Use synthetic division to perform the division.
−8x^3+6x^2−9x+4 / x−2
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Part 1
−8x^3+6x^2−9x+4 / x−2=enter your response here
​(Simplify your​ answer.)

Yes, the logistic regression model is adequate to the response variable y. The parameter Beta 1 in this model measures the change in the log odds of the response variable when the independent variable (household income) increases by one unit. This is a measure of how the likelihood of home ownership changes in response to an increase in household income.

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The graphs of y = x and y = -1 are related to each other because they intersect at the point (-1, -1)

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

The standard equation of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Given the graphs of y = x and y = -1.

As we can see from the graphs, they intersect at the point (-1, -1)

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Considering  A, B, C, and D are colinear the length of line BC is 7cm.

In mathematics, a circle is a geometric shape that consists of all points that are the same distance from a fixed point called the center. This distance is called the radius of the circle. A circle is a two-dimensional object and is usually represented by a curved line, often drawn as a closed shape.

Since line DE is tangent to circle A at point E, we know that line AE is perpendicular to line DE. Therefore, we can use the Pythagorean theorem to find the length of AE:

AE² = AD²- DE²

Since A, B, C, and D are collinear, we can find AD by subtracting CD from BC:

AD = BC - CD

Substituting this into the equation above, we get:

AE² = (BC - CD)² - DE²

We are given that CD = 8cm and DE = 12cm, so we can substitute these values into the equation:

AE² = (BC - 8)² - 12²

We also know that AE = BE, since E is the point of tangency. Therefore, we can use the Pythagorean theorem again to find the length of BE:

BE² = AE² + AB²

Substituting AE^2 with the expression we found above, we get:

BE² = (BC - 8)² - 12² + AB²

Since A, B, C, and D are collinear, we know that AB + BC = CD = 8cm. Solving for AB, we get:

AB = 8 - B

Substituting this into the expression for BE², we get:

BE² = (BC - 8)² - 12² + (8 - BC)²

Simplifying this expression, we get:

BE^² = -16BC + 256

We want to find the value of BC, so we set BE equal to 12cm (since DE = 12cm):

12² = -16BC + 256

144 = -16BC + 256

-112 = -16BC

BC = 7 cm

Therefore,considering  A, B, C, and D are colinear the length of line BC is 7cm.

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Answer:

X = 1

Step-by-step explanation:

[tex]2x + 8 = 4x + 6 \\ collect \: the \: like \: terms \\ 8 - 6 = 4x - 2x \\ 2 = 2x \\ x = 1[/tex]

Answer:

x = 1

Step-by-step explanation:

first subtract 6 from both sides

2x + 8 = 4x + 6

     -6           -6

2x + 2 = 4x

Now get the variable on to one side by subtracting 2x from both sides

2x + 2 = 4x

-2x         -2x

2 = 2x

Now divide both sides by two to get the value of x

2 (÷ 2) = 2x (÷ 2)

1 = x

x = 1

to check your work, plug in one for x

2x + 8 = 4x + 6

2(1) + 8 = 4(1) + 6

2 + 8 = 4 + 6

10 = 10

this statement is true which means the solution is true

Hope this helps!

c) 2x^-3 + 5x^-1 - x

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, and raised to non-negative integer powers.

Answer:

Only the (a) and (c) can be classified as polynomials here.

Reason is that  a polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable. A polynomial can have one or more terms, where each term contains a product of a coefficient and a variable raised to a non-negative integer power. For example, 2x^3 + 5x^2 - 3x + 7 is a polynomial with four terms.

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https://en.wikipedia.org/wiki/Polynomial

The two positive, consecutive, even numbers are 12 and 14.

To find the two numbers, we need to use algebra to solve the equation given in the question.

Let x be the first even number and x + 2 be the second even number, since they are consecutive.

According to the question, the square of the sum of these two numbers exceeds the sum of their squares by 336. So we can write the equation as:

[tex](x + x + 2)^{2} - (x^2 + (x + 2)^2) = 336[/tex]

Simplifying the equation gives:

4x^2 + 8x + 4 - x^2 - x^2 - 4x - 4 = 336

2x^2 + 4x - 336 = 0

Dividing the equation by 2 gives:

x^2 + 2x - 168 = 0

Using the quadratic formula, we can find the value of x:

x = (-2 ± √(2^2 - 4(1)(-168)))/(2(1))

x = (-2 ± √676)/2

x = (-2 ± 26)/2

The two possible values of x are:

x = 12 or x = -14

Since we are looking for positive even numbers, we can disregard the negative value of x.

