Question
The product of two consecutive positive integers is 42. Find the integers.

The sum of the arithmetic sequence is S = 207 and the summation notation is S = ∑i=1 to 6 ( 5n + 17 )

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the value of A is

A = 22 + 27 + 32 + 37 + 42 + 47

The number of terms n = 6

So , the value of i ranges from 1 to 6

Now , the summation is represented as ∑i=1 to 6 ( 5n + 17)

when n = 1

S₁ = 5 ( 1 ) + 17 = 22

when n = 2

S₂ = 22 + 5 ( 2 ) + 17

S₂ = 22 + 27

when n = 3

S₃ = 22 + 27 + 5 ( 3 ) + 17

S₃ = 22 + 27 + 32

Hence , the sum of the arithmetic sequence is S = 207

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The number line would be

|---------|---------|
0        1/3      2/3

What is a number line?

A number line is a visual representation of real numbers on a straight line. It is used to graphically illustrate the relative position and size of numbers, and to perform operations like addition, subtraction, and comparison. The number line starts at a certain minimum value, and each point on the line represents a specific real number. The numbers increase as one moves to the right on the line, and decrease as one moves to the left. A number line is often used in mathematics education to help students understand basic concepts of numbers and operations.

2/3 + 2/3 = 4/6 = 2/3

|---------|---------|
0        1/3      2/3

hence, the number line would be

|---------|---------|
0        1/3      2/3

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Complete question:

Draw a number line for 2/3 + 2/3 on the given number line.

The cost of the inn's nightly before the tax is added will be $120.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let 'x' be the cost before tax is added. Then the equation is given as,

5% = [(126 - x) / x] × 100

0.05x = 126 - x

1.05x = 126

x = 126 / 1.05

x = $120

The cost of the inn's nightly before the tax is added will be $120.

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The value of expression after divide is,

⇒ (3x + 18) / (3 + 5x)

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ (x + 6) divided by 3+5x divided by 3.

Now, We can write as;

⇒ (x + 6) ÷ (3 + 5x) ÷ 3

⇒ (x + 6) ÷ (3+ 5x) / 3

⇒ (x + 6) × 3 / (3 + 5x)

⇒ 3 (x + 6) / (3 + 5x)

⇒ (3x + 18) / (3 + 5x)

Thus, The value of expression after divide is,

⇒ (3x + 18) / (3 + 5x)

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Answer:true

Step-by-step explanation:

In the rectangle, the measure of the length is 30 meter and width is 16 meter,

.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. The length and breadth are the two dimensions that define a rectangle. The rectangle's longer side is its length, while its shorter side is its breadth.

Let the width of the rectangle is x meter, than the length of the rectangle is 2x-2.

Perimeter of rectangle = 2*(length + width)

⇒ 92 = 2*(2x-2 + x)

⇒ 92 = 2*(3x-2)

⇒ 92 = 6x - 4

add 4 in both side

⇒ 92 + 4 = 6x

⇒ 96 = 6x

divide oth side by 6

⇒ x = 96/6

⇒ x = 16

So the width of rectangle is 16 meter

The length of the rectangle = 2x-2

⇒ The length of the rectangle = 2*16-2

⇒ The length of the rectangle = 32-2

⇒ The length of the rectangle is 30

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Answer: To solve the inequality 1/4b−1/5b > 3/10b−1/2, we need to simplify both sides:

1/4b - 1/5b > 3/10b - 1/2

5/20b > 7/20b

Then we isolate b by subtracting 7/20b from both sides:

-2/20b > -7/20

Finally, we divide both sides by -2/20 to get:

b < 35/2

The solution in interval notation is (-∞, 35/2).

Step-by-step explanation:

At this rate, Earl should receive $54 from his grandmother when he turns 18.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

The table shows how much money Earl's grandmother gave him each birthday.

Age   Birthday Money

5       15

8       24

10     30

18       ?.

Here, we find the common ratio,

15/5 = 3,

24/8 = 3.

Hence, r = 3.

Now, the missing value,

= 18 x r

= 18 x 3

= 54.

Therefore, Earl  will receive $54.

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The postulate or theorem you would use to prove MXQ = PXN is (b) SAS

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

The triangles

On the triangles, we can see that

This means that two corresponding sides and one angle are equal

So, the triangles are congruent by SAS

The

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The future value of the loan is $5807.65.

It is expressed as a percentage of the amount borrowed and is paid over a specific period of time. The interest rate represents the cost of borrowing money and is one of the key factors in determining the overall cost of a loan. Interest is usually calculated on a yearly basis and can be compounded, meaning that the interest earned on a loan is added to the original principal and the interest rate is then applied to the new, higher amount. This process continues over time, leading to the growth of the original loan amount. The purpose of charging interest is to compensate the lender for the risk they are taking in lending the money and for the opportunity cost of not being able to invest the money elsewhere.

