Understand the Pythagorean

The given lines represented by 2x + 3y - 9 = 0 and 4X + 6y - 18 = 0 will have an infinite number of solutions so the lines are coincident lines.

2x + 3y - 9 = 0

4x + 6y - 18 = 0

We need to find the representation of lines.

Here the equation form is

a₁+ b₁ + c₁ = 0

Comparing a, b and c

a₁/a₂ = 2/4 = 1/2

b₁/b₂ = 3/6 = 1/ 2

c₁/c₂ = (-9) /(- 18) = 1/ 2

so

a₁/a₂ = b₁/b₂ = c₁/c₂

Hence this will have an infinite number of solutions so the lines are

coincident lines.

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The time required for the second lap so that the overall average speed will be 2 miles per minute is 0.6 minutes.

Speed is the distance traveled in a certain unit of time. Speed can be calculated by dividing the distance by time:

Speed = distance / time

Given information:

Distance = 2 miles

Time spent for the first track (time₁) = 2 minutes

Speed for the first lap (speed₁) = 1 mile per minute

Overall speed ([tex]speed_{t}[/tex]) = 2 miles per minute

[tex]speed_{t}[/tex] = (speed₁ + speed₂) / 2

      2 = (1 + speed₂) / 2

2 * 2 = 1 + speed₂

      4 = 1 + (distance₂ / time₂)

       4 = 1 + (2 / time₂)

       3 = 2 / time₂

time₂ = 2 / 3 ≈ 0.6 minutes

Thus, the time required for the second lap so that the overall average speed will be 2 miles per minute is 0.6 minutes.

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(10 × 4) + (11 × 4)

(10 × 4) + 44 or 40 + (11 × 4)

The output values of the function are (a) 7, (b) -6 and (d) 10

From the question, we have the following parameters that can be used in our computation:

(4,7),

(−3,8),

(11,14),

(12,−6),

(1,10)

The domain is the set of the x values

So, we have the following representation

x = {4, -3, 11, 12, 1}

Remove repeated entries

x = {4, -3, 11, 12, 1}

The range is the set of the output values

So, we have

Range = {7, 8, 14, -6, 10}

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The diameter of the sphere tank is 27.2 ft.  

Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object.

The capacity of a sphere is defined as its volume or the area that the sphere occupies. Cubic units are used to measure a sphere's volume.

The formula for the Volume of a sphere is given by

Here we have

A spherical water tank holds 10,500 ft³ of water.  

Here capacity of the sphere = Volume of the sphere  

As we know the volume of the sphere = 4/3 πr³  

=> 4/3 πr³ = 10500

=> πr³ = 10500(3/4)

=> (22/7)r³ = 7875

=> 22r³ = 7875(7)    

=>  r³ = 55125/22  

=>  r³ = 2505

=> r = 13.6  (Approx)  

As we know diameter = 2 × Radius

=> Diameter of sphere = 2(13.6) = 27.2 ft

Therefore,

The diameter of the sphere tank is 27.2 ft.  

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Answer: The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

Hoped This Helped!

When you solve an equation for one variable and then substitute the resulting expression in for that variable in the other equation This is known as the  substitution method.

Describe the substitution formula?

In algebra, substitution refers to replacing the variables' (expression's) letters with their corresponding numerical values. The expression's overall value can then be calculated.

What is substitution in math definition?

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As implied by the name, this strategy involves replacing a variable's value from one equation with another.

                            A technique for resolving systems of equations that entails figuring out the answer for one variable before locating the other. When a teacher offers a table containing example sentences and a variety of options for students to choose from using a predetermined pattern, that table is known as a substitution table.

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The required standard deviation as calculated from the data given above is found out to be as , 2.1 answer.

As given in the question , S = x + y ,

here , x = the variance of Randi and let y be the variance of Leah.

Therefore ,

σ total² = σ²randi + σ²leah

= 1.1² + 1.8²  

=4.45

Hence , σ total = √4.45 = 2.1.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is known as the square root of the variance of the given population. It is algebraically simpler, though in practice less robust, than the average absolute deviation.