So the first even number is 12 and the second even number is 12 + 2 = 14.

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14. x = -1 or x = -7

17. x = 0, x = 3, x = -3

18. x = (-3 + 4√2)/2 or x = (-3 - 4√2)/2

The solutions and verification for the given equations are explained below:Solution 1:Given equation is x2 + 8x + 7 = 0.Let's solve the above equation by using the quadratic formula.The quadratic formula isx = [ -b ± sqrt(b2 - 4ac) ] / 2aIn the given equation, a = 1, b = 8, and c = 7x = [-8 ± sqrt(82 - 4(1)(7))] / 2*1x = [-8 ± sqrt(64 - 28)] / 2x = [-8 ± sqrt(36)] / 2Therefore, the solutions are x = -4 + 3 or -4 - 3i.e., x = -1 or x = -7Solution 2:Given equation is x3 – 9x = 0.The given equation can be rewritten as x(x2 - 9) = 0.We know that a * b = 0 if either a = 0 or b = 0.Using this concept, we can say that either x = 0 or x2 - 9 = 0Therefore, x2 = 9 => x = ± 3So the solutions for the given equation are x = 0, x = 3, x = -3Solution 3:Given equation is (x + 6)(x - 3) = 10.The given equation can be rewritten as x2 + 3x - 28 = 0.Let's solve the above equation by using the quadratic formula.The quadratic formula isx = [ -b ± sqrt(b2 - 4ac) ] / 2aIn the given equation, a = 1, b = 3, and c = -28x = [-3 ± sqrt(32)] / 2Therefore, the solutions are x = (-3 + 4√2)/2 or x = (-3 - 4√2)/2Solutions for the given equations are:x = -1, -7, 0, 3, -3, (-3 + 4√2)/2, (-3 - 4√2)/2.Verification:Let's verify the solutions of the given equations.Verification for x2 + 8x + 7 = 0When x = -1, -7, x2 + 8x + 7 = 0 satisfies.Verification for x3 – 9x = 0When x = 0, 3, -3, x3 – 9x = 0 satisfies.Verification for (x + 6)(x – 3) = 10When x = (-3 + 4√2)/2, (-3 - 4√2)/2, (x + 6)(x – 3) = 10 satisfies.

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a) The equation of the circle is x² + y² 169.

b) The coordinates of the other endpoint of the diameter are (-5, 12).

The equation of a circle is given by:

(x-a)² + (y-b)² = r²

Where (a, b) is the centre of the circle and r is the radius.

In this case, the centre of the circle is at (0, 0), so the equation of the circle simplifies to: x^2 + y^2 = r^2

To find the radius, we can use the distance formula between the centre and the point

P: r = √((5-0)^2 + (-12-0)²) = √(25 + 144) = √169 = 13

Therefore, the equation of the circle is: x² + y² = 13^2 or x² + y² = 169

To find the coordinates of the other endpoint of the diameter that passes through the point P, we can use the fact that the diameter is a straight line that passes through the centre of the circle. The slope of this line is: m = (-12-0)/(5-0) = -12/5

The equation of this line is: y = -12/5x

Since the other endpoint of the diameter also lies on the circle, we can substitute this equation into the equation of the circle: x² + (-12/5x)² = 169

Solving for x, we get: x = -5 or x = 5. Since the point P has an x-coordinate of 5, the other endpoint of the diameter must have an x-coordinate of -5.

Substituting this value of x back into the equation of the line, we get: y = -12/5(-5) = 12

Therefore, the coordinates of the other endpoint of the diameter are (-5, 12).

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The equipment will be worth approximately $3,145.73 after 7 years.

To find the value of the printing equipment after 7 years, we need to first determine the common ratio (r) of the geometric sequence.

We can do this by dividing any term by the preceding term. Let's divide the value in year 2 by the value in year 1:

r = 9,600/12,000 = 0.8

Now we can use the formula for a geometric sequence to find the value of the equipment after 7 years:

a₇ = a₁r⁶

where;

Plugging in the values we have:

a₇ = 12,000 x 0.8⁶

a₇ ≈ $3,145.73

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The expression b²/b⁻⁷ when simplified with a positive exponent only will become b⁹.