The future value of a loan is equal to the present value plus the interest earned over a specified time period. The formula to calculate the future value of a loan with simple interest is:

FV = PV (1 + rt)

where:

PV is the present value of the loan, which is $5250

r is the interest rate as a decimal, which is 5.3% ÷ 100 = 0.053

t is the time period in years, which is 24 months ÷ 12 months/year = 2 years

Substituting the values into the formula, we get:

FV = $5250 (1 + 0.053 * 2)

FV = $5250 (1.106)

FV = $5807.65

So, the future value of the loan is $5807.65. This is the amount Lynne will have to repay to her grandmother after 24 months, including the interest earned.

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The number of sequences of seven ternary digits containing a single 1 and a single 2 is given as follows:

42.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When elements repeat [tex]n_1, n_2, n_3, \cdots, n_n[/tex] times, the number of arrangements is given as follows:

[tex]A_{n}^{n_1, n_2, n_3, \cdots, n_n} = \frac{n!}{n_1!n_2!n_3! \cdots n_n!}[/tex]

In this problem, we have an arrangement of seven elements, in which:

Hence the number of sequences is given as follows:

N = 7!/(5! x 1! x 1!)

N = 7 x 6

N = 42.

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The error interval for x is given as follows:

27.5 ≤ x < 28.5.

The number x was rounded to the nearest integer.

The rule to round a number to the nearest integer depends on the first decimal digit of the number, as follows:

For both cases, the decimal digit is removed.

Then, considering the two bullet points above, the error interval for x is given as follows:

27.5 ≤ x < 28.5.

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Answer:

f(x)= (x-3)^2

domain: set= {x| xER}

interval= (-infinity, Infinity)

Step-by-step explanation:

hope this helps

Answer:

I have tried

Step-by-step explanation:

Formula= πrl + πr²

π × 4 × 10 + π + 4²

40π + 16π

56π

56 × 3.14

175.952

A square's possible coordinates will be 7, as it has a perimeter of 28 units and a surface area of 49 units.

The perimeter is the space surrounding a shape's edge. Find the perimeter of various forms by multiplying their side lengths.

The circumference of an object is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet. How do you calculate perimeter?

The circumference of a shape is known as its perimeter.

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Answer:

a) 8 b) x= 8

Step-by-step explanation:

the coordinate of x is 8 because its a straight line nad the equation is x =8

The period of the sinusoidal function is given as follows:

8 units.

A periodic function is a function that has the behavior repeating in intervals over the domain of the domain.

Then the period of the function is defined as the shortest difference between two points in which the function has the same behavior.

Two consecutive points where the function has the same behavior (same numeric value, increase/decrease and concavity) are given as follows:

x = 4 and x = 12.

Hence the period is of:

12 - 4 = 8 units.

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12.403 can be expanded in the following manner -

[tex]10 + 2 + \frac{4}{10} + \frac{0}{100} + \frac{3}{1000} \\ [/tex]

hope helpful! ;-;

Answer:

10 + 2 + 4/10 + 3/1000

Step-by-step explanation:

Hope it helps! =D

Answer:

Down 2 and a flip with (-1,3)(1,0)(2,3)and(1,4)

Step-by-step explanation:

hope this works

Sequence of transformations that maps quadrilateral ABCD onto quadrilateral A"B"C"D".

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation or dilation.

The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function.

Given,

Quadrilateral ABCD and A"B"C"D" in the graph.

Transformation of quadrilateral ABCD to A"B"C"D"

By the graph, Steps of transformation are as follows

Hence,

Reflection of ABCD over Y-axis.

Shift of factor 2 downwards.

are the steps to transform ABCD to A"B"C"D".

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Solution is in the attachment!!

Answer: [tex]\Large\boxed{(0,\:3)}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)2x+4y=12[/tex]

[tex]2)3x+y=3[/tex]

Multiply 4 on both sides of the 2) equation

[tex]3x\times (4)+y\times(4)=3\times(4)[/tex]

[tex]12x+4y=12[/tex]

Update the system of equations

[tex]1)2x+4y=12[/tex]

[tex]2)12x+4y=12[/tex]

Subtract the 1) equation from the 2) equation

[tex](12x+4y)-(2x+4y)=(12)-(12)[/tex]

Expand the parenthesis and simplify

[tex]12x+4y-2x-4y=12-12[/tex]

[tex](12x-2x)+(4y-4y)=0[/tex]

[tex]10x+0=0[/tex]

[tex]10x=0[/tex]

Divide 10 on both sides

[tex]10x/10=0/10[/tex]

[tex]x={0}[/tex]

Substitute the x value into one of the equations

[tex]3(0)+y=3[/tex]

[tex]0+y=3[/tex]

[tex]y=3[/tex]

Answer:

It is 100 times less than the value of the number 167,892.

