A rectangular vegetable garden will have a width that is 2 feet less than the length area of 48 square feet. If represents the length, then the length can be found by s equation:
x(x - 2) = 48
What is the length, x, of the garden?
The length is
feet.

The monthly payment of a 30-year amount $450,000 mortgage with an interest rate of 4.2% is $2,071.09.

P = 450000

r = 0.042

n = 30

M = 450000 * 0.042/12 * (1 + 0.042/12)^360 / (1 + 0.042/12)^360-1

M = $2,071.09

a) There are 26 letters in the English alphabet so the number of six-letter passwords that can be formed from letters in the English alphabet if a letter can only be used once is 26P_6 = 26!/(26 - 6)! = 26!/(20!) = 300,750,000

b) There are 10 digits (0,1,2,3,4,5,6,7,8,9) so the number of passwords that can be formed if the digits 0, 1, 2, ..., 9 can be used is 10P_6 = 10!/(10 - 6)! = 10!/(4!) = 5040.

The monthly payment of a 30-year amount $450,000 mortgage with an interest rate of 4.2% is $2,071.09. There are 300,750,000 six-letter passwords that can be formed from letters in the English alphabet if a letter can only be used once, and there are 5040 pass-words that can be formed if the digits 0, 1, 2, ..., 9 can be used.

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Answer:

2(n+17)/8 = 3/8

2(n+17)/8 × 8 = 3/8 ×8

2(n+17) = 3

2n +34 = 3

2n = -31

n = -15.5

Answer: Let's call the number of pages printed "x". After printing x pages, the total cost for the Hewlett-Packard printer will be:

$200 + $0.03 * x

And the total cost for the Brother printer will be:

$240 + $0.01 * x

We want to find the number of pages "x" such that the cost of the two printers is the same, i.e., when:

$200 + $0.03 * x = $240 + $0.01 * x

We can isolate x by subtracting $240 from both sides and subtracting $0.01 * x from both sides:

$200 - $240 + $0.03 * x - $0.01 * x = 0

$-40 + $0.02 * x = 0

$0.02 * x = 40

x = 2000

So, the number of pages that need to be printed for the cost of the two printers to be the same is 2000 pages.

Step-by-step explanation:

The medium size gets the most ice cream per dollar.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given three types of soft-serve ice cream,

A; small,

ice cream for $1.96 = 3 ounces

ice cream for $1 = 3/1.96 = 1.53 ounce per dollar

B; medium,

1 ounce of icecream cost = $0.64

ice cream for $1 = 1/0.64

ice cream for $1 = 1.5625 ounce per dollar

C: Large

ice cream for $6.85 = 10 ounces

ice cream for $1 = 10/6.85 = 1.459 ounce per dollar

Hence medium size gets the most ice cream per dollar.

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Answer:

120-x

Step-by-step explanation:

For me in class there were 6 parts to this problem and this problem is the same in my class so I will add all the answers

So for how many grams of 25% syrup it will be 120-x because the some amount + x = 120 grams of 15% syrup

so 120-x = the some amount of syrup.

This will be the answer for the problem you were asking for

If you have 6 parts keep scrolling since I will supply some more answers

Next part: How much pure sugar is in the 25% syrup?

For the amount of pure sugar there is in the 25% syrup

that will equal 0.25(120-x) = 30-0.25x

Next: How much sugar is in 120 grams of 15% sugar syrup?

10% of 120 is 12

5% = 12/2 = 6

12+6 = 18

Now the earlier stuff from the problem will come in handy

use the previous answers to write an equation

0.25(120-x)+0.10x=18

= 30-0.25x+0.10x=18

30 -0.15x=18

Now the final part to solve the equation and find the 10% solution and the 25% solution

-0.15x=18-30 = -12

-0.15x=-12

x= -12/-0.15

x=80

the problems not done yet though

we need to find the 25% solution

25% solution = 120-x and x = 80

120-80 = 40

The 10% solution is 80 grams and the 25% solution is 40 grams

The height of the right cone will be 9.86 units.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that the volume of the cone is 2325 cubic units and the radius of the cone is 15 units.

