An investor buys stock in a company and in the 12 months after she invests the value of the stock decreases by 30%. By what amount will the value of the stock need to go up from there in order that the price of the stock will be equal to what investor first paid for it?

The following set of inequalities is satisfied by the coefficients a, b, and c:

-a < b < (-3/8) - (4a/8)

c > -1

-2a - 2b < 2

Any solutions for the coefficients a, b, and c that meet the requirements can be found using this system of inequalities.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

from the question:

In order to solve for the coefficients a, b, and c, we must construct a system of inequalities using the provided information.

Let's start by creating the following inequalities using the values of f(-1), f(1), and f(3) that are given:

[tex]a(-1)^2 + b(-1) + c < 1[/tex]

[tex]a(1)^2 + b(1) + c > -1[/tex]

[tex]a(3)^2 + b(3) + c < -4[/tex]

Simplifying these inequalities, we get:

a - b + c < 1

a + b + c > -1

9a + 3b + c < -4

Given that an is not equal to zero, we may use this information to find the values of the remaining coefficients. In order to construct an expression for c in terms of a and b, we can first utilize the second inequality as follows

c > -1 - a - b

The first and third inequalities can then have this expression for c to yield the following result:

a - b + (-1 - a - b) < 1

9a + 3b + (-1 - a - b) < -4

Simplifying these inequalities, we get:

-2a - 2b < 2

8a + 2b < -3

Now, we can solve for b in terms of a using the first inequality:

b > -1 - a - (1/2)(-2a)

b > -a

And we can solve for b in terms of a using the second inequality:

b < (-3/8) - (4a/8)

Combining these two formulas for b, we obtain:

-a < b < (-3/8) - (4a/8)

Lastly, we may enter the following equation for b into the earlier-derived expression for c:

c > -1 - a - (-a)

c > -1

As a result, the following system of inequalities is satisfied by the coefficients a, b, and c:

-a < b < (-3/8) - (4a/8)

c > -1

-2a - 2b < 2

Any solutions for the coefficients a, b, and c that meet the requirements can be found using this system of inequalities.

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complete question:

let[tex]f(x)=ax^2+bx+c[/tex] and f(-1)<1,f(1)>-1,f(3)<-4 and a is not equal to zero then

Thus, the length of the other side of Ross's garden is 18 feet.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

To find the length of the other side of Ross's garden, we can use the Pythagorean theorem.

In this case, let's assume the length of the other side of Ross's garden x.

We can set up the following equation:

x² + 30² = 33²

Solving for x, we get:

x² = 33² - 30²

x² = 1089 - 900

x² = 289

x = √289

x = 17.

Thus, the length of the other side of Ross's garden is 18 feet.

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Answer:

Step-by-step explanation:

a: in the quadratic formula, no real roots would mean b^2 - 4ac<0 because of the discriminant. b^2 is 4, so all 4c has to satisfy is that it’s greater than 4. Solving, c>1

b: casework:

Both are negative: This is impossible because square roots are always positive, so at least one would always be positive.

Both are positive: sqrt(4-4c)<2.  0<c<=1.

c. I’m not entirely sure of what you mean, but when c=0, 0 is a root of the quadratic equation, but the other root is positive 2, so no value?

d. sqrt(4-4c)>2. Another possibility is that the same thing is less than -2, but square roots are always positive. This remains true for c<0.

If the cost of customer acquisition is $50 and the cost of customer retention is $30, then the cost of Software C would be $80,000. This is because 10,000 customers x ($50 acquisition cost + $30 retention cost) = $80,000.

Acquisition cost is the cost associated with obtaining an asset or resource. It includes the purchase price, transportation costs, installation costs, taxes, and any other associated costs.

The cost of Software C can be determined by calculating the total cost of lost customers due to software issues. To do this, companies typically look to the customer lifetime value (CLV) of each customer. CLV is the total revenue generated by a customer over the course of their relationship with the company. By multiplying the CLV by the number of unsatisfied customers, companies can get a good idea of what the cost of Software C is.

For example, if a company has 10,000 customers and their CLV is $100, then the cost of Software C would be $1,000,000. This is because 10,000 customers x $100 CLV = $1,000,000.

