Given the sequence 24, 12, 6, 3......., where x = 1, 2, 3, 4, .........What is the first term? 24 12 6 3

Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for how many factors there are in total for a given number.

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for how many factors there are in total for a given number.

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Endpoint A has coordinates (3,12) since the slope of AB is 1/3 and B is (9,4). Point P has coordinates (7,8) since P is 5/6 the directed path of BA.

Point P divides BA in the ratio of 5:6.

How much of one quantity is in the other can be found by comparing two amounts of the same unit and calculating the ratio. Ratios can be categorized into two groups. Part to part ratio is the opposite of part to whole ratio. A two distinct things or groupings are related to one another as shown by the part-to-part ratio. For instance, the boy-to-girl ratio in a class is 12:15, but the part-to-whole ratio describes how one group of people compares to the total population. For instance, five out of ten people say they like to read. The ratio of the part to the whole is therefore 5: 10, which indicates that 5 out of every 10 people enjoy reading.

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Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of inequality comes out to be x > 6/5  and y > -13/5.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are. Many fundamental inequality problems can be addressed by flipping the two aspects until only the variables are left

Here,

Given :

=> y ≤ 2x-5

=> y > -3x + 1

and

=>  y  ≤ 2x-5

=>  2x - 5  > -3x + 1

=> 2x + 3x > 1 +5

=> 5x > 6

=> x > 6/5

=> y > -3(6/5) + 1

=>  y > -18/5 + 1

=> y > -13/5

Therefore , the solution of the given problem of inequality comes out to be x > 6/5  and y > -13/5.

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Answer:

hypotenuse = 55

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse c is equal to the sum of the squares on the other 2 sides, that is

c² = 33² + 44² = 1089 + 1936 = 3025 ( take square root of both sides )

c = [tex]\sqrt{3025}[/tex] = 55

The names of the terms of m/5+4.6 are m/5 and 4/6

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

m/5 + 4.6

Considering an expression a + b

The terms of the expression are a and b

This means that the terms of the expression m/5 + 4.6 are m/5 and 4/6

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The equation of the linear function represented by the table  is y = - x + 2 .

What is linear Equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given points,

(-1, 3), (1, 1), (3, -1), (5, -3)

Slope-intercept form:

y = mx + b

Finding the slope using slope formula and the first two points:

m = (1 - 3)/(1 - (-1))

= -2 / 2 = -1

Finding y-intercept using the slope and the first point:

3 = (-1)*(-1) + b

3 = 1 + b

b = 3 - 1

b = 2

Hence, The equation of the linear function represented by the table  is

y = - x + 2 .

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Answer:

Step-by-step explanation:

The equation of the line passing through the points [tex](x_{1},y_{1} ) and (x_{2} ,y_{2} )[/tex] is

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )[/tex]

plug the two points [tex](x_{1},y_{1} )=(-6,-4) and (x_{2} ,y_{2} )=(-5,-4)[/tex] into the equation.

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)[/tex]

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)\\y+4=0\\y=-4[/tex]

The equation of line that runs through the points (-6, -4) and (-5, -4) is y = -4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line that passes through the points (-6, -4) and (-5, -4).

First, we find the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -4 - (-4) )/( -5 - (-6) )

Slope m = ( -4 + 4 )/( -5 + 6 )

Slope m = ( 0 )/( 1 )

Slope m = 0

Next, find the y-intercept b.

y = mx + b

Plug in slope m = = and point 1( -6, -4 )

-4 = 0(-6) + b

Solve for b

-4 =  b

b = -4

Now, plug slope m = 0 and y-intercept b = -4 into the slope intercept form to determine the equation of the line.

y = mx + b

y = 0(x) + -4

y = -4

Therefore, the equation of line is y = -4.

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Answer:

the reduced price must be increased by 32% to have a 12% higher price than the original price

The percentage that must the reduced in the reduced price so that the new price is 12% higher than the original price is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Let the price of the suit = 100

Reduced = 20%

Now,

The reduced price of the suit.

= 100 - (20% of 100)

= 100 - (20/100 x 100)

= 100 - 20

= 80 _____(1)

Now,

New price.

= 100 + (12% of 100)

= 100 + 12

= 112

Now,

From (1)

100% = 80

Multiply 112/80 on both sides.

112/80 x 100% = 112

140% = 112

This means,

40% increased

Thus,

40% increase in the reduced price.

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Answer: 9

Step-by-step explanation:

The hike between the pictures will be 22.32 miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that along a hike, Jon takes 6 pictures. He takes 1 picture at equal distances along the 3.72-mile trail.

The hike will be calculated as:-

Hike = 6 x 3.72

Hike = 22.32 miles

Hence, the hike will be 22.32 miles between the pictures.

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Answer:

8 hours

Step-by-step explanation:

The rate at which the candle burns is:

5.5 in/11 hr = 0.5 in/hr

The 4 in candle burns at the same rate.  Find the time for a 4 in candle to burn down:

time = (4 in) / (0.50 in/hr) = 8 hr

This system has no solution because the two equations are not consistent.

An equation is a statement that asserts the equality of two expressions. For example, the equation "2x + 3 = 7" asserts that the value of the expression "2x + 3" is equal to the value of the expression "7".