The height of the cone will be calculated as:-

Volume = 2325

(1/3)πr²h = 2325

( 1/3 ) x π x 15)² x h = 2325

h = ( 2325 x 3 ) / ( 15 x 15 x π )

h = 9.86 units

Therefore, the height of the right cone will be 9.86 units.

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The sum of the series b 2 b 4 b 6 b 8 b {10} is [tex]$\dfrac{180}{3}$[/tex] since it is a geometric series with a common ratio of [tex]$\dfrac{7}{4}$[/tex].

Since the given series [tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of[tex]$\dfrac{7}{4}$[/tex]. This means that the ratio of any two consecutive terms in the series is a constant, [tex]$\dfrac{7}{4}$[/tex]. Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:

[tex]$S = b2 + b4 + b6 + b8 + b_{10}$[/tex]

[tex]$= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$[/tex]

[tex]$= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$[/tex]

[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$[/tex]

[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$[/tex]

[tex]$= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

Since the sum of the series[tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] is 180, we can substitute $b2$ with [tex]$\dfrac{180}{3}$[/tex]nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:

[tex]$S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

[tex]$= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

Therefore, the sum of the series [tex]$b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$[/tex].

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The new set that follows has a mean that is 4 more than the mean of the previous set: (-2, -2, -2, -2, -2, -34).

A set is a graphical function of many object classes. One of the terms or elements that compose a set could include any kind of mathematical object. Symbols, digits, lines, other geometrical features, space-based points, variables, and even other quantities. In mathematics, a proposition is a structured set of components that can be written as a list or a hypothesis builder. To designate sets, curly brackets are usually applied. A = 1, 2, 3, and 4 is an illustration of a set. Basically, a set is an assortment of objects that are displayed together. A set's components or elements are the components that make up the set. Any object might make up a set's components, but for the purposes of the discussion,

given

Mean is the sum of all numbers divided by the amount of numbers. That means the sum of the first set would be 8*-2=-16.

With that in mind, you can simply have the first set be eight -2s (-2, -2, -2, -2, -2, -2, -2, -2).

Now we need to calculate the sum of the second set. This set has 9numbers, and the mean is 2. 9*2=18. To find the number to add to your set, take 48–63. Your set becomes (-2, -2, -2, -2, -2, -2, -2, -34).

The new set that follows has a mean that is 4 more than the mean of the previous set: (-2, -2, -2, -2, -2, -34).

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Yes, it's possible that the triangles are similar. With value of x is 6. Therefore, the side length Triangle ABC are 27,54 and 63. While Triangle DEF are 18,36 and 42.

A flat shape that has 3 angles is what we usually call a triangle. If there are 2 similar triangles, and an equation is made that will be able to express the ratio of the sides, then we will get a ratio of similar triangles. In simple terms, congruence is two shapes that have the same angles and side lengths. Congruence also has a special notation, namely ≈. To find this, a certain formula will be needed.

Based on the question above, we could find value of x:

with comparison

27/18= 9x/36

27 × 36 = 9x × 18

972=162x

x= 6

X is 6 so we can multiply the length that contain x with the value 6.

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Answer:

I believe the answer is A. true

Answer:

True

Step-by-step explanation:

Answer:

-8/-4

Step-by-step explanation:

-8/-4

The x cancel each other

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{3x^2 - 8x - 3}{2x^2 - 6x}}[/tex]

[tex]\large\text{We cannot do too much to this equation because we do not have any}\\\\\large\text{like terms. So we will solve it this way to make it easier to get to the}\\\\\large\text{answer.}[/tex]

[tex]\mathsf{= \dfrac{(3x + 1)(x - 3)}{2x(x - 3)}}[/tex]

[tex]\mathsf{= \dfrac{3x + 1 \ * \ x - 3}{2x \ * \ x - 3}}[/tex]

[tex]\large\text{Simplify it}[/tex]

[tex]\mathsf{= \dfrac{3x + 1}{2x}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{3x + 1}{2x}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

For b to be  in the plane spanned by a1 and a2, h= -17 .