The cost of Software C can also be determined by looking at the cost of customer acquisition and retention.

In addition to the cost of lost customers, companies must also factor in the cost of fixing the software issue. This cost can vary depending on the complexity of the issue and the size of the company. Companies should also consider the cost of lost productivity due to the software issue, as well as any other costs associated with the issue.

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Answer:

54665655

Step-by-step explanation:

The monthly percent decrease in average weekly crate production from Month A to Month B is 40%.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for it. Percentages are frequently used to represent change or growth over time and to compare two values. Finding the proportion of the quantity you are interested in to the total is necessary before you can compute a percentage. The percentage is then calculated by multiplying the ratio by 100.

For Month A the production is:

2000 + 3000 + 2000 + 3000 = 10,000

Thus, average weekly production is:

A = 10,000 / 4

A = 2500

For month B we have:

2000 + 1000 + 3000 + 0 = 6000

Average weekly crate production is:

= 6000 / 4

= 1500

The percentage decrease is given by:

percent decrease = [(original value - new value) / original value] x 100%

= [(2500 - 1500) / 2500] x 100%

= 40%

Therefore, the monthly percent decrease in average weekly crate production from Month A to Month B is 40%.

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The required equivalent fractions for 1 10/15 and 9/12.

Given, two mixed fractions 1 2/3 and 3/4, determine equivalent fractions using 15 as the common denominator.

Simplification:

The process in mathematics of manipulating and interpreting functions to make a function or expression simpler or easier to understand is called simplification, and the process is called simplification.

1. Simplify fractions by canceling all common factors of the numerator and denominator and writing the fraction in its lowest/simplest form.

2. Simplify mathematical expressions by grouping and combining similar terms. This makes expressions easy to understand and solve.

According to the Question:

Here,

First

= 1 2/3

= 1+ 2 / 3

= 1 + 2 × 5 / 3 × 5

= 1 + 10 / 15

Again,

Second,

=  3 / 4

=  3 × 3 / 4 × 3

= 9/12

Thus, the required equivalent fractions for 1 10/15 and 9/12.

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The value of 151.8% of £613.71 is £931.55.

An informed estimate or a flimsy explanation for a phenomena or observation that may be evaluated by more research is called a hypothesis. It serves as the basis for scientific inquiry and is often formed using known facts and observations.

A theory, on the other hand, is a proven explanation for a phenomenon or group of occurrences that has undergone significant testing and is backed by empirical data. A theory may be thought of as a framework that predicts and explains how and why things happen the way they do.

Given that, 151.8% of £613.71

To find the value, first convert the percentage to a decimal by dividing it by 100:

151.8 ÷ 100 = 1.518.

Multiply this decimal by:

£613.71: 1.518 × £613.71 = £931.55

Hence, the value of 151.8% of £613.71 is £931.55.

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Using perimeter fοrmula , 521 ft tabe is used tο cοver baseball cοurt.

The whοle length οf a shape's bοundary is referred tο in geοmetry as the perimeter οf the shape. Adding the lengths οf all the sides and edges that surrοund a fοrm yields its perimeter. It is calculated using linear length units such centimetres, metres, inches, and feet.

Here the basketball cοurt is cοmbined with twο half circle , οne circle and οne rectangle.

In the rectangle , Length = 94ft and width = 44ft.

Perimeter οf rectange = 2(length+width) = 2(94+44) = 2*138 = 276 ft.

In the half circle , Diameter = 44 ft  then radius = 44/2 = 22ft

Perimeter οf circle = πr+d = 3.14*22+44 =113.08 ft

Nοe , In the circle , Diameter = 12ft ,then radius = 12/2=6 ft.

perimeter οf circle = πd = 3.14*6=18.84 ft

Then Tοtal perimeter = 276+113.08+113.08+18.84 = 521 ft.

Hence 521 ft tabe is used tο cοver baseball cοurt.

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Let's represent the number of students as "S" and the number of rooms as "R".

From the problem, we can set up the following system of equations:

Equation 1: 3S + 20 = R

Equation 2: S + 2 = (1/3)R

We can solve for S and R by substituting Equation 1 into Equation 2:

S + 2 = (1/3)(3S + 20)

S + 2 = S + (20/3)

(2/3) = (20/3) - S

S = 18

Now we can substitute S = 18 into Equation 1 to solve for R:

3(18) + 20 = R

R = 74

Therefore, there are 18 students and 74 rooms in the boarding school.