To simplify the expression b²/b⁻⁷, we can use the rules of exponents. The rules of exponents, also known as laws of exponents, are a set of mathematical rules that govern the manipulation of exponential expressions. These rules are essential in simplifying and solving various mathematical problems involving exponents.

Quotient rule of exponent states that when dividing two exponential expressions with the same base, we subtract their exponents, such that:

xᵃ / xᵇ = xᵃ⁻ᵇ.

In this case, we can simplify the expression b²/b⁻⁷ as follows:

b²/b⁻⁷ = b²⁻⁽⁻⁷⁾ = b⁹.

So, the simplified expression is b⁹. This answer is written with a positive exponent only, as requested.

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The amount in the second case is more. Then the better job is the second one.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

If he can make $2,000 worth of sales per week. Then the total amount in the first case is given as,

⇒ $31,200 + $2,000 x 0.09 x 52

⇒ $40,560

And the total amount in the second case is given as,

⇒ $26,000 + $2,000 x 0.15 x 52

⇒ $41,600

The amount in the second case is more. Then the better job is the second one.

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The ball traveled a horizontal distance of roughly 75.6*cos(theta) feet. Keep in mind that this is supposing a level, homogeneous surface and that the ball has no spin.

What is the equation?

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.

To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific program typically correspond. An illustration would be 2x - 4 = 2.

75.6 feet are equal to ymax = 472/(2*32.2) + 4.

As the ball's motion is symmetrical, the time it takes to reach its highest point is equal to half the length of its flight. As a result, the total flight time is:

[tex]\frac{Sin(\theta)}{g} = 247;[/tex]

[tex]t_{total} = 2[/tex];

[tex]t_{max} = 247[/tex]

[tex]\frac{cos(\theta)*y_{max}}{vi^{2}},\\[/tex]

where t max is the time needed to reach the highest point. Again, we cannot precisely solve for theta, but we may leverage the knowledge that the ball's horizontal travels as follows:

[tex]Vi \ \times cos(\theta)\times t_{total} = x.[/tex]

Hence, by entering the data we are aware of, we can determine x:

x = 47cos(θ) (θ)

75.6/47 = [tex]\frac{2y_{max}}{vi}[/tex]

= 47cos(θ)75.6cos (θ).

Hence, the ball traveled a horizontal distance of roughly 75.6*cos(θ) feet. Keep in mind that this is supposing a level, homogeneous surface and that the ball has no spin.

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So the values of a, h, and k in the vertex form of the parabola are a = 6/11, h = -1/2, and k = 3.

A parabola's vertex form is given by:

y = a(x - h)^2 + k

where an is a constant that governs the parabola's shape and (h, k) is the parabola's vertex.

The vertex is (-1/2, 3), and the directrix is x = -13/24, according to the information provided.

The value of a can be calculated using the common parabola formula:

4a = 1/ (distance from vertex to directrix) (distance from vertex to directrix)

4a = 1 / (|(-1/2) - (-13/24)|)

4a = 1 / (11/24)

4a = 24/11\sa = 6/11

The vertex form of the parabola can now be simplified by substituting the vertex and a values:

y = (6/11)(x + 1/2)^2 + 3

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Answer:

In the image

Hope this helps!

Step-by-step explanation:

Based on the given information, the equation that can be used to find the n^(th) term in the sequence, a_(n) is a_(n) = 18n + 6.

To find the equation for the sequence, we need to first determine the common difference between the terms. We can do this by subtracting a_(3) from a_(4), a_(4) from a_(5), and so on:

66 - 48 = 18
84 - 66 = 18
102 - 84 = 18
120 - 102 = 18

The common difference between the terms is 18. This means that the sequence is an arithmetic sequence with a common difference of 18.

Now, we can use the formula for the n^(th) term of an arithmetic sequence, which is:

a_(n) = a_(1) + (n - 1)d

Where a_(1) is the first term, n is the term number, and d is the common difference.

We can plug in the values we know into the formula:

a_(n) = a_(1) + (n - 1)18

We don't know the value of a_(1), but we can use one of the given terms to find it. For example, we can use a_(3) = 48:

48 = a_(1) + (3 - 1)18
48 = a_(1) + 36
a_(1) = 12

Now, we can plug in the value of a_(1) into the formula:

a_(n) = 12 + (n - 1)18

We can simplify the formula by distributing the 18:

a_(n) = 12 + 18n - 18

And then combining like terms:

a_(n) = 18n - 6

So, the equation for the n^(th) term of the sequence is a_(n) = 18n - 6.

