Determine if the sequence below is arithmetic
or geometric and determine the common
difference / ratio in simplest form.
2, 7, 12, ...

Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method. Substitute the solution back into one of the original equations and solve for the third variable.

In order to solve systems of equations in three variables, known as three-by-three systems, the primary goal is to eliminate one variable at a time to achieve back-substitution. A solution to a system of three equations in three variables (x,y,z)  is called an ordered triple.

To find a solution, we can perform the following operations:

Graphically, the ordered triple defines the point that is the intersection of three planes in space. You can visualize such an intersection by imagining any corner in a rectangular room. A corner is defined by three planes: two adjoining walls and the floor (or ceiling). Any point where two walls and the floor meet represents the intersection of three planes.

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The complete table is given and rate of change is 1 per 28 pair of jeans.

How quickly something evolves over time is referred to as its rate of change (ROC).

Given, of the 84 pair of jeans only 3 are defected.

And rate of change is constant.

And 1 defected pair of jeans is 84 /3 = 28.

That means,

total number of jeans = n x 28

Where n is the number of defected pair of jeans.

So, for n = 3,6,8,12,15

Then, number of jeans =84, 168, 224, 336, 420.              

The table is given in the image.

The basic formula for the rate of change is:

Rate of change = (Change in quantity 1) / (Change in quantity 2)

In every 28 pair of jeans there is one defected jeans.

Therefore, the complete table is given and rate of change is 1 per 28 pair of jeans.              

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Answer:

r = 6 feet

Step-by-step explanation:

Ler r represents the radius

Hence perimeter = edge speed times 3second

2 times 3.14 times r = 12.56 times 3

r = 6 feet

According to the distribution , The general formula for the variance varies, For the discrete and continuous probability distribution, The expected values formula varies. The variance is given by   [tex]E(X^2)-(E(X))^2[/tex] .

The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

If distribution is discrete  , E(X) = x*P(x).

If distribution is continuous , E(x) = x *f(x).

Variance = [tex]E(X^2)-(E(X))^2[/tex]

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It is a quadratic equation, indeed.  7x =2x²

A quadratic equation is any equation of the form where x is a variable, b, and c are any real values, and a 0.

As is common knowledge, the formula for the quadratic equation's roots is the discriminant formula

By replacing, we can create the following equation given the information in the question:7x =2x²

2x^2-7x=0

This is a quadratic equation because, as we can see, x has a power of two.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

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Answer:

To find a, you'll put the value 8.3 as x in the equation to get the value of y which is equal to a. For the second point you'll put -10.2 as the value of y in the equation to get x which is equivalent to b.

Step-by-step explanation:

every point represents an ordered pair of (x, y) values.

if the point is on the given line (or any other form of curve/ function), then these x and y values make the functional equation true. if the equation turns out to be false with these values, then the point is not on that functional curve.

so, we need to find a and b to make the equations true.

(8.3, a)

3×8.3 - 4a + 24 = 0

24.9 + 24 = 4a

48.9 = 4a

a = 48.9/4 = 12.225

(b, -10.2)

3b - 4×-10.2 + 24 = 0

3b + 40.8 + 24 = 0

3b + 64.8 = 0

3b = -64.8

b = -64.8/3 = -21.6

Answer:

15 ft

Step-by-step explanation:

The amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.

The amount of water an Olympic-sized pool can hold is, 660,000 gallons.

The pool is 63% full at the moment

The of water in the pool now is:66% of  660,000 gallons

If the pool is 90% full then the amount of water in the pool is:

90% of 660,000 = 594,000 gallons

The amount of water added by the pool maintenance is:

Amount of water added = 90% of 660,000 - 63% of 660,000

594,000 - 415,800

= 178200                                  

Thus, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.

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Answer:

£135

Step-by-step explanation:

70% of £450

=£315

£450-£315=135

The triangles are congruent if two angles and the excluded side of one triangle match equivalent areas in another triangle, it is known as the AAS similarity theorem.

Angle-Angle-Side is abbreviated as AAS.

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

AAS congruence can be demonstrated with a few simple methods.

If and only if the corresponding sides and angles are in proportion, two triangles are said to be comparable.

Similar to how there are particular ways to demonstrate triangle congruence (SSS, ASA, SAS, AAS, and HL), there are particular ways to demonstrate triangle similarity.

Therefore, the triangles are congruent if two angles and the excluded side of one triangle match equivalent areas in another triangle, it is known as the AAS similarity theorem.