The solution to the equation is x = 22.5.

To solve the equation x-9 = (3/5)x, we can first simplify the right-hand side by multiplying both sides by 5 to get rid of the fraction:

5(x-9) = 3x

An equation is a mathematical statement that indicates the equality of two expressions. Equations typically contain variables, which are represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equals sign are called the left-hand side and right-hand side of the equation.

Expanding the left-hand side, we get

5x - 45 = 3x

Next, we can simplify by subtracting 3x from both sides:

2x - 45 = 0

Adding 45 to both sides, we get:

2x = 45

Finally, dividing both sides by 2, we get:

x = 22.5

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The expression that corresponds to the volume of the rectangular prism is "Yes."

Expression 1: Yes

Expression 2: No

Expression 3: Yes

Expression 4: No

Let's determine if each expression can be used to determine the volume of the rectangular prism with dimensions 4, 6, and 2.

Expression 1: 8 × 6

To calculate the volume, we need the product of the length, width, and height. The expression 8 × 6 matches these dimensions, so the answer is Yes.

Expression 2: (2 × 4) + 6

This expression does not involve all three dimensions of the rectangular prism. It only includes the length and width, but not the height. Therefore, it cannot be used to determine the volume. The answer is No.

Expression 3: 4 × (6 × 2)

This expression involves all three dimensions of the rectangular prism: length, width, and height. It is the correct formula for calculating the volume. The answer is Yes.

Expression 4: 2 × (4 + 6)

This expression does not include all three dimensions. It only includes the length and width, but not the height. Hence, it cannot be used to calculate the volume. The answer is No.

Therefore:

Expression 1: Yes

Expression 2: No

Expression 3: Yes

Expression 4: No

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The complete question:

Can the following expressions be used to determine the volume of the rectangular prism in cubic inches? Please select "Yes" or "No" for each expression:

Expression 1: 8 × 6

Expression 2: (2 × 4) + 6

Expression 3: 4 × (6 × 2)

Expression 4: 2 × (4 + 6)

The length, width, and height of the prism are 4, 6, and 2 respectively.

Factοring is the prοcess οf reversing the distributive prοperty sο that a pοlynοmial can be written as the prοduct οf simpler pοlynοmials is true.

Factοring is the prοcess οf finding the factοrs οf a pοlynοmial, that is, rewriting the pοlynοmial as the prοduct οf simpler pοlynοmials. The distributive prοperty is used in reverse during the factοring prοcess tο find the cοmmοn factοrs οf a pοlynοmial.

Fοr example, cοnsider the pοlynοmial expressiοn [tex]2x^2 + 6x[/tex]. We can factοr οut a cοmmοn factοr οf 2x tο get:

2x(x + 3)

This is the reverse οf the distributive prοperty, which is used tο expand expressiοns. In this case, we are taking the cοmmοn factοr 2x and distributing it tο each term οf the pοlynοmial tο write it as a prοduct οf simpler pοlynοmials.

Factοring is an impοrtant skill in algebra and calculus because it helps simplify expressiοns and sοlve equatiοns. It is alsο used in many οther areas οf mathematics and science, including number theοry, graph theοry, and physics.

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The volume V of the cylinder can be expressed as the polynomial function: V(x) = πx³ + 30πx² + 297πx + 972π

The formula for the volume of a cylinder is given by:

V = πr²h

where r is the radius and h is the height.

In this case, the radius is x+9 units, and the height is 3 units more than the radius, which means the height is (x+9)+3 = x+12 units.

Substituting these values into the formula, we get:

V = π(x+9)²(x+12)

Expanding the square, we get:

V = π(x² + 18x + 81)(x+12)

Multiplying out the brackets, we get:

V = π(x³ + 30x² + 297x + 972)

Therefore, the volume V of the cylinder can be expressed as the polynomial function:

V(x) = πx³ + 30πx² + 297πx + 972π

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Answer:

Shape  Area (units^2)

   A          20

   B            2

   C            4

   D            6

Total =      32

Step-by-step explanation:

See the attached worksheet.  These calculations assume that the "6" is the length of the line segment as marked.  Using the expressions for areas or traingles and rectangles, as noted, each area is calculated and the sum is 32 units^2.