Thank you for using brainly:

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Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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Answer:

Last choice

Step-by-step explanation:

There are two ways to solve this problem.

1. Simplify both fractions

2. Cross multiply (If a/b = c/d, then ad = bc)

Now for the answer choices:

1. 5/7 is less than one while 7/5 is greater

2. 3/12 = 1/4, which is not equal to 3/4

3. 16/20 = 4/5, while 15/25 = 3/5

4. 6/9 = 2/3, and 10/15 also equals 2/3.

Answer:

6 / 9 and 10 / 15

Step-by-step explanation:

Hope this helps :)

13

Step-by-step explanation:

taaaahthyyyyyfffffdddddddddddddddddddddddddddddd

Step-by-step explanation:

Triangle A: Equilateral triangle, all angles are equal (60 degrees) and all sides are equal. Unique.

Triangle B: Isosceles triangle, two sides are equal (6 cm) and two angles are equal. Unique.

Triangle C: Not unique, as different triangles can have two sides of equal length and an included angle of 55 degrees.

Triangle D: Not unique, as different triangles can have a base of 6 cm and base angles of 50 degrees.

Answer:

Step-by-step explanation:

Triangle A and Triangle B

Step-by-step explanation:

I think this is the answer because Triangle A, has a unique that all sides have a measure of 60 degrees. And I also think that Triangle B is unique because It's an Equilateral triangle, which means that all sides have the same length.

So hence, I think the answer is A and B

Always keep more than 2 smiles! You have to share them with people who don't have one too, right??

Thanks!

:D

The person who would win the dash is Mansoor by 4.26 seconds.

The first step is to determine the average speed of each of them. Average speed is the total distance travelled per time.

Average speed = total distance / total time

Average speed of Mansoor = 100 / 7.6 = 13.16 meters / second

Average speed of Saif = 30 / 2.6 = 11.54 meters / second

Mansoor is faster because he covers more meters in one second.

Time it would take to compete the dash = total distance / average speed

Time it would take Mansoor to complete the dash = 400 / 13.16 = 30.40 seconds

Time it would take Saif to complete the dash = 400 / 11.54 = 34.66 seconds

Difference = 34.66 - 30.40 = 4.26 seconds

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Answer:

A. 0.25

Step-by-step explanation:

The coefficient of friction can be calculated as follows:

friction coefficient = force of friction / force of weight

The force of friction is equal to the force applied to the book bag, which is 5 pounds, and the force of weight is equal to the weight of the book bag, which is 20 pounds.

friction coefficient = 5 / 20

friction coefficient = 1/4 or 0.25

So the coefficient of friction between the floor and the book bag is 0.25.

On solving the provided question, we can say that, by Least Common Multiple the amount to buy - 4 packs of buns and 5 packs of hot dogs.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, also known as the least common multiple, or the least common multiple of two numbers a and b. Least Common Multiple is referred to as LCM. The least frequent multiple of two numbers is also the least frequent multiple of both. A number and an integer are combined to create a multiple of that number. For instance, 10 is a multiple of 5, as 10 can be divided by 5, 2, and 5, making it a multiple of 5. The smallest positive integer that can be divided by both 5 and 2 is 10, making it the lowest common multiple of these numbers.

Least Common Multiple (LCM) between 10 and 8 is =  40

Buns is = 10-20-30-40

Hot dogs is =  8-16-24-32-40

So, stock would be equal for both products.

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The fifth term of this arithmetic sequence 5, 2, –1, –4,... ..... is equal to -7.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 2 - 5

Common difference, d = -3

Substituting the given parameters into the formula, the 5th term of this arithmetic sequence is given by;

a₅ = a₁ + (5 - 1)d

a₅ = 5 + (4)(-3)

a₅ = 5 - 12

a₅ = -7.

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When a new spending tax of 25% is placed on electrical items, the price of a product that costs £100 before the tax is imposed is reduced to $25.

In economics, a percentage is a percentage or ratio that is specified as a fraction of 100. Occasionally, this same acronyms "percentage points.," "%," and "pm" are also used. But it is broadly classified into the following by the percent sign, "%." The % sum has no dimensions. Rates are effectively fractions when the sum is 100. Use the percent sign (%) to indicate that a number seems to be a fraction by placing it next to it. So instance, you score a 75% if you properly answer 75 out from 100 respondents on a test (75/100). Divide the money by the total as well as multiply it by 100 to calculate percentages. The formula used to calculate the percentage is (value/total) x 100%.

given

All prices must be reduced by a certain amount in order to return to their pre-tax levels.

percentage = £100 / 100 * 25%

= 25

When a new spending tax of 25% is placed on electrical items, the price of a product that costs £100 before the tax is imposed is reduced to $25.

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