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1. Independent Variable: Group (No News or watch news)

Dependent Variable: Depression Scores

2. Null Hypothesis: μ = 0

Alternative Hypothesis: μ < 0

3. Yes, you can reject the null hypothesis at a = 0.05 because there is a considerable difference in the depression ratings of the two groups

1. According to the information provided, the score for depression depends on whether a group watches the news or not.

Group is an independent variable (No News or watch news).

Depression scores are a dependent variable.

2. Null Hypothesis: The two groups do not differ in their depression levels, which is the null hypothesis.

Alternate Hypothesis: Those who don't read or watch the news will score less depressed than people who receive therapy as usual.

μ = 0 is the null hypothesis.

Between the two groups, there is no difference in depression scores.

Differential Hypothesis:  μ < 0

Those who don't read or watch the news will score less depressed than people who receive therapy as usual.

3. Due to the p-value of (0.024) < α(0.05) at α = 0.05, we can rule out the null hypothesis.

The rejection zone of the t-distribution with 12 degrees of freedom has the t-score of -2.58.

As a result, it is clear that there is a considerable difference in the depression ratings of the two groups, with the group that does not watch or read the news scoring significantly lower on the depression scale than the group that continues to get therapy as usual.

The proper response is "Yes".

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The complete question is:

Dr. Z is interested in discovering if there is a difference in depression scores between those who do not watch or read the news and those who continue with therapy as normal. She divides her clients with depression into 2 groups. She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 to continue with therapy as normal. The dataset score is a record of the results of the measure, administered after 2 weeks.

Independent Samples T-Test

                                   t                          df                          p

Score                      -2.580                    12                      0.024

1. Identify IV and DV.

2. State the null hypothesis and the directional (one-tailed) alternative hypothesis

3. Can you reject the null hypothesis at a = 0.05?

Answer:

0.07

Step-by-step explanation:

Percentages are on a scale of 1. 100% is 1, 1% is 0.01

we can convert percentage to decimal by moving the decimal point 2 places left.

Therfore, the answer is 0.07

Answer: y = -15/14x - 1/2

Step-by-step explanation:

Start:

15x + 14y = -7

Subtract 15x from each side:

14y = -15x - 7

Divide 14 on each side:

y = -15/14x - 1/2

If you want to simplify the slope, it would be:

y = -1 1/14x - 1/2

Hope this helps!

Answer:

To find how many more items the first plant produces daily than the second plant, we need to subtract the daily production levels of the two plants.

First plant: 5x + 11

Second plant: 2x - 3

Difference: (5x + 11) - (2x - 3)

= 5x + 11 - 2x + 3

= 3x + 14

Therefore, the first plant produces 3x + 14 more items daily than the second plant.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The statistical measures are:

Min: 2

Q1: 4

Med: 8

Q3: 13

Max: 15

The box and whiskers plot is attached.

Box and whiskers plot is a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value.

The lower and upper quartiles are shown as horizontal lines on either side of the rectangle.

The statistical measures are as follows:

The minimum value is the lowest number in the data set. Thus:

Min = 2

The lower quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order. That is:

2, 2, 3, 4, 5, 5, 8

Q1 = 4

The median is the value in the middle of an ordered set of

numbers.

2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15

Med = 8

The upper quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

10, 10, 11, 13, 15, 15, 15

Q3 = 13

The maximum value is the highest number in the data set. Thus:

Max = 15

Check the attached for image of the plot.

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Answer:

To find the total area of the figure, we need to find the area of each of the individual triangles and rectangles and then add them up.

The rectangle on the left has a length of 6 and a width of 3, so its area is 6 x 3 = 18 square units.

The triangle on the left has a base of 6 and a height of 5, so its area is 1/2 x 6 x 5 = 15 square units.

The triangle on the right has a base of 6 and a height of 3, so its area is 1/2 x 6 x 3 = 9 square units.

The rectangle on the right has a length of 3 and a width of 6, so its area is 3 x 6 = 18 square units.

Adding up the areas of each shape, we get:

18 + 15 + 9 + 18 = 60 square units

Therefore, the total area of the figure is 60 square units. Answer: (d) 60 units squared.

Answer:

Step-by-step explanation:

41+x=81

x=40

The rabbits score 40 points in the second half.