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Answer:

7.31 × [tex]10^{-2}[/tex]

Step-by-step explanation:

a number expressed in scientific notation has the form

a × [tex]10^{n}[/tex]

where 1 ≤ a < 10 and n is an integer

the only one fitting this description is

7.31 × [tex]10^{-2}[/tex]

The number indicated on the number line is -0.896

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

Each spacing = 0.0005

Exact middle between -0.895 and -0.896 is -0.8955

But, there is a slight more distance

So, it is -0.8956

Rounded to 3 decimal places -0.896 ( Because 6 at last is > 5, add 1 to 5)

The number indicated on the number line is -0.896

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To distribute 33 treat to her 6 dogs Ariana has 1947792  ways

Since the order of distribution doesn't matter we will apply concepts of combination.

combination = nCr =n!/(r!(n-r!)

where n is the total number of objects

r is the number of chosen objects from the total.

Here, 33C6 =36!/6!.30!

= 36x35x34x33x32x31/6x5x4x3x2

1947792

Therefore, Ariana can distribute 33 treats between her 6 dogs in 1947792 ways.

Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!

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There exist 155 retail stores there were in 2003.

We can solve one-step equations in four different ways: by adding, subtracting, multiplying, and dividing. Both sides of an equation will stay equal if we add the same amount to each side.

y=11x+12

Substituting the equation,

2003-1990=13

13×11=143

Simplifying

y=143+12

We get

155=143+12

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The fractions which is greater than   [tex]\frac{2}{4}[/tex]  , but denominator of 6 are [tex]\frac{4}{6} ,\frac{5}{6},\frac{6}{6}[/tex] .

What is fraction?

The fraction contains both numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator. The numerator indicated the parts which is taken from whole portion.

Here Amount of Juice in Pedro glass is [tex]\frac{2}{4}[/tex]

So, [tex]\frac{2}{4} = \frac{1}{2}[/tex]

Now, we want fraction which is greater than  [tex]\frac{2}{4}[/tex]  , but denominator of 6.

So ,the fraction having denominator 6 are,

[tex]\frac{1}{6},\frac{2}{6},\frac{3}{6} = \frac{1}{2} , \frac{4}{6} ,\frac{5}{6},\frac{6}{6}[/tex]

Hence the fractions which is greater than   [tex]\frac{2}{4}[/tex]  , but denominator of 6 are [tex]\frac{4}{6} ,\frac{5}{6},\frac{6}{6}[/tex] .

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The other equations in the system are:

y = (-1/6)x  + 3

y = (1/2)x  - 1

The value of x is 18.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation

We have,

The solution to the system of equations is (6, 2).

Now,

y = (-1/6)x  + 3

2 = (-1/6) x 6 + 3

2 = -1 + 3

2 = 2

This is true.

y = (1/2)x  - 1

2 = (1/2) x 6 - 1

2 = 3 - 1

2 = 2

This is true,

Now,

(1/2)x - 7 = 1/3 (x - 12)

(1/2)x - 7 = (1/3)x - 4

(1/2)x - (1/3)x = -4 + 7

(3 - 2)x / 6 = 3

(1/6)x = 3

x = 3 x 6

x = 18

Thus,

The other equations are:

y = (-1/6)x  + 3

y = (1/2)x  - 1

The value of x is 18.

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1.  Other equations of the system are y = (-1/6)x + 3 and y = (1/2)x - 1

2. Solution of the equation  is x = 18.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = .Learn more about equation here:

Given,

1. Solution of the system of equation = (6 , 2)

To be the equation of the system, solution should satisfy the equations,

A) y = -3x

Putting value x = 6 , y = 2

2 = -3(6)

2 ≠ 18

LHS ≠ RHS

This equation is not in the system.

B) y = -3/2 x + 6

Putting value x = 6 , y = 2

2 = (-3/2)6 + 6

2 = -9 + 6

2 ≠ -3

LHS ≠ RHS

This equation is not in the system.

C)y = (-1/6)x + 3

Putting value x = 6 , y = 22 = (-1/6)6 + 3

2 = -1 + 3

2 = 2

LHS = RHS

This equation is in the system.

D) y = (2/3)x -1

Putting value x = 6 , y = 2

2 = (2/3)6 - 1

2 = 4 - 1

2 ≠ 3

LHS ≠ RHS

This equation is not in the system.

