Jerry, Jack and Sophie are all hoping to save​ money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with​ $125, and then save​ $50 each month. Jack was given​ $3520 from his​ Grandma, and decides to put the money
into an account that has a​ 6.5% interest rate that is compounded annually. Sophie has earned​ $3500 working at the movie theater decides to put her money in the bank in an account that has a​ 7.05% interest rate that is compounded continuously
Part 1​: Describe the type of equation that models​ Jerry’s situation. Create that equation of​ Jerry’s situation. Using the equation you​ created, how much money will be in​ Jerry’s account after 3​ years? 10​ years?
Think​: What do I know and what does it​ mean? What plan am I going to​ try?

PLEASE HELP!!!!!

Answer: To solve the equation 16=3x-7/2, you can follow these steps:

Multiply both sides of the equation by 2 to get rid of the fraction:

16 * 2 = (3x - 7/2) * 2

32 = 6x - 7

Add 7 to both sides of the equation to isolate the term with x:

32 + 7 = 6x

39 = 6x

Divide both sides of the equation by 6 to solve for x:

39 / 6 = x

6.5 = x

Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.

Step-by-step explanation:

Answer:

ㅤ

ㅤㅤ [tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{x = \dfrac{13}{2}}}}}}}[/tex]

ㅤ

Step-by-step explanation:

ㅤ

[tex]\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{39 = 6x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{\cancel{39}}{\cancel{6}} = x}}}}[/tex]

ㅤ

[tex]\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}[/tex]

ㅤ

━━━━━━━━━━━

ㅤ

[tex]\large{\underline{\underline{\sf{Verification:-}}}}[/tex]

ㅤ

• Substituting the value of (x) in the given equation,

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = 16}}}}[/tex]

ㅤ

As LHS = RHS,

Hence Verified

A zero balance in Armando's account can be achieved by subtracting $250 from the account balance. This can be done through a combination of withdrawals and/or transfers out of the account.

Subtracting is a mathematical operation that involves taking one number away from another. It is the inverse of addition, and is represented by the minus sign (-). Subtracting is used to determine the difference between two numbers, or to reduce a number by a given amount. In algebraic terms, subtracting is represented by the equation: a - b = c, where a is the starting number, b is the number to be subtracted, and c is the resulting difference. Subtracting can also be used on fractions, decimals, and other forms of numbers.

For example, Armando could make a $250 withdrawal from the account or transfer $250 to another bank account.

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It is important that our understanding and spreading of the gospel comes from the biblical text itself, and it is equal important that we continue to preach and defend the one true gospel. Jesus died and rose again for the forgiveness of our sins.

The word gospel occurs ninety-nine times in the NASB and ninety-two times in the NET Bible. In the Greek New Testament, the gospel is a translation of the Greek noun "good news" occurring 76 times and of the verb "to bring or announce good news" 54 times. Both words are derived from the noun angelos, "messenger". In classical Greek, euangelos is one who brings news of victory or other joyful political or personal news.

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The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:

P(x > 52) = 1 - P(x ≤ 52)

P(x ≤ 52) = (52 - 58) / 6 = -1

P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.

Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.

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The point-slope form of the line equation that passes through the points (- 9, - 9) and (- 8, 1) is equals to the y= 10x + 81.

The standard equation of a line is, y = mx + b where m is the slope and b is the y-intercept. This is a very useful form of the linear equation when comparing lines. We have to determine the equation of the line that passes through the points (- 9, - 9) and (- 8, 1). First we determine the value of slope of line. The formula for slope of line that passing through the points (x₁,y₁),(x₂,y₂) is [tex]m = \frac{y_2 - y_1}{x_2- x_1} [/tex]

here, x₁ = -9, y₁ = -9 , x₂ = -8, y₂ = 1, so

[tex]m = \frac{1-(-9)}{-8-(-9)} = \frac{10}{1} = 10[/tex]

The point-slope form for line passing through points (x₁,y₁),(x₂,y₂) is y − y₁ = m(x − x₁)

=> y - (-9) = 10( x -(-9))

=> y + 9 = 10( x + 9)

=> y + 9 = 10x + 90

=> y = 10x + 81

Hence required equation is y = 10x + 81.

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Answer: Infinitely many solutions

Step-by-step explanation:

On the graph I have attached, you can see the two lines overlap each other. This means the linear equations have an infinite amount of solutions.

To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Given that two random variables follow a normal distribution with mean 0 and variance 1.

Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)

Now, The expected value of the product of two random variables is given by;

E[XY] = E[X]E[Y] + Cov(X,Y)

Where E[X] and E[Y] are the means of the two random variables X and Y respectively.

Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;

Cov(X,Y) = E[XY] - E[X]E[Y]

Now, E[X] = E[Y] = 0 as both have a mean of 0.