2.62 seconds before the ball Martin threw hits the ground.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared component must be included. These are also known as quadratic equations.

Let t be the time in seconds

h(t) be he height of the ball, in feet

we have

h(t) = −16t² + 40t + 5

we know that

When the ball hits the ground, the height is equal to zero

so

−16t² + 40t + 5=0

The equation solving formula for a quadratic equation of the type

at²+bt+c=0

is equal to

t=(-b±√(b²-4ac))/2a

in this problem we have

−16t² + 40t + 5=0

so

a=-16

b=40

c=5

substitute in the formula:

t = (-40±√(40²-4×40×5))/2×-16

t = (-40±√(1600-800))/-32

t=2.62sec

therefore, 2.62 seconds before the ball Martin threw

hits the ground.

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The prοbability οf sοmeοne pulling 1-10 in cοnsecutive οrder frοm a bad that cοntains 10 balls labeled 1-10 is 1/3628800.

Prοbability is simply the pοssibility that sοmething will happen. Since we dοn't knοw hοw sοmething will turn οut, we can talk abοut the pοssibility οf οne οutcοme οr the likelihοοd οf several.

There are 10 balls in a bag with the numbers marked 1 thrοugh 10.

Nοw,

The ball with the number 1 οn it is picked in exactly 1 time

There are twο different ways tο pick the ball with the number 2.

Thus there is just οne pοssible technique tο chοοse a ball with a specific number.

There is nο lοnger a substitute.

Sο, when οne ball is taken, the tοtal number οf balls decreases by οne.

Then,

The prοbability οf selecting ball numbered 1= 1/10

The prοbability οf selecting ball numbered 2= 1/9

The prοbability οf selecting ball numbered 3= 1/8

That is dοne up tο last ball....

Last 1 is, the prοbability οf selecting ball numbered 10= 1/1

Tοtal prοbability οf chοοsing the balls in cοnsecutive οrder = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Hence, the prοbability οf sοmeοne pulling 1-10 in cοnsecutive οrder frοm a bad that cοntains 10 balls labeled 1-10 is 1/3628800.

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The cost for renting a car can be represented by the equation: c = a + bm

The cost of renting a car can be expressed as a function of the number of miles driven. This function is typically linear, with a fixed cost component and a variable cost component. The fixed cost component represents the cost of renting the car regardless of the number of miles driven, while the variable cost component represents the additional cost per mile driven.

The equation that represents the cost of renting a car is c = a + bm, where c represents the total cost of renting the car, m represents the number of miles driven, a represents the fixed cost component, and b represents the variable cost component.

The equation shows that the cost of renting a car is dependent on the number of miles driven. As the number of miles driven increases, the cost of renting the car also increases, reflecting the additional variable cost per mile. By knowing the values of a and b, we can estimate the total cost of renting the car for a given number of miles.

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It has been proven that the lines bc and ad are equal.

Given that the lines ac and bd bisect each other, we can prove that the lines bc and ad are equal.

Firstly, we need to calculate the length of each side of the figure and label them accordingly. Let’s assume that the length of ac is x and the length of bd is y.

We know that the two lines ac and bd bisect each other, so the midpoint of ac and bd must be the same point, which is point c. We can use the midpoint formula to calculate the distance between points a and c:

Midpoint of ac = (x/2, 0)

Similarly, we can calculate the midpoint of bd:

Midpoint of bd = (y/2, 0)

Since the midpoints of ac and bd are the same, we have:

(x/2, 0) = (y/2, 0)

Therefore, we can calculate that x = y. This means that the lengths of ac and bd are equal and so the lengths of bc and ad must also be equal.

Therefore, bc = ad.

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Lauri spent 4% of 800 hours at her part time job, which is about 32 hours. The property of equality was used to solve for x.