What is plane?

In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.

A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.

A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.

Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0

Now,

y is a linear combination of a1 and a2 if it is in the plane, For the plane spanned by a1 and a2,

y = a a1 + b a2, a and b are constants here

[4,1,h] = a[1,4,-2] + b[-2,-3,7]

[4,1,h] = [a - 2b,4a -3b,-2a+ 7b] Vectors are equal if their components are equal by the rules of vector addition and multiplication.

4 = a - 2b

1 = 4a - 3b

h = -2a + 7b

solve for a and b from the two equations for h:

a = -2

b = -3

h = -17

We see that -2[1,4,-2] - 3[-2,-3,7] = [4,1,-17].

Hence,

             For b to be  in the plane spanned by a1 and a2, h= -17 .

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we can see that Rule 2 has a higher probability of accepting a shipment containing 20% defectives. Therefore, Rule 2 has a smaller probability of accepting a shipment containing 20% defectives.

To compare the probabilities of acceptance of a shipment containing 20% defectives for the two rules, we can calculate the probabilities for both rules and compare the results.

For Rule 1, the probability of accepting a shipment containing 20% defectives is given by the probability of having 0 defectives in a sample of 10 components. This can be calculated as

P(Accept | 20% defectives) = (0.8)¹⁰

= 0.107374

For Rule 2, the probability of accepting a shipment containing 20% defectives is given by the probability of having 0 or 1 defectives in a sample of 20 components. This can be calculated as:

P(Accept | 20% defectives) = (0.8)²⁰ + ²⁰C₁ * (0.8)¹⁹ * (0.2)

= 0.276

Comparing the two probabilities, we can see that Rule 2 has a higher probability of accepting a shipment containing 20% defectives. Therefore, Rule 2 has a smaller probability of accepting a shipment containing 20% defectives.

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For a variety of reasons, files on your computer shouldn't be destroyed. One, you might have to keep them since your work is crucial. Two, I should have them just in case.

A computers is a piece of electrical equipment used to manipulate data or information. It has the ability to store, retrieve, and process data.You may already be aware of the fact you are able to use a computers to surf the Internet, send emails, type documents, and play games.

Modern computers are given their names after the jobs that they replaced. The term "computer" was first used in the English language in the 17th century to refer to a person who performed mathematical computations. It made its first mention of a calculator in 1897. The "human" computer is now outdated in the age of the "machine."

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You need to order 2 36" bulbs and 4 24" bulbs in order to keep twenty of each size in stock.

The stock is a type of security that represents ownership in a company. It is a financial asset that can be traded, and the price of the stock is determined by the supply and demand of the market. When a company issues stock, the stockholders gain a share of the company’s ownership.

36" bulbs:

First storage closet: 5 boxes with 2 in each box = 10

Second storage closet: 3 boxes with 4 in each box = 12

Total = 10 + 12 = 22

Need to order = 20 - 22 = 2

24" bulbs:

First storage closet: 4 boxes with 4 in each box = 16

Total = 16

Need to order = 20 - 16 = 4  

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On solving the provided question, we cans ay that By unitary method 1 packs of gum = 17.52 /20 = $0.876 and  = 26.09/30 = $0.866

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

We have,

$17.52 for 20 packs of gum

$26.09 for 30 packs of gum​

By unitary method

$17.52 for = 20 packs of gum

1 packs of gum = 17.52 /20 = $0.876

$26.09 for 30 packs of gum​

1 pack = 26.09/30 = $0.866

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The image of the function f(x) is equal to g(x) = - (1 / 2) · f(x). (Correct choice: C)

In this problem we find a graphic representation of a function f(x) and its image g(x) on Cartesian plane. Let f(x) a representation of the original function and g(x) is the image of the former by means of rigid transformations.

