ax + b = 0 is the standard form of linear equation in one variable, but why is 0 given as the answer to the equation? Shouldn’t it be a constant there, one which is not 0? Please answer

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:

a. Goron 224

b. Smith 96

Fishman 256

Step-by-step explanation:

a. For Goron: 640 x 0.35 = 224

b. For Smith: 640 x 0.15 = 96

   For Fishman: 640 x 0.40 = 256

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°

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

Therefore, if the relationship between time and distance is proportional and the turtle swims 25 feet in 40 seconds, the table above shows the corresponding distances for other times.

A proportion is a statement that two ratios or fractions are equal. It is a way to express the relationship between two quantities that are proportional to each other. In other words, if we have two ratios that are equal, we can write them as a proportion. Proportions are used in a wide range of fields, including mathematics, science, finance, and engineering. They are often used to make predictions, estimate values, or analyze data.

Here,

To determine the missing values in the table, we can use the fact that the relationship between time and distance is proportional. We can set up a proportion using the initial values given:

25 feet / 40 seconds = d feet / t seconds

Simplifying the left-hand side, we get:

5/8 = d/t

5/8 * 20 = 12.5

Using this proportion, we can fill in the missing values in the table:

Time         Distance

(seconds)  (feet)

1                  5

12.5            10

30            187.5

40             25

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An assembly has 225 chairs in 15 rows and there are 15 chairs per row in the assembly.

To find the number of chairs per row in an assembly, we need to divide the total number of chairs by the number of rows.

Given that there are 225 chairs in 15 rows, we can find the number of chairs per row by dividing the total number of chairs by the number of rows:

225 chairs ÷ 15 rows = 15 chairs per rows

It's important to note that this assumes that each row has the same number of chairs. If the number of chairs per row varies, then the calculation would need to be adjusted accordingly.

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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.

(a) Total Number of Subsets of A:
In set theory, any set is a subset of itself. Additionally, the empty set is a subset of every set. As a result, there are 2^12 subsets of A.

Number of Subsets of A = 2^12 = 4096

(b) Number of Subsets of A having One or More Elements:
To find the number of subsets of A having one or more elements, we must subtract the empty set from the total number of subsets of A.
∴ Number of Subsets of A having One or More Elements = (2^12) − 1 = 4095

(c) Number of Subsets of A having Exactly One Element:
We can use the formula given below to compute the number of subsets of A having exactly one element. Here, n represents the number of elements in the set.

Formula: nC1 = n
∴ Number of Subsets of A having Exactly One Element = 12C1 = 12

(d) Number of Subsets of A having Two or More Elements:
Using parts (b) and (c), we can obtain the number of subsets of A having two or more elements by subtracting the number of subsets of A having exactly one element from the number of subsets of A having one or more elements.
∴ Number of Subsets of A having Two or More Elements = (2^12) − 1 − 12 = 4083.

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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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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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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

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:

1 2/5, 1 3/4, 1 7/10 from least to greatest is 1 2/5, 1 7/10, 1 3/4

This is because when you convert these fractions to decimals you get 1.4, 1.75, and 1.7. which can easily be organized

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 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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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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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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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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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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The appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

In a two-variable linear equation, x and y have a linear connection, meaning that the value of any one of the variables, y, relies upon that value of the other, x.

Cost for first mile of  taxi service  = $2.00

Additional cost = $1.20 per mile.

Peak distance = 25 miles.

a = number of miles traveled by taxi.

y = total cost of the taxi ride

The linear equation forms:

y = $1.20a + $2.00

When a = 0; y = $2.00

a = 25 ; y = $1.20*25 + $2.00 = 32

Thus, the appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

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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:

Answer:

circumference=50.24

Step-by-step explanation:

c=2x3.14xr

c=2x3.14x(8)

c=50.24

Answer:

36

Step-by-step explanation:

PxW=p

30x120=p

3600=p

x100%

$36=p

(overpriced ticket of you ask me lol)

Answer:

A. Less than

Step-by-step explanation:

The limit of the expression is 7.

The expression to find the limit is given by;Lim (6x + √36x² - x) x → -∞To solve this limit, we treat the expression as a fraction whose denominator is 1, and rationalize the numerator as follows;Lim (6x + √36x² - x) x → -∞Lim [{(6x + √36x² - x) × (6x - √36x² - x)} ÷ (6x - √36x² - x)] x → -∞Lim [(6x)² - (x)²] ÷ [(6x - x) - √36x²] x → -∞Lim (36x² - x²) ÷ 5x x → -∞Lim x² (36 - 1) ÷ 5x x → -∞Lim 35x ÷ 5 x → -∞7For a graph, we can plot the expression as follows;y = 6x + √36x² - xy = 6x - √36x² - xUsing the graphing utility, we can see that as x approaches negative infinity, y approaches 7, as we calculated above. Thus, the limit of the expression is 7.

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The phase angle, in degrees is -135.

A wave that repeats as a function of time and position is referred to as a periodic wave. Amplitude, frequency, wavelength, speed, and energy describe the properties of the wave. The phase angle is used to describe the characteristics of a periodic wave.

In phasors, a wave exhibits twofold characteristics: Magnitude and Phase. The phase angle refers to the angular component of a periodic wave.

The Phase Angle is one of the crucial characteristics of a periodic wave. It is similar to the phrase in many properties. The angular component periodic wave is known as the Phase Angle. It is a complex quantity measured by angular units like radians or degrees. A representation of any pure periodic wave is as follows.

A∠θ, where A is the magnitude and θ represents the Phase Angle of the wave.

A is the magnitude

θ is the phase angle

The expression is, which can be reduced to. Since angles are not unique, they can differ by multiples of 360, the answer is -135 degrees, which is in the range of -180 to 180 degrees.

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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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