Cov(X, Y) = E[XY] - E[X]E[Y]

⇒ E[XY] = the expected value of the product of X and Y.

As X and Y are independent, their covariance will be zero, which implies;

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.

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Answer:

A. Less than

Step-by-step explanation:

Answer: 3.2.1. Money, goods, services, and factors of production flow between Jacob's Pet Shop, consumers, and the government as follows:

Money flows from consumers to Jacob's Pet Shop when they purchase pet food and accessories, and from Jacob's Pet Shop to the government in the form of taxes.

Goods and services flow from Jacob's Pet Shop to consumers when they purchase pet food and accessories, and from the government to Jacob's Pet Shop in the form of contracts or grants for the delivery service.

Factors of production flow from Jacob's Pet Shop to the economy in the form of employment opportunities for the shop manager, shop assistants, and driver, and from the economy to Jacob's Pet Shop in the form of raw materials and supplies for the business.

3.2.2. The diagram below illustrates the flow of money, goods and services, and factors of production between Jacob's Pet Shop, consumers, and the government:

               +--------------------+

               |                    |

               |     Consumers      |

               |                    |

               +--------+-----------+

                        | Purchase pet food and accessories

               +--------v-----------+

               |                      |

               | Jacob's Pet Shop     |

               |                      |

               +-------+--------------+

                       | Sell pet food and accessories

                       |

             +---------v-----------+

             |                     |

             |      Government      |

             |                     |

             +---------------------+

3.3. Two features that a closed economy will prohibit are:

International trade: A closed economy does not engage in trade with other countries. All economic activity is confined within the borders of the country.

Movement of capital: A closed economy does not allow the free movement of capital, such as investments or loans, in and out of the country. All capital transactions are restricted within the economy.

was this worth 5 points no way.

Step-by-step explanation:

The shipping company will need 2,688 one cubic centimeter blocks to fill the box.

The volume of the box can be calculated as:

Volume = length x width x height

Volume = 14 cm x 12 cm x 16 cm

Volume = 2,688 cubic cm

Since each block is also one cubic cm in volume, we can simply divide the total volume of the box by the volume of one block to find the number of blocks needed to fill the box:

Number of blocks = Volume of box / Volume of one block

Number of blocks = 2,688 cubic cm / 1 cubic cm

Number of blocks = 2,688

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Therefore , the solution of the given problem of equation comes out to be B has a value of -6.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a distinct algorithm that divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.

Here,

The initial line can first be expressed in slope-intercept form as follows:

=> 3x + 6y = 18

=> 6y = -3x + 18

=> y = (-1/2)x + 3

Therefore, the initial line has a slope of -1/2. The negative reciprocal, or 2, is the inclination of the line that is perpendicular to it.

Now that we know the equation of the line parallel to the initial line and passing through the point (3, 0), we can use the point-slope form of a line to determine it:

=> y - 0 = 2(x - 3)

=> y = 2x - 6

So, through position (3, 0), y = 2x – 6 is true.

Y = mx + b, where m = 2 is the slope and b = -6 is the y-intercept, is the slope-intercept version of this equation.

B therefore has a value of -6.

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The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.

One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.

Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.

Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.

Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.

By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.

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Answer:

Step-by-step explanation:

you are going to give more info ?????

Answer:

perimeter=42

Area=90

Step-by-step explanation:

find the length of DEFG:

perimeter=a=b+a+b

28=10+b+10+b

28=20+2b

8=2b

4=b

finding the scale factor:

15/10=3/2

to find the perimeter of WXYZ:

the missing side:

=4x3/2

=6

perimeter=a+b+a+b

perimeter=15+6+15+6

perimeter=42

Area of WXYZ:

Area=bh

Area=15x6

Area=90

The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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Answer:

circumference=50.24

Step-by-step explanation:

c=2x3.14xr

c=2x3.14x(8)

c=50.24

X = -80538738812075974, Y = 80435758145817515,

and Z = 12602123297335631 are the values of  x,y,z of whole numbers.

What in mathematics is a whole number?

Complete numbers the sum of all natural numbers plus zero. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.

                            Natural numbers with a starting value of 1 and higher are considered whole numbers. Let's examine a few instances of entire numbers. The alphabet "W" stands for the collection of whole numbers. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}

x3+y3+z3=k, with k being all the numbers from one to 100

X = -80538738812075974,

Y = 80435758145817515,

and Z = 12602123297335631

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The line [tex]12x + 6y = 432[/tex] is represented by the red line, and the line equation [tex]9x + 3y = 270[/tex]is represented by the blue line. The point where these two lines intersect is (36,0).

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex]states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" [tex]x^2 + 2x - 3 = 0[/tex]," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.