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Answer:

D. y = 2

Step-by-step explanation:

It can't be A because this is the equation for the slope is undefined.

It can't be B because this equation has no y-intercept!

It can't be C because the equation is y=mx + b. And we see that this equation has a slope of 2, so it is wrong.

So, the answer is D

Line MN is the side in between the 2 angles which are ∠LMN and ∠LNM in triangle △LMN.

An edge is a specific kind of line segment that connects two vertices of a polygon, polyhedron, or higher-dimensional polytope in geometry.

An edge, also known as a polygon side, is a line segment that forms the boundary of a polygon.

The sides of the angle are the two straight lines that unite to make it.

The intersection of two lines or rays that make an angle is known as its vertex.

So, according to the given figure, the side between ∠LMN and ∠LNM in triangle △LMN is side MN.

Therefore, line MN is the side in between the 2 angles which are ∠LMN and ∠LNM in triangle △LMN.

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The answers for the given proof of a parallelogram are explained below:

A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it. In contrast, a quadrilateral with just one set of parallel sides is referred to as a trapezoid or trapezium in British or American English. A parallelepiped is the parallelogram's three-dimensional counterpart.

1) CPCTC(corresponding parts of congruent triangles are congruent)

2) Reflexive property

3) Corresponding angles theorem converse(If corresponding angles are equal then the lines are parallel)

4) Alternative angles theorem converse(If alternative angles are congruent then the lines are parallel)

5) SSS

6) Given.

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The adjusted trial balance for revenue in the accounting worksheet is 20,000.

Trial balance in the accounting worksheet is a financial report where the credit entries and debit entries are listed which is used to audit the accounting system of business or organization internally. It is used to confirm that the sum of all credits and debits must be equal.

Here we have the credit of 15,000 for revenues.

Then the trial balance is adjusted with a credit of 5000.

If we have two debits or credits, we will add them.

So the adjusted trial balance = 15,000 + 5,000 = 20,000

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The term (7 + 3x) is a factor of the quadratic equation 3x² + 7x  .

A number is called a factor of the quadratic equation if that number satisfies the equation .

the term is given as : 7 + 3x ,

solving it we get ; 3x = - 7

So , x = -7/3 .

to check whether it is a factor , we substitute the value of x in the equation ,

we get , 3x² + 7x

= 3(-7/3)² + 7(-7/3)

= 49/3 - 49/3

= 0

Therefore , Yes , (7 + 3x) is the factor of 3x² + 7x  .

The given question is incomplete , the complete question is

Is (7 + 3x) is a factor of the quadratic equation 3x² + 7x  ?

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The effect of good debt to ones credit score is that is would increase it. That is option B.

A credit score is defined as the expression that can be used to show a customer's worth regarding the payment of their debts.

A customer's credit score can be rated as follows:

A good debt is the ability of a customer to quickly pay off their debt which has been noted as one of the qualities that raise their credit score.

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Answer:

[tex]a=1, h=-5, k=-24[/tex]

Step-by-step explanation:

[tex]f(x)=x^2+10x+1 \\ \\ =x^2+10x+25+1-25 \\ \\ =(x+5)^2-24 \\ \\ \therefore a=1, h=-5, k=-24[/tex]

This is a multiplication issue, as shown by the usage of the multiplication symbol. The multiplication issue is the solution.

When data is represented by symbols, mathematical statements are easier to comprehend. For all real numbers, the four fundamental arithmetic operations in mathematics are:

+ Addition

Subtraction (-) (-)

Multiplication (x) (x)

() Division

As we proliferate, there are more elements in the group. The product, the two factors, and the product are all components of a multiplication problem. The numbers 6 and 9 are the factors in the multiplication equation 6 x 9 = 54, and 54 is the result. The multiplication formula is represented as Multiplicand x Multiplier = Product. The first figure is multiplicand (factor). the multiplier following figure (factor). The outcome of multiplying the multiplicand and multiplier is the product.

3 x 1 , shows a multiplication signs between them.

which signifies It is a multiplication problem with result 3.

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The length of the arc of the curve from point p to point q of the equation  x2 = (y − 4)3 as calculated is 8 units.

as to calculated  the length of the arc we will differentiate the given equation x² = (y-4)³ with respect to y

=> 2x = 3( y - 4 )²

=> 2x = 3( y²  -8y + 16)

=> 2x = 3 y²  - 24y + 48

=> 3 y²  - 24y + 48 - 2x = 0

now , x = 5 - 1 = 4

y = 8 - 1 =7

Therefore, length = 3 x 8²  - 24 x 8 + 48 - 2x 4 = 0

=192 - 192 - 8 = -8

On taking modulus we get the length as 8 units.