First, write the original function:

f(x)

Second, use a reflection about the x-axis:

f(x) → - f(x)

Third, apply a dilation on previous step:

- f(x) → - (1 / 2) · f(x)

Fourth, write the resulting expression:

g(x) = - (1 / 2) · f(x)

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Answer:

d^3-2d^2-5d+6

Step-by-step explanation:

Step 1: (d-1)(d+2)=d^2+d-2

Step 2: (d-3)(d^2+d-2) = d^3+d^2-2d-3d^2-3d+6 = d^3-2d^2-5d+6

Answer: The product of the binomials (d-1)(d+2)(d+3) is [tex]d^3 + 4d^2 +d - 6[/tex].

Step-by-step explanation:

When multiplying the binomials, you can break it down and multiply two expressions first then multiply that last expression:

(d−1)(d+2)(d+3)

first: (d−1)(d+2)

when multiplying expressions you can multiply using the 'box method' where you would draw a box and put each part of the expression on the top and the left side of the box, multiplying each on into the box and adding like terms.

You can also multiply it by first taking the expression, (d−1)(d+2) and multiplying the variable 'd' to the (d + 2) and then multiplying the '-1' to the (d+2) and then adding like terms:

(d−1)(d+2)

[tex]d^{2} + 2d - d - 2[/tex]

'd' is the only like term in this expression so lets add 2d and -d together

[tex]d^{2} + d - 2[/tex]

finally, we need to multiply the (d + 3) to expression, [tex]d^{2} + d - 2[/tex]

We will treat this multiplying process the same as before.

[tex](d + 3)(d^{2} + d - 2)[/tex]

[tex]d^3 + d^2 -2d + 3d^2 + 3d - 6[/tex]

now lets add like terms

[tex]d^3 + 4d^2 +d - 6[/tex]

So the product of the binomials (d-1)(d+2)(d+3) is [tex]d^3 + 4d^2 +d - 6[/tex].

Using the law of Sine, the value of y becomes 1.6 units.

Correct option: B

Rule of Sines The sine law, sine formula, sine rule, or law of sines is an equation in trigonometry that connects the lengths of any triangle's sides to the sines of its angles. The ratio of a triangle's sides and angles may be calculated using the sine rule.

The formula: a/sinA = b/sinB = c/sinC

It may be used to describe the sine rule. Here, the triangle's angles are A, B, and C, while its sides' lengths are denoted by the letters a, b, and c.

The sine rule:

a/Sin A = b/Sin B = c / Sin C = 2R

Given, a = 2 and b = y

∠A = 75° and ∠B = 50°

by sine rule:

⇒ 2/ Sin 75° = y/ Sin 50°

⇒ 2 × Sin 50° = y × Sin 75°

⇒ y = 1.586 ≈ 1.6 units

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a is smaller than 0.

on the natural numbers scale on the left side of value 0 are negative numbers.

Answer:

anything under 0 such as -1 -2 -3 -4 and anything below so you write any number below 0

Answer:

y=-2/5x

Step-by-step explanation:

The slope-intercept form of a linear function is y = mx +b, where m is the slope and b is the y-intercept.

Currently, 2x + 5y = 0 is in standard form and we can convert it to slope intercept form by simply isolating y (put the equation in terms of y):

[tex](2x+5y=0)-2x\\(5y=-2x)/5\\y=-2/5x[/tex]

Answer:

∠ B = 23°

Step-by-step explanation:

vertical angles are congruent , then

∠ B = ∠ A , that is

5x - 17 = x + 15 ( subtract x from both sides )

4x - 17 = 15 ( add 17 to both sides )

4x = 32 ( divide both sides by 4 )

x = 8

Then

∠ B = 5x - 17 = 5(8) - 17 = 40 - 17 = 23°

Answer:

1.8

3 percent of 60 is 1.8

Here's how I will do it:

1. Recite the Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]

2. Substitute the variables of a and b, so the equation will look like this [tex]3^{2} +6^{2} =c^{2}[/tex] now.  

3. Simplify the equation which gives you, [tex]9+36=c^{2}[/tex]. Simplifying more would give you [tex]45=c^{2}[/tex].

4. Solve for the c value :

[tex]c=\sqrt{45}[/tex]
Plug this into a calculator and it will give you 6.70820....
Rounding to the nearest tenth will give you, about 6.7.