To plot these lines on a graph, we first need to solve for y in terms of x for each equation.

can plot these lines

[tex]12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90[/tex]

[tex]|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300[/tex]

The line[tex]12x + 6y = 432[/tex]is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).

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Answer:

In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.

ASA Postulate:

ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.

SSS Postulate:

SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.

SAS Postulate:

SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.

Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.

Answer:

They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent

Step-by-step explanation:

and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

The expression for the marginal revenue function is MR(q) = 600r - 7.

The given product's revenue function is R(q) = - 7q + 600qr.

To find an expression for the marginal revenue function, we can use the following steps:

Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).

Step 2: Simplify the expression for MR(q) to record the final result.

In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.

So, we have to differentiate R(q) with respect to q to get MR(q).

The derivative of - 7q with respect to q is - 7.

The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.

MR(q) = dR(q) / dq

= (d/dq)(- 7q + 600r)

= (- 7) + (600r)

= 600r - 7

The equation that represents the marginal revenue function is MR(q) = 600r - 7.

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Answer:

36

Step-by-step explanation:

PxW=p

30x120=p

3600=p

x100%

$36=p

(overpriced ticket of you ask me lol)

Answer:

Step-by-step explanation:

Let's use the variable "s" to represent the number of slices in each pizza.

The drama club bought 999 large pizzas, and each pizza had s slices. So, the total number of pizza slices is given by the product of 999 and s, which can be written as:

999s = 727272

To solve for s, we can divide both sides of the equation by 999:

s = 727272/999

Using a calculator, we can simplify this fraction to:

s ≈ 728.73

Therefore, each pizza has approximately 728 slices. Note that this is an unusual number of slices for a pizza, so it's possible that the problem is not intended to be taken literally, but rather as a math puzzle or word problem.

Answer:

Each pizza has 729 slices.

Step-by-step explanation:

A. deposit $735.03 one year from now. B. $210.48 for each of the four years. C. choose the lump sum of $750 from your father. D. Interest rate of 7.4% compounded annually. E. Interest rate of 12%.

a. To have a balance of $1,000 four years from now, you need to calculate the present value of this amount. Using the compound interest formula, we can calculate that you need to deposit $735.03 one year from now to have a balance of $1,000 four years from now.

b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, you can use the annuity formula to calculate the required payments. The formula gives us a payment of $210.48 for each of the four years.

c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 one year from now, you can compare the present value of both options. The present value of the four payments of $210.48 each, using an 8% annual interest rate, is $682.96. Therefore, you would choose the lump sum of $750 from your father.

d. If you have only $750 one year from now, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 7.4% compounded annually.

e. If you can only deposit $186.29 each at Years 1 through 4, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 12% compounded annually.

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Complete question:

Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.

a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?

b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?

c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?

d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now? 7.4%

e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?

The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.

To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.

We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".

The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.

Differentiating both sides with respect to time, we get:

dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)

We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.

Substituting these values into the formula, we get:

dV/dt = 2π(150)(0.5) + π(150)^2(0)

dV/dt = 47123.74 cubic feet per minute

Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.

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Answer:

112°

Step-by-step explanation:

Finding the unknown angle in a quadrilateral:

        Sum of all angles of a quadrilateral = 360

                                      a + 49 + 72 + 127 = 360

                                                     a + 248  = 360

                                                                a = 360 - 248

                                                                a = 112°

Hence, 1) 6 cm (smallest value), 2) 6 cm, and 3)15.167 cm are the approximate dimensions which will result in a material with the biggest volume (largest value).

A 3D object's surface area is indeed the entire area that all of its faces cover. For instance, the surface area of a cube has been its surface area if we need to determine how much paint is needed to paint it. It's always calculated in square units.

Let the height be y as well as the side length of a square base be x. The rectangular solid's surface area is then determined by:

When we simplify this equation, we obtain:

The rectangular solid's volume is determined by:

V = x² × y = x² × (433.5 - 4x²) / (2x)

When we simplify this equation, we obtain:

V = 216.75x - 2x³

We must determine the value of x that maximizes V in order to determine the dimensions that lead to a solid with the maximum volume. Using V's derivative with x as the base, we can calculate:

dV/dx = 216.75 - 6x²

By setting this to 0 and figuring out x, we obtain:

216.75 - 6x² = 0

x² = 36.125

x ≈ 6.005

When we rewrite the equation for y using this value of x, we obtain:

y ≈ 15.167

Thus, the following dimensions will produce a solid with the largest volume:

1. 6 cm (smallest value)

2. 6 cm

3.15.167 cm (largest value)

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A statement which is true include the following: C. The functions have opposite slopes.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models one of the function is given by;

y = 4x

mx = 4x

Slope, m = 4.

For the other function, the slope can be calculated as follows;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(1 - 0)

Slope (m) = -4/1

Slope (m) = -4.

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