Answer:

55

Step-by-step explanation:

the total cost of the clarinet, including shipping and handling, is $600.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Jordan bought a clarinet priced at $517. Shipping and handling cost an additional 16% of the price.

The cost of shipping and handling is 16% of the price of the clarinet, which is:

0.16 * $517 = $82.72

the total cost of the clarinet including shipping and handling, we need to add the cost of the clarinet and the cost of shipping and handling:

Total cost = $517 + $82.72 = $599.72

Rounding this to the nearest dollar, we get:

Total cost = $600

Therefore, the total cost of the clarinet, including shipping and handling, is $600.

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The value of the Upper quartile is 12.5 for the set of data represented by the box and whisker plot.

When presented in increasing order, the value that 75% of data points fall within is known as the upper quartile, or third quartile (Q3). As the second quartile, the median is used (Q2). Interquartile range (IQR) refers to the space between the upper and lower quartiles.

Median, representing or having to do with a value or quantity that sits in the middle of a frequency distribution of observed values or quantities, with an equal chance of falling above or below it.

In box and whiskers plot, The upper quartile is the point at the right border of the box. In this case, that value is 12.5. It reflects the median of the data set's upper half.

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An expression to represent the total amount of juice left in the jar is "Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks"

First, let's start by labeling the quantities of juice we have. We have 0.85 liters of strawberry juice, 0.50 liters of mango juice, and 0.15 liters of watermelon juice. When we combine these three quantities, we get the total amount of juice in the jar before Celina drinks any of it. We can express this as:

Total amount of juice in jar before Celina drinks any = 0.85 + 0.50 + 0.15

Simplifying this expression, we get:

Total amount of juice in jar before Celina drinks any = 1.50 liters

Now, we know that Celina drinks 0.30 liters of the mixture. So, the total amount of juice left in the jar after she drinks some can be expressed as:

Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks

Substituting in our values, we get:

Total amount of juice left in jar = 1.50 - 0.30

Simplifying this expression, we get:

Total amount of juice left in jar = 1.20 liters

Therefore, the expression that represents the total amount of juice left in the jar after Celina drinks 0.30 liters of the mixture is:

Total amount of juice left in jar = 1.50 - 0.30 = 1.20 liters

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Complete Question:

A jar contains 0.85 liter of strawberry juice and 0.50 liter of mango juice. Celina poured 0.15 liter of watermelon juice into the jar. She then drank 0.30 liter of the mixture.

Part A: Write an expression to represent the total amount of juice left in the jar.

Answer:

4 to power of 3 in expanded form is 4 x 4 x 4.

HOPE THIS HELPS :)

The greatest number of 0.25 pounds hamburgers Sonia can make using the hamburger meat she has is 16.

What is Average total cost?

The average total cost is calculated by dividing the total cost of production by the total output.

To find the total amount of hamburger meat Sonia has, we need to add the weights of the two packages:

Total weight = 1.76 + 2.29 = 4.05 pounds

To find the greatest number of 0.25 pounds hamburgers that Sonia can make, we need to divide the total weight of hamburger meat by the weight of each hamburger:

Number of hamburgers = Total weight / Weight of each hamburger

Number of hamburgers = 4.05 / 0.25

Number of hamburgers = 16.2

Since Sonia cannot make a fraction of a hamburger, she can make a maximum of 16 hamburgers. Therefore, the greatest number of 0.25 pounds hamburgers Sonia can make using the hamburger meat she has is 16.

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The pair of equations is y = 25x + 8 and y = 12 + 5x where 'x' is the number of months and 'y' is the total cost.

A system of equations refers to a set of two or more equations that need to be solved simultaneously. The solution of a system of equations is a set of values that satisfy all the equations in the system.

To represent the following situations use variables like x, y, z.. etc. to represent the number of months and total cost and form the equations.

Here we have

An online video streaming service offers two plans for unlimited streaming.

Plan A has a one-time $8 membership fee and is $25 per month.  

Let Plan A run for 'x' number of months and 'y' be the total cost

Total cost for 'x' months, y = 25x + 8  

=> y = 25x + 8

Plan B has a $12 membership fee and is $5 per month.

Let Plan B run for 'x' number of months and 'y' be the total cost

Total cost for 'x' months, y = 12 + 5x

=> y = 12 + 5x

Therefore,

The pair of equations is y = 25x + 8 and y = 12 + 5x where 'x' is the number of months and 'y' is the total cost.

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Answer: 12 no caculator needed

Step-by-step explanation: