In the diagram below, the horizontal lines are parallel. Find the value of x.

The value of k is 0, as the equations will have the same solution regardless of the value of k.

What is equation?

An equation is a mathematical statement that expresses the equality of two expressions. It consists of variables, constants, and operators that represent a relationship between the two expressions. Equations can be used to solve for unknown values, and to express relationships between different variables. Equations are a key component of mathematics, and are used to describe physical phenomena, and to analyze and predict the behavior of systems.

The value of k for which the equations do not have a unique solution is when the equations are dependent, which occurs when the equations are multiples of each other. For example, if the two equations are 2x + 6y = 10 and 4x + 12y = 20, then the equations are dependent because they are multiples of each other. In this case, the value of k is 0, as the equations will have the same solution regardless of the value of k.

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Complete question:

For what value of k do the equations not have a unique solution?

The value of k = 9 for which the equations not have a unique solution.

A mathematical statement that expresses two expressions' equality is known as an equation. Its components—variables, constants, and operators—represent the relationship between the two expressions. Equations can be used to express relationships between various variables and to solve for unknown values. Equations are a fundamental part of mathematics and are used to explain physical phenomena as well as to examine and forecast system behaviour.

When the equations are dependent, as they are when they are multiples of each other, the value of k for which the equations do not have a single solution is called the value of k. When two equations are multiples of one another, as they are when 2x + 6y = 10 and 4x + 12y = 20, for instance, they are said to be dependent.

The slopes should be equal

Or

a/d = b/e

Apply the condition in the given equations

In the question given above, a = 3, b = 4, d = k and e = 12.

Therefore, 3k = 412

We find that for 'k' should be equal to 9 for the system of linear equations to NOT have a unique solution.

When k = 9, the system of equations will represent a pair of parallel lines (their y-intercepts are different). Meaning, there will be NO solution to this system of linear equations in two variables.

Thus, the correct answer is a) 9.

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Complete question:

For what values of 'k' do the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?

a. 9

b. 12

c. 3

d. 7.5

e. 2.5

After simplify the algebraic fraction whose numerator is 21n and who’s denominator is 3n, we get the value which is 7.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Algebraic fraction:

= 21n/3n

= 21/3   [as n is common in both numerator and denominator]

= 7   [21 is divisible by 3]

So, after simplification the value becomes 7

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To graph a vertical inequality, plot the boundary line of the inequality using a solid line. Any points that are above the line represent the solution set for the inequality. To graph a horizontal inequality, plot the boundary line of the inequality using a dashed line.

A vertical inequality is graphed by plotting the boundary line of the inequality on a coordinate plane using a solid line. Points that are above the line represent the set of values that satisfy the inequality. A horizontal inequality is graphed by plotting the boundary line of the inequality on a coordinate plane using a dashed line. Points that are below the line represent the set of values that satisfy the inequality. When graphing inequalities, it is important to remember that the boundary line is not part of the solution set. Additionally, the line should be drawn in such a way that all points that satisfy the inequality are included in the solution set. By following these simple steps, one can easily graph a vertical or horizontal inequality.

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The time that it took Evan to mow the front yard was 26 .25 minutes.

Assuming that x is the time it took Evan to mow the front yard, the formula would be:

x + 1.4x = 63 minutes

This is because we know that Evan mowed the front and back yards in 63 minutes.

The minutes it took Evan to mow the front yard is therefore:

x + 1.4x = 63 minutes

2 .4x = 63

x = 63 / 2. 4

x = 26. 25 minutes

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The question is:

Evan mowed the front and back yards at his grandmother's house. He finished mowing both yards in 63 minutes. Evan mowed the back yard for 1.4 times as many minutes as he mowed the front yard.

How long did he take to mow the front yard ?

The required number of pieces Demarco does to the rest of the fabric is 4.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

here,
Demarco has a piece of frabric 6yd long. He uses a piece 3yd long.
Piece left = 6 - 3 = 3yd

Now, he cuts the rest into 3/4 long.
= length of rest piece/length of each piece
= 3 / [3/4]
= 4 pieces

Thus, the required number of pieces Demarco does to the rest of the fabric is 4.

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The distance covered by Vlad is (7m + 10) miles

To calculate the total distance find the distance that is individually covered each day of the week. From that find the sum of all the distances to find the distance covered in a week.  

Here we have

The track at the park is a loop that covers a distance of m miles.  

Given that, Vlad jogged 2 loops each on Tuesday and Thursday and 3 loops on Saturday. On Sunday, Vlad jogged 10 miles.    

The distance covered on Tuesday and Thursday = (2 + 2) = 4m miles

The distance covered on Saturday = 3m miles

The distance covered on Sunday = 10 miles

From the above information,

The distance covered by Vlad = (4m + 3m) miles + 10 mile

= (7m + 10) miles

Therefore,

The distance covered by Vlad is (7m + 10) miles

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Gentiana has $12 left to spend on the pizza pie as of the equation model.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,

Let the amount spend on pizza pie be x,
According to the question,
40 = 10 + 25% of 40 + 20% of 40 + x

40 = 10 + 40 × 0.25 + 40 × 0.20 + x
40 = 10 + 10 + 8 + x
x = 40 - 28
x = 12

Thus, Gentiana has $12 left to spend on the pizza pie as of the situation model.

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From the formula or linear equation y = 7 - 9x, when x=0, y = 7.

An equation is said to be linear if the highest power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

given that y = 7 - 9x

The value of y when x=0, putting x=0 in this equation, we get

y = 7 - 9*0

y = 7 - 0

y = 7

So that the value of y = 7, when x = 0.

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Charles has 66 blue marbles

The ratio of red to blue marbles is 4 to 3, which means for every 4 red marbles, there are 3 blue marbles.

We know Charles has 88 red marbles. To find the number of blue marbles, we can use the proportion:

(Number of red marbles) / (Number of blue marbles) = (4) / (3)

Since we know the number of red marbles and the ratio, we can solve for the number of blue marbles by multiplying both sides of the equation by the number of blue marbles:

88 / (Number of blue marbles) = 4/3

To find the number of blue marbles, we can cross-multiply and divide:

Number of blue marbles = 88 * 3/4 = 66

I hope this helps :)

The hex representation of −5.375 is 0xB3F8.

The 16-bit FP number representation of −5. 375 has a 1-bit sign, 4-bit biased exponent, and 11-bit fraction, where bias offset = 7. The sign bit is 1, which indicates a negative number.

The biased exponent is obtained by subtracting the bias offset from the actual exponent. For -5.375, the actual exponent is -3. Subtracting the bias offset of 7 from -3 gives the biased exponent of 4, which is represented in 4 bits as 0100.

The fraction is obtained from the mantissa, which is the significant digits after the decimal point. For -5.375, the mantissa is 0.375. This can be represented in 11 bits as 1111 000 00, which gives the hex representation of 0xB3F8.

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Your formula would be A/B if you were comparing data points A and B. This implies that you are dividing Information A by Information B.

The ratio formula is used to compare the connection between two numbers or quantities.

The ratio is defined as the comparison of the amounts of two or more objects, and it shows how much of one object is present in the other.

A ratio between two quantities, let's assume a and b, is represented generally as

a : b

where,

If a = Antecedent, b = Consequence,

In the sections below, we'll go over the ratio formula in more detail.

Example :

A line is drawn connecting points A, B, C, and D in the manner AB = 2BC = CD.

The ratio of BD to AD is thus

BD / AD = BC + CD / AB + BC + CD

= BC + 2BC / 2BC + BC + 2BC

= CD = 2BC and also AB = 2BC

=3BC / 5.BC

= 3/5  after division.

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The three different ways are:

The greatest common divisor (GCD) of 3 and 4 is 1, which can be expressed as a linear combination of 3 and 4 in multiple ways. The above expressions are three examples of how 1 can be represented as a linear combination of 3 and 4.

The greatest common divisor (GCD) is the largest positive integer that divides two or more integers without leaving a remainder.The GCD of two or more integers can be found using various algorithms, such as the Euclidean algorithm, the binary GCD algorithm, and the extended Euclidean algorithm.

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Answer:

c. help each other

Step-by-step explanation:

I hope this helps

Answer: 56

Step-by-step explanation:

The sampling method described below appears to be flawed because it is a voluntary response sample.

Survey sampling, as used in statistics, is the process of choosing a sample of constituents from a target population to perform a survey. The word "survey" can be used to describe a wide range of observational methods or procedures. Most frequently, a questionnaire meant to assess people's traits and/or opinions is employed in survey sampling. The topic of survey data collecting is various methods of contacting sample participants after they have been chosen. Sampling is done to cut down on the expense and/or labor required to survey the complete target population.

Voluntary response sample: The researcher asks members of a population to participate; participants can choose whether or not to participate.

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Therefore ,solution of unitary method is she can only obtain one piece of 18 foot board since she needs one that is 18 feet long.

The amount of a tiny subset that exists must be calculated before multiplying that amount by two in order to complete a task utilizing the unitary variable approach. In order to isolate a standard programming value from a given set, the unit technique is used, to put it simply. For instance, the price of 40 pens is 400 rupees ($1.01), or Rs. It's feasible that the strategy used to achieve this will be controlled by just one nation. Almost every creature has a unique quality. It has the same capacities for reciprocity and integration (mathematics, algebra).

Here,

A wood board belongs to Lucy.

The board measures 34 feet long.

She intends to divide it into 18-foot chunks.

Let x denote the maximum number of wood boards that can be cut.

The formula 34 / 18 will indicate how many pieces will be cut.

=> 34/18

=> 1.888

x = 1.888

She can only obtain one piece of 18 foot board since she needs one that is 18 feet long.

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In the exponential function y = 61 (0.95)^t, the change represents a decay.

The percentage of decay rate is 5%.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The given exponential function is -

y = 61 (0.95)^t

Here, it can be seen that there is a decay rate as the base value 0.95<1.

The percentage rate of decrease is 1-0.95.

Find the percentage decay rate as -

= 1 - 0.95

= 0.05

Convert it into percentage -

= 0.05 × 100

= 5 %

Therefore, the exponential function is a decay function with 5% decay rate.

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The minimum Nyquist sample rate for representing the typical human hearing range is 44.1 kHz.

The human hearing range is typically considered to be between 20 Hz and 20 kHz. In order to accurately reproduce sounds in this frequency range, a sample rate of at least twice the highest frequency of the range must be used. This means that a sample rate of at least 44.1 kHz is necessary for accurately representing the typical human hearing range.

In digital audio, the Nyquist-Shannon sampling theorem states that a sample rate of at least twice the highest frequency of the signal being captured must be used in order to accurately reproduce the signal.

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When we divide 3 / 4 by 1 / 2 we get 3 / 2.

The given number to be divided is 3 / 4.

The given divisor is 1 / 2.

When we divide 3 / 4 by 1 / 2, we are supposed to multiply 3 / 4 by the reciprocal of 1 / 2 which is 2 / 1.

When we multiply 3 / 4 by 2 / 1  we get 3 / 2 as the final answer.

Thus, When we divide the given number 3 / 4 by 1 / 2 which is the given divisor we get 3 / 2 as the final answer.

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In the direct variation equation y = kx, k represents the proportionality constant. Similar to this, in the inverse variation equation y = kx, k is the constant of variation.

A ratio called a constant of variation (k) shows how the independent variable (x) and the dependent variable are related to one another (y). If both of those variables have known values, you can find it by dividing y by x.

In order to obtain k given any position, we must divide the y-coordinate by the x-coordinate because k is constant (the same for every point). For instance, the variation constant is k = 3 if y changes straight as x and y = 6 when x = 2.

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Therefore , the solution of the given problem of equation comes out to be 8 as it will make equation true.

When the equal letter (=) is used to indicate equality, a math equation like a formula connecting the two claims. Algebraic equations are statements of fact that show the equivalence of many mathematical variables. For instance, the values doc d + 6 or 12 are separated by an equal sign in the formula data logger + 6 = 12. How many syllables each side of each letter corresponds to can be expressed quantitatively. The message of a symbol frequently contradicts itself.

Here,

the formula 4x + 8 = 4x +?

Let's first make the expression simpler.

4x from each side is subtracted.

4x + 8 - 4x = 4x - 4x + ?

8 = ?

From the outcome, we must figure out the undetermined value for any x values that are not 8.

In this scenario, the unknown value can be any other value other than 8.

The needed value for the variable with all values of x must be 8.

There won't be a number after 4x for just single value of x because this is an impossibility.

Therefore , the solution of the given problem of equation comes out to be 8 as it will make equation true.

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Answer:

Atheism

Step-by-step explanation:

Former atheist myself. That was an interesting phase.

Answer:

37.5%

Step-by-step explanation:

Keep the base constant and multiply the exponents when increasing a base with a power to another power.

The quantity of times a number has been multiplied by itself is known as an exponent. To the third, for instance, is expressed as 23, which signifies that 2 x 2 x 2 = 8. 2 x 3 = 6 and 23 are not equivalent. Don't forget that a number raised to the power of one equals that number. Exponent is the process of representing huge numbers as powers, according to the definition. Accordingly, the exponent describes the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6 6 6 6. 64 can be used to represent this.

given

as in: 81 Equals 8. By include exponents, a product of powers with similar bases (the same base number) can be made simpler.

Exponents must be added when multiplying numbers with the same base. Exponents laws. Keep the base constant when multiplying like bases and add the exponents.

When dividing using like bases, keep the base constant and deduct the exponents of the numerator and denominator.

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The value of f(x) = 3x-5 is -20

Now, According to the question:

f(x) means that x is put into the variable on the right.

f(-5) means that -5 is put into the variable on the right.

So you put a -5 in where you see an x on the right.

f(-5) = 3 × (-5) - 5

f(-5) = -15 - 5

f(-5) = -20

Hence, The value of f(x) = 3x-5 is -20.

The given question is incomplete, complete question is:

If f(x) = 3x - 5, then what is the value of f(-5)?

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3x2=6 3x1=3 6x - 3x = 3x

Hey there!

Answer:

The product would be [tex]6x^2-3x[/tex]

_________________________

Apply the distributed law [tex]a(b-c)=ab-ac[/tex].

[tex]3x(2x-1)=3x*2x-3x*1[/tex]

Simplify [tex]3x*2x-3x*1[/tex].

[tex]6x^2-3x[/tex] ← Hence, our solution.

__________________________

Hope this helps!

The number of times a number is multiplied by itself is referred to as its exponent. Exponent qualities include Product of Powers and Power to a Power.

The seven exponent properties are as follows in algebra :

1. Product of powers rule.

2. The power quotient governs.

3. The rule of a power.

4. The rule of product power.

5. The effectiveness of a quotient rule.

6. The rule of zero power.

7. The rule of the negative exponent.

For instance, 2 to the third (written as 2³) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 2³. Keep in mind that a number raised to the power of one is itself.

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the answers are, (11m)^2- (5m)^2 & solution: 96m^2.

A square root of a number is a value that, when multiplied by itself, gives the number.

here, we have,

given that,

121m^2 - 25m^2

Now,

expressing, as difference of two squares,

we get,

(11m)^2- (5m)^2

Again, we get,

(11m+5m) * (11m-5m)

=16m*6m

=96m^2

Hence, the answers are, (11m)^2- (5m)^2 & solution: 96m^2.

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