-by-step explanation: To find the population in 2030, we need to calculate one decade of growth from 2020 to 2030:

Population in 2030 = 15,000 x (1 + 0.12)^1 = 16,800

Therefore, the population in Gastonia is expected to be 16,800 in 2030.

To find the population in 2040, we need to calculate two decades of growth from 2020 to 2040:

Population in 2040 = 15,000 x (1 + 0.12)^2 = 18,816

Therefore, the population in Gastonia is expected to be 18,816 in 2040.

Boolean expressions that are equivalent to the expression num ≥ 15 are (B) (num > 15) OR (num = 15) and (D) NOT (num < 16).

In Boolean algebra, a Boolean expression is an algebraic expression made up of Boolean variables and logical operations. Boolean logic deals with logical variables and has only two values: 1 or 0 or TRUE or FALSE. Boolean expressions evaluate to a Boolean value of either 0 or 1 or TRUE or FALSE.(A) (num > 15) AND (num = 15) - this expression is not equivalent to num ≥ 15 because (num > 15) is false for all values of num that are less than or equal to 15.

However, num ≥ 15 is true for all values of num that are greater than or equal to 15.(C) NOT (num < 15) - this expression is not equivalent to num ≥ 15 because NOT (num < 15) is true for all values of num that are greater than or equal to 15. However, num ≥ 15 is true for all values of num that are greater than or equal to 15.(B) (num > 15) OR (num = 15) - this expression is equivalent to num ≥ 15 because if num is greater than 15, then (num > 15) is true and (num = 15) is false. However, if num is equal to 15, then (num > 15) is false and (num = 15) is true.

In either case, (num > 15) OR (num = 15) is true, which means that num ≥ 15 is true.(D) NOT (num < 16) - this expression is equivalent to num ≥ 15 because if num is less than 16, then (num < 16) is true and NOT (num < 16) is false. However, if num is greater than or equal to 16, then (num < 16) is false and NOT (num < 16) is true. In either case, NOT (num < 16) is true, which means that num ≥ 15 is true.

Learn more about Booloean algebra:

https://brainly.com/question/30755763

#SPJ11

Answer:

82

Step-by-step explanation:

divide this shape into a triangle and rectangle and use 24 as the base of the triangle using the Pythagoras theorem you get that the perpendicular is 7 and since 13 is also parallel to that side, 13+7=20 so one side equals 20 one side equals 25 one side equals 24 and one side equals 13 now add all of these to get 82

Step-by-step explanation:

See image below ..... perimeter = 25 + 13 + 24 + 13 + x

  x is found using pythagorean theorem for right triangles

x = 7 units

total perimeter is then 82 units

The dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.

The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.A rectangular poster is given that is to contain 450 square inches of print. The margins at the top and bottom of the poster are 2 inches, and the margins on the left and right are 1 inch. Let us suppose the width of the poster is x in and the length of the poster is y in. Also, we need to find the least amount of poster used.Therefore, the dimensions of the poster be x in × y in. The printable area of the poster is given as 450 sq in. Hence, the area of the poster minus the area of the margins should be 450 sq in. Therefore,x × y = (x - 2) (y - 4) + 450x × y = xy - 2x - 4y + 8 + 450xy - xy - 2x + 4y = 8 + 450(y - 4)x = (450(y - 4) - 8) / (y - 1)x = (450y - 1808) / (y - 1)Now we need to calculate the dimensions of the rectangular poster. We need to find the value of x and y. Substituting the value of x in the first equation we get,y = (450 / (x - 2)) + 4We also know that x > 2 and y > 4. We need to minimize the amount of poster used. Hence we need to minimize x × y. The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.Therefore, the dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.

Lean more about Dimensions

brainly.com/question/8048555

#SPJ11

The selling price of laptop after VAT (15 percent) is Rs 4830.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

A number that is expressed as a fraction of hundred is what it is.

it is mostly used to compare and determine ratios and is represented by the symbol %.

We are given that:-

so the amount after VAT = 4200+4200*15%

= 4200+4200+0.15

= 4200+630= 4830.

therefore, the selling price of laptop after VAT is Rs 4830.

To know more about percent go through:-

https://brainly.com/question/24877689

#SPJ4

The value of k in the cubic equation is 2 and factorization of the equation is 2(x-1)^2(x+1)

If 2x^3 + 15x^2 + 24x + k has three linear factors, then it must be in the form:

[tex]2x^3 + 15x^2 + 24x + k = a(x-b)(x-c)^2[/tex]

where a, b, and c are constants, and (x-c)^2 means that (x-c) is a repeated factor.

Expanding the right side, we get:

[tex]2x^3 + 15x^2 + 24x + k = a(x^3 - 2cx^2 + cx^2 - 2cx + c^2x - c^2)[/tex]

Simplifying, we get:

[tex]2x^3 + 15x^2 + 24x + k = ax^3 - 2acx^2 + ac^2x - 2acx + ac^2 + a(-c^2)\\2x^3 + 15x^2 + 24x + k = ax^3 + (-2ac + ac^2)x^2 + (-2ac + ac^2)x - ac^2[/tex]

Equating the coefficients of each power of x on both sides, we get:

[tex]a = 2\\-2ac + ac^2 = 15\\-2ac + ac^2 = 24\\-ac^2 = k\\\\[/tex]

From the second and third equations, we can see that -2ac + ac^2 = 15 and -2ac + ac^2 = 24. These equations are equivalent, so we can set them equal to each other:

[tex]-2ac + ac^2 = 15 = 24[/tex]

Simplifying, we get:

ac^2 - 2ac + 9 = 0

This is a quadratic equation in ac. Solving for ac using the quadratic formula, we get:

[tex]ac = [2 \± \sqrt(4 - 4(1)(9))] / 2[/tex]

[tex]ac = 1 \± \sqrt(-5)[/tex]

Since ac is the product of two real numbers (b and c), we know that the square root of -5 must cancel out. This is only possible if ac = 1 and c = -1. Therefore, b = -c = 1, and we can find k by setting ac^2 = -k:

[tex]1 = 2a\\15 = -2ac + ac^2 = -2a + a^2\\24 = -2ac + ac^2 = -2a + a^2\\-k = -ac^2 = 2(-1)^2 = 2\\[/tex]

Therefore, k = -2, and the factorization of 2x^3 + 15x^2 + 24x - 2 is:

2x^3 + 15x^2 + 24x - 2 = 2(x-1)^2(x+1)

Learn more on cubic equations here;

https://brainly.com/question/20896994

#SPJ1