E) y = (1/2)x - 1

Putting value x = 6 , y = 2

2 = (1/2)6 -1

2 = 3 - 1

2 = 2

LHS = RHS

This equation is in the system.

F) y = 4x - 2

Putting value x = 6 , y = 2

2 = 4(6) - 2

2 = 24 - 2

2 ≠ 22

LHS ≠ RHS

This equation is not in the system.

2. (1/2)x - 7 = 1/3(x - 12)

Using distributive property

(1/2)x - 7 = (1/3)x - 4

Moving like terms to same side

(1/2)x - (1/3)x = 7 - 4

Simplifying

(3x - 2x)/6 = 3

x = 3 × 6

x = 18

Hence,

1. y = (-1/6)x + 3 and y = (1/2)x - 1 are the the other equations of the system.

2. x = 18 is Solution of the equation.

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Using elimination method, the solution of the system of equation 3x + 5y = -2, -x + 2y = 8 is x = -4 and y = 2.

System of equation can be solved using different method such as graphical method, elimination method and substitution method.

Let's solve the system of equation by elimination method.

3x + 5y = -2

-x + 2y = 8

multiply equation(ii) by 3

3x + 5y = -2

-3x + 6y = 24

add the equation

11y = 22

divide both side of the equation by 11

y = 22 / 11

y = 2

Let's find the value of x.

-x = 8 - 2y

-x = 8 - 2(2)

-x = 8 - 4

-x = 4

x = -4

Therefore,

x = -4 and y = 2.

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a. Is there a real number x such that x^2 = -1?

b. Does there exist x such that x^2 = -1?

A variable in mathematics is an alphabet or phrase that stands for an unknown amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilized. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

According to the mathematical operation, the variable is a quantity that can change or is not fixed. Typically, in algebra, we use the terms "x" and "y" to express an unknown integer. However, this is not unique, and we are free to employ any alphabet.

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After 222.5 days, only 0.25 mg amount of the original 3.00 mg sample of Iron-59 will remain due to its 44.5 day half-life.

1. Calculate the number of half-lives in 222.5 days: 222.5 days / 44.5 days = 5 half-lives

2. Calculate the amount of Iron-59 left after 5 half-lives: 3.00 mg x (1/2)^5 = 0.25 mg

Iron-59 has a half-life of 44.5 days. A half-life is the time it takes for half of a given amount to decay. After a single half-life, half of the original amount will have decayed. After two half-lives, three-fourths of the original amount will have decayed, and so on.

In this case, we are given a 3.00 mg sample of Iron-59 that we need to determine how much of it will remain after 222.5 days. To do this, we first need to calculate the number of half-lives in 222.5 days. We can do this by dividing 222.5 days by 44.5 days, which gives us 5 half-lives.

Next, we need to calculate the amount of Iron-59 left after 5 half-lives. We can do this by taking the original amount (3.00 mg) and multiplying it by (1/2)^5, which gives us 0.25 mg. Therefore, after 222.5 days, only 0.25 mg of the original 3.00 mg sample of Iron-59 will remain.

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Answer:

lower option

Step-by-step explanation:

As time passes (as x increases) the sunfish's mass grows exponentially, meaning that its growth each 5 weeks increases rather than staying constant, as a linear function would.

Thus, the lower option is the correct one, as the line's growth is exponential, rather than linear, as the top one is.

The value of the function f(8) would be equal to -239

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We are given that the function is

f(x)= -3x² - 6x + 1

Therefore, we have;

-3(8) ²-6(8)+1

-19²-48+1

-240+1

=-239

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The complete question is;

F(x)=−3x ² −6x+1 Find f(8)

The word problem is "In a restaurant, the constant fee for a table is $ 16 and every food item costs $ 8 if a family wants to spend only $ 75 how many items they can order?"

and the inequality 8x + 16 ≤ 75.  

Inequality simply means that two things aren't equal. One of the items might be lower too, greater than, or equivalent to the other things.

Signs that can be used in Inequalities are

≠  means not equal  

<  means less than

>  means greater than

≤  means less than or equal

≥  means greater than or equal

Here we need to create a word problem that can lead to Writing an inequality in the form of Ax + B ≤ C.

The word problem can be written as follows

In a restaurant, the constant fee for a table is $ 16 and every food item costs $ 8 if a family wants to spend only $ 75 how many items they can order?

And the problem can be solved as follows

Let the family order x items

Then the amount can be spent by the family = 8x + 16

As we said the family wants to spend only $ 75

=> 8x + 16 must be less than $ 75

The inequality that can be represented is 8x + 16 ≤ 75  

Therefore,

The word problem is "In a restaurant, the constant fee for a table is $ 16 and every food item costs $ 8 if a family wants to spend only $ 75 how many items they can order?"

and the inequality 8x + 16 ≤ 75.  

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The inequalities whose symbol will be reversed are -4.5c > 9 and -21/5 ≤ -5/2d

A relationship between two expressions or values that are not equal to each other is called inequality.

Given are given some inequality,

We know that, when anytime you are multiplying or dividing an inequality by a negative, you must reverse the inequality symbol

-4.5c > 9 will have its inequality symbol reversed

-21/5 ≤ -5/2d will have its inequality symbol reversed

Hence, the correct options are -4.5c > 9 and -21/5 ≤ -5/2d

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Yes, a parabola can be represented as a function in the form of y = ax^2 + bx + c, where a, b, and c are constants. It is a quadratic function, and it is a type of a conic section.

Parabolas are commonly used in mathematics, particularly in the fields of algebra, calculus, and physics. They are used to model a wide range of phenomena, such as the trajectory of a projectile, the shape of a parabolic antenna, and the path of light through a lens. Parabolas also have many applications in engineering, such as the design of parabolic mirrors and the optimization of parabolic troughs for solar energy collection. They are also used to find the vertex of a parabola and the focus point.

The difficulty of working with parabolas depends on the specific context and the mathematical skills of the person using them. Understanding the basic properties of parabolas and how to graph them is a fundamental concept in algebra and is typically taught in high school. Solving problems involving parabolas can range from relatively simple, such as finding the vertex or axis of symmetry, to more advanced, such as optimization or intersection with other functions.

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Answer:

A. [tex]6x+2[/tex]

Step-by-step explanation:

Combine like terms.

[tex]8x-5-2x+7=6x+2[/tex]

Answer:

A. 6*+2 tell if correct.

you need simplify so you do (8*-5) +(-2*+7) = 6*+2.

Answer:

106 bucks

Step-by-step explanation:

Answer:

x = - 1/6c + 1/6k

Step-by-step explanation:

...........

Answer:

1. The two turkeys that had to be excluded weighed less than 25 pounds and more than 40 pounds. So the combined weight of the two turkeys would be 25 + 40 = 65 pounds.

2. The largest turkey exceeded the maximum weight of 40 pounds by 40 - 33 = 7 pounds.

3. Of the six turkeys Zara was permitted to sell, the combined weight of the turkey that weighed the least and the turkey that weighed the most would be 25 + 40 = 65 pounds.

The coordinates of F' would be (2, 4). This is because F was translated 6 units to the left and 3 units up. To calculate the coordinates of F', you must subtract 6 from the x-coordinate of F and add 3 to the y-coordinate of F. Therefore, if F was (8, 1), then F' would be (2, 4).

F = (8, 1)

F' = (8 - 6, 1 + 3)

F' = (2, 4)

The coordinates of F' can be found by translating F 6 units to the left and 3 units up. To calculate the coordinates of F', you must subtract 6 from the x-coordinate of F and add 3 to the y-coordinate of F. For example, if F is located at (8, 1), the coordinates of F' would be (2, 4). This is because 8 - 6 = 2 and 1 + 3 = 4. Therefore, translating F 6 units to the left and 3 units up would result in the coordinates of F' being (2, 4). This principle applies to any initial coordinates, so you can use this method to calculate the coordinates of F' for any starting point.

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Answer: We can start by using the proportion method to find the number of girls in the class.

If the ratio of girls to total students is 4:7, that means for every 4 girls, there are 7 students in total. We can set up a proportion:

4/x = 7/21

where x is the number of girls in the class.

To solve for x, we can cross-multiply and get:

4* 21 = 7* x

84 = 7x

Dividing both sides by 7 gives:

x = 12

So there are 12 girls in the class.

Step-by-step explanation:

Answer: you didn’t even say please

explanation: why don’t you ask your mother you make me sad