The length of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem: c^2 = a^2 + b^2.

Given that a = 3 meters and b = 6 meters, we can substitute those values into the equation:

c^2 = 3^2 + 6^2

c^2 = 9 + 36

c^2 = 45

c = sqrt(45)

c = 6.7 meters

Rounding to the nearest tenth, c = 6.7 meters becomes c = 6.7 meters.

The balance account is prepared in accordance with the provided statement, and both the liabilities and assets total 2800000.

A balance sheet provides you with a quick overview of ones company's financial standing at any particular moment. A balance sheet, along with a revenue statement as well as a cash-flow statement, can aid business leaders in assessing the financial health of their organisation.

Computation of Current assets and Current Liabilities

Current Ratio  (CR) = Current Assets (CA)/ Current Liabilities (CL)  = 2.5

So, CA= 2.5 CL

Current Assets (C.A) - Current Liabilities (C.L) now equals Rs. 60000 as working capital.

Therefore, CA - CL = 60000 0

     2.5 CL-CL = 600000

     1.5 CL = 600000

        CL = 600000/1.5

     C.L = Rs.40000 0

C.A. now equals 2.5 x 400000, or Rs. 1000,000.

Computation of stock

Liquid ratio   = Liquid  assets/Current  liabilities

Or, 1.5 = (Current Assets - Stock )/400000

Or, 1.5  = (10,00, 000 - Stock)/4,00,000

1.5 *400000 = 1000000-Stock

600000 = 1000000- Stock

Therefore, stock = 100000-600000 = 400000

Computation of Proprietary fund; Fixed assets; Capital and Sundry payables (creditors)

Proprietors Fund divided by Permanent Assets equals Proprietors Fund.

Permanent assets therefore equal 0.75 proprietary fund, and

Net working capital  =  0.25 Proprietary fund

Therefore Proprietary fund = 600000/0.25

Proprietary fund = 24,00,0000 and  Fixed assets = 0.75 proprietary fund

= 0.75 of  24,00,000

Therefore, Fixed Assets = 18,00,000

Equity Capital = Proprietary fund - Reserves & Surplus

Therefore, Equity Capital = 2400000-400000

Equity Capital = 20,00,000

Variable payables (creditors) = (Current liabilities - Bank overdraft)

= (400000 - 100000) = 300000

Sundry payables = 300000

Net Current Assets =  (Current Assets - Stock) = 1000000-400000 = 600000

                                            Balance Sheet

Liabilities                      Amt in INR                         Assets              Amt in INR

Equity Capital               2000000                          Fixed Assets      1800000

Reserves & surplus          400000                        Stock                   400000

Bank Overdraft                  100000                  Net Current Assets  600000

Sundry Payable                 300000

________________________________________________________

                                         2800000                                                2800000

________________________________________________________

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In 2011 cattle prices remain relatively stable, total expenses increase slightly, and cattle income increase significantly. Therefore, option A is the correct answer.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

In the graph we can see in 2011 total expenses increase slightly, and cattle income increase significantly.

Therefore, option A is the correct answer.

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Answer:

C. Monthly

Step-by-step explanation:

If a business uses a monthly accounting period, it would prepare a post-closing trial balance once a month, at the end of the accounting period. Therefore, the correct answer is option C, monthly.

A post-closing trial balance is a list of all the accounts and their balances after adjusting entries have been made and closing entries have been posted to the general ledger. It is used to verify that the debits and credits are equal and that all temporary accounts have been closed out. The post-closing trial balance is prepared after the closing entries have been made at the end of the accounting period. For a business that uses a monthly accounting period, this would typically be done once a month, at the end of each month.

The equation of a line perpendicular to line y = 1/5x-2 in slope-intercept form that contains point (-3, 1) is y = -5x - 14.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided, an equation of the first line WX is given by;

y = x/5 - 2

Therefore, slope (m) = 1/5

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/5 × m₂ = -1

m₂ = -5.

At point (-3, 1), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

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

y - 1 = -5(x + 3)

y = -5x - 15 + 1

y = -5x - 14

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