To estimate x, we can use the property of equality. This property states that if two equations are equal, then the two sides of the equation are equal. Therefore, if we know that 4% of x is about 32 hours, we can set up an equation and solve for x. The equation is 4% of x = 32 hours. We can convert 4% to a decimal by dividing 4 by 100, which gives us 0.04. This can then be rewritten as 0.04x = 32 hours. To solve for x, we can divide both sides by 0.04. This gives us x = 800 hours. This means that if Lauri spends 4% of x hours at her part time job, then x must be 800 hours.

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Points found on y = h(x) are (7, -6) and (-2,-1).

Using these two points, we will solve for the exact equation of y = h(x).

To solve the equation, we will get the slope (m) of the two points first using the following formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-1-(-6)}{-2-7} =\dfrac{5}{-9} =-\dfrac{5}{9}[/tex]

Now that we have a slope, we can now proceed in solving the equation using Point-Slope Formula.

 [tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-6)=-\dfrac{5}{9}(x-7)[/tex]

  [tex]y+6=-\dfrac{5}{9}(x-7)[/tex]

 [tex]9y+54=-5x+35[/tex]

 [tex]9y=-5x+35-54[/tex]

     [tex]9y=-5x-19[/tex]

     [tex]y=-\dfrac{5}{9}x-\dfrac{19}{9}[/tex]

Now that we have the equation of the dashed line, we will now solve for its inverse function y = h^-1 (x).

To solve for the inverse, we will reverse y and x with each other. The new equation will be:

[tex]x=-\dfrac{5}{9}y -\dfrac{19}{9}[/tex]

From that equation, we will now equate or isolate y.

[tex]x=-\dfrac{5}{9}y -\dfrac{19}{9}[/tex]

[tex]x=-\dfrac{5y-19}{9}[/tex]

[tex]9x=-5y-19[/tex]

[tex]5y=-9x-19[/tex]

[tex]y=-\dfrac{9}{5}x -\dfrac{19}{5}[/tex]

In this equation, our slope (m) here is -9/5 and our y-intercept is at (0, -19/5). The graph for this equation will look like this.

Drag the endpoints of the solid segment to the coordinates shown above to graph y = h^-1 (x).

Or drag the endpoints to (-6,7) and (-1,-2). It's the same graph anyway.

Yes, Enid is correct that the distance she jogs and the number of calories she burns are in a proportional relationship. This means that as the distance she jogs increases, the number of calories she burns also increases at a constant rate.

To see this proportional relationship, we can look at the data from her last four jogs on the treadmill. Let's say that the distance she jogged is represented by x and the number of calories she burned is represented by y.

If we divide the number of calories she burned (y) by the distance she jogged (x), we should get the same constant rate for each of her four jogs.

For example, if she jogged 2 miles and burned 200 calories, the constant rate would be 200/2 = 100. If she jogged 4 miles and burned 400 calories, the constant rate would also be 400/4 = 100.

This shows that there is a proportional relationship between the distance she jogs and the number of calories she burns on the treadmill. The constant rate in this case is 100, which means that for every 1 mile she jogs, she burns 100 calories.

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Hence, Option A is the set of values that will give PV the same value as the specified expression. N = 5, 1% = 0, PV =, PMT = 505, FV = 0, P/Y = 12, C/Y = 12, and PMT:END

Using the TVM Solver on a graphing calculator, we may identify the set of values that will give PV the same value as the supplied expression.

The sentence is as follows:

PV = ($505)((1+0.004)^0-1) / (0.004)(1+0.004)^60

If we condense this phrase, we get:

PV = -$23,724.59

Now, we can examine each set of data to determine which one yields the same PV value.

Option A: The PV is -$23,724.59 when N=5 and 1%-0.4 are used. The specified expression's value for PV is returned by this option.

Option B: The PV obtained by using N=60 and 1%-0.4 is -$153,167.63, which is not the same as the equation.

Option C: The PV obtained by using N=60 and 1%-4.8 is $18,981.10, which is not the same as the equation.

Option D: A PV of $590.68 is produced using N=5 and 1%=4.8, which differs from the stated expression.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

  about $10

Step-by-step explanation:

You want the difference in interest earned after 5 years between an account earning 4.3% compounded quarterly and one earning 4% compounded continuously when the investment in each is $590.

The account balance when interest is compounded quarterly for t years is ...

  A = P(1 +r/4)^(4t) . . . . . P is the principal invested at annual rate r

The account balance with interest is compounded continuously for t years is ...