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Answer:

2 3/8 + 1 1/3        (LCD is 24)

= 2 9/24 + 1 8/24

= 3 17/24 cups

Step-by-step explanation:

Answer:

3 17/24

Step-by-step explanation:

2 3/8  + 1  1/3

2 3/8 = 19 /8

1 1/3 = 4/3

The common factor is 24

57/24 + 32/24 = 89/24

89/24 = 3 17/24

Weighing the available information and assigning a probability.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.

So, as per the definition of subjective probability

Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus

Weighing the available information and assigning a probability.

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A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number, 8 is divisible by 2 and 4 other than itself and 1, so 8 is not a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.

factor of 8 = 2x2x2,

since 8 is divided by 2, so it is not a prime number.

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Number of Rows per Worksheet: 1,048,576. Number of Rows per Worksheet: 16,384. Total cells per Worksheet: 17,179,869,184.

Now, According to the question:

The specifications for Excel Worksheet current versions include: Number of Rows per Worksheet: 1,048,576. Number of Rows per Worksheet: 16,384. Total cells per Worksheet: 17,179,869,184.

How many sheets can Excel have?

Set default number of worksheets

It means you can set the number of how many worksheets initially be in a workbook. Inside the General options, you will find an option "Include this many sheets". You can change it to between 1 to 255. Step 1: First of all, open MS Excel and create a new workbook.

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The domain and range of g(x) = |x - 3| are all real numbers and all positive real numbers while the domain and range of the function h(x) = x - 3 are all positive real numbers.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given function,

g(x) = |x - 3|

Since it is a mode function thus the value of the function will always positive.

Thus, the range will be [0, ∞) or all positive real numbers.

In the function h(x) = x - 3 here we have negative real numbers as well as positive thus the range of it will be all real numbers.

Hence "While the domain and range of the function h(x) = x - 3 are all positive real numbers, those of g(x) = |x - 3| are all real numbers and all negative real numbers.".

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Answer:

860 cards

Step-by-step explanation:

[tex]\frac{5}{100} =\frac{43}{x}[/tex]

43 cards only represents 5% of the total cards sold on Mother's Day. So create proportions and solve for the number of cards that represents 100%.

5x = 43*100

5x = 4300

x = 860

When the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.

When the sides and angles of two triangles match, the triangles are said to be congruent. When the angles of two triangles match, the triangles are said to be similar. Thus, two triangles can be superimposed side to side and angle to angle.

Hence, when the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.

If two triangles have an equal number of comparable angles and sides, they are said to be similar. Similar figures are items that have two or more figures with the same shape but varying sizes.

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The value 1 is the multiplicative identity of any number.

In the field of mathematics, the 1 value can be described as the multiplicative identity of any number which has any mathematical value. 1 value describes that when any number is multiplied by the digit 1, the result that arises is the number itself. Hence, value 1 represents the multiplicative identity.

Based on the 1 value, we know that any mathematical expression, digit, or value when multiplied by the digit 1 has an answer that is the same value. As this property is common to all the numbers when multiplied by 1, hence it is referred to as 1 value.

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We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

The n-th term of the sequence (a n) is provided by: If the first term of an arithmetic progression is a and the common difference between each succeeding component is

{a {n}=a+(n-1)d},

If the AP contains m terms, then a m denotes the final term, which is provided by:

{a {m}=a+(m-1)d}.

The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.

The given sequence is -3,0,3,6,....

 We know that an=a + (n-1)d where d is the common difference

  ⇒ 0= -3 + d

∴ d=3

So hence proved that the given sequence is arithmetic.

We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.

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There are a few ways to find discontinuities in a function. One way is to look for places where the function is not defined or where it produces an undefined result, such as division by zero. Another way is to look for places where the function exhibits a sudden change in behavior, such as a jump or a sharp turn.

To find discontinuities more formally, you can use mathematical techniques such as limits or derivatives. If you are familiar with these concepts, you can use them to identify discontinuities in a function.

For example, if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.

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if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.

The probability from the odds is 3/7

The value of the odds is given as

Odds = 3 to 4

Represent the odds as a fraction

So, we have the following representation

Odds = 3/4

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

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

Evaluate the sum

Probability = (3/4)/(7/4)

Evaluate the quotient

Probability = 3/7

Hence, the probability is 3/7

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