  A = Pe^(rt)

The attached calculator screen shows the account balances for an investment of $590 for 5 years in accounts earning 4.3% compounded quarterly and 4% compounded continuously.

Scarlett's account, compounded quarterly, earns about $10 more interest over 5 years than does Ajay's account compounded continuously.

Answer:13

Step-by-step explanation:

Answer:

Gradient of the line segment:

The gradient of a line segment is given by the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

m = (3 - 4) / (8 - 6) = -1/2

Therefore, the gradient of the line segment is -1/2.

Midpoint of the line segment:

The midpoint of a line segment is given by the formula:

((x1 + x2) / 2, (y1 + y2) / 2)

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)

Therefore, the midpoint of the line segment is (7, 3.5).

Length of the line segment:

The length of a line segment is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

d = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(2^2 + (-1)^2) = sqrt(5)

Therefore, the length of the line segment is sqrt(5).

Answer:

To find the gradient of the line segment, we use the formula:

gradient = (change in y) / (change in x)

So, gradient = (3 - 4) / (8 - 6) = -1/2

To find the midpoint of the line segment, we use the formula:

midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

So, midpoint = ((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)

To find the length of the line segment, we use the distance formula:

length = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So, length = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(5)

Therefore, the gradient of the line segment is -1/2, the midpoint is (7, 3.5), and the length is sqrt(5).

The speed of the ball thrown from third base to first base is approximately 106.1 feet/second.

From the question, we are to calculate the speed of the ball

Assuming the ball traveled in a straight line from third base to first base, we can use the distance formula to find the distance the ball traveled and then use the formula for speed to find the speed of the ball.

The diagonal of the square infield can be found using the Pythagorean theorem:

Diagonal = sqrt(90² + 90²) = 127.28 feet

Therefore, the distance the ball traveled from third base to first base is approximately equal to the diagonal of the square, which is 127.28 feet.

To find the speed of the ball, we can use the formula:

Speed = Distance / Time

Plugging in the values, we get:

Speed = 127.28 feet / 1.2 seconds

= 106.06667 feet/second

≈ 106.1 feet/second

Hence, the speed of the ball is approximately 106.1 feet/second.

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The probability that Brian does not win as required is; -2 / (n - 2).

As evident from the task content; the probability that Brian wins a raffle is given by the expression;

n / (n + 2)

Hence, it can be inferred from convention that the probability that Brian does not win is given by;

P (not win) = 1 - n / (n - 2)

Hence, when expressed as a single fraction; we have that;

P (not win) = (n - 2 - n) / (n - 2)

P (not win) = -2 / (n - 2)

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Answer:

Max worked 15 hours while John worked 10 hours

The given sequence is not an arithmetic sequence. Option B is correct.

Given the sequence below

-2, -8, -32, -128

The nth term of an arithmetic sequence is given as Tn = a + (n-1)d

The common difference is the difference between the preceding and the succeeding term.

First term = -2

Second term = -8

Common difference = -8 -(-2) = -6

d= -32 + 8 = -24

Since the values are not equal, hence the sequence is not an arithmetic sequence.

Hence the common difference of the sequence is 8

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The missing term is:  [tex]\frac{4}{p}[/tex]

A solution of an equation is a value or set of values that, when substituted into the equation, makes it true. In other words, a solution is a value that satisfies the equation.

The given equation is, 4/p - 2/3q = ?-2p/3pq

or we can write as, [tex]\frac{4}{p} - \frac{2}{3q} = x - \frac{2p}{3pq}[/tex]

here find the missing term x in above equation.

Simplification,

[tex]\frac{4}{p} - \frac{2}{3q} + \frac{2p}{3pq} = x[/tex]

[tex]\frac{(4*3q)-2p}{3pq} + \frac{2p}{3pq} = x[/tex]

[tex]\frac{12q-2p}{3pq} + \frac{2p}{3pq} = x[/tex]

[tex]\frac{(12q-2p)+2p}{3pq} = x[/tex]

[tex]\frac{12q}{3pq} = x[/tex]

[tex]\frac{4}{p} = x[/tex]

Therefore, the missing term is:  [tex]\frac{4}{p}[/tex]

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