A system of linear equations is a set of two or more linear equations that are to be solved simultaneously. Linear equations are equations in which the highest degree of the variable is 1. For example, the equations "2x + 3y = 7" and "x - 4y = 2" are both linear equations, and solving them together forms a system of linear equations. These systems can be represented graphically by straight lines in a two-dimensional coordinate system, and the solution of a system of linear equations is the point or points of intersection of the lines.

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The angle that the golfer has between the spectator and the hole is cos^-1((a^2 + b^2 - c^2)/(2ab))

The angle that the golfer has between the spectator and the hole can be found using the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we know that a = 140 (the distance from the golfer to the spectator), b = 200 (the distance from the golfer to the hole), and C = 120 (the angle between the golfer and the spectator).

We can use these values to solve for c, which is the distance from the spectator to the hole. Once we have this value, we can use the Law of Cosines again to find the angle between the golfer and the hole.

c^2 = 140^2 + 200^2 - 2 * 140 * 200 * cos(120)

c = sqrt(140^2 + 200^2 - 2 * 140 * 200 * cos(120))

Now we can use this value of c to find angle A:

A = cos^-1((a^2 + b^2 - c^2)/(2ab))

Note that the angle A is what we're looking for, the angle between the golfer and the hole.

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The rational function to define this situation would be p = 3.45 + 0.33c.

A rational function in mathematics is any function that can be expressed as a rational fraction, which is an algebraic fraction in which the denominator and numerator are both polynomials. It is not necessary for the polynomials' coefficients to be rational numbers; they can be taken from any field K.

In this instance, a rational function and a rational fraction over K are used. The variables' values can be entered into any field L that contains K. In this case, L is the codomain and the domain of the function is the collection of variable values for which the denominator is not zero.

They charge $3.45 to develop a roll of film and $0.33 for each photo that it prints.

The rational function define this situation would be

p = 3.45 + 0.33c

Thus, the rational function to define this situation would be p = 3.45 + 0.33c

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170 out of 300 students in the school own a dog.

A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.

Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.

Given that,

Total number of students surveyed = 30

Total number of students that own a dog = 17

Total number of students in the school = 300

In order to find the equivalent of 17/30 with the bottom number 300

we get, 10 times of 30 is equal to 300 so based on this,

17/30 times 10/10 = 170/300

Thus, 170 out of 300 students in the school own a dog.

Correct question: Out of 30 students surveyed, 17 have a dog. Based on these results, predict how many of the 300 students in the school have a dog.

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The feet of wiring that are still on the truck at the end of the second day is 629 feet.

Arithmetic operations implies solving a given question by addition, subtraction, division or multiplication as required in the question.

From the given question, total feet of copper wire at the start of the first day is 600 feet.

During the first day,

the total length of wire used = 100 + 82 + 25 + 40

                                      = 247

Total length of copper used in the first day is 247 feet.

Length of copper wire remaining at the end of the first day = 600 - 247

                                                          = 353 feet

He purchased 400 feet of the wire so that;

total length of wire = 353 + 400

                                = 753 feet

the total length of wire used the second day = 41 + 39 + 44

                                                = 124 feet

Total length of copper wire left after the second day = 753 - 124

                                                            = 629 feet

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The x-value of where the beam should be placed is X = (x1+x2)/2.

Given: the distance between the two trusses is 2 feet and the reinforcement beam will extend from one truss to the other.

We can set up an equation using the distance formula to determine the x-value of where the beam should be placed.

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²)

Let's assume that the trusses are located at point (x1, y1) and (x2, y2) and the beam is located at point (x, y).

We know that the distance between the trusses is 2 feet, so we can set d = 2.

We can use the coordinates of the trusses and the point where the beam is located to set up the equation:

d = √((x2 - x1)² + (y2 - y1)²) = 2

Since the trusses are located on the same line and only the x-coordinate changes, we can assume that y1=y2

Therefore the equation can be simplified to √((x2 - x1)²) = 2

Square both sides: (x2 - x1)² = 4

x2 - x1 = 2

Now we know that the difference between the x-coordinates of the two trusses is 2 feet.

So, to find the x-value of the point where the reinforcement beam should be placed, we can take the average of the x-coordinates of the two trusses.

x = (x1+x2)/2

We don't know the values of x1 and x2, so we can't solve for x. But we know that the reinforcement beam should be placed exactly in the middle of the trusses.

Thus, The x-value of where the beam should be placed is X = (x1+x2)/2.

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Answer:

y = 5 + √-3 + x

y = 5 - √-3 + x

Step-by-step explanation:

X=3+(y-5)^2

Let's simplify, and we will get

x = 3 + (y^2 -10y + 25)

x = 3 + y^2 - 10y + 25

x = y^2 - 10y + 28

0 = y^2 - 10y + 28 - x

We use the formula

-b ± √ b^2 -4(ac) / 2a

10 ± √(-10)^2 - 4 · (1 ( 28 - x) ) / 2

The answer will be

y = 5 + √-3 + x

y = 5 - √-3 + x

If the scale factor is a fraction, the shape will be smaller. This is called reduction. Therefore, a 1/2 scaling factor means that the new shape is half of the original shape

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If the scale factor is a fraction, the shape will be smaller. This is the so-called recovery. So a scale factor of 1/2 means that the new shape is half the original shape.

Half scale is 1.

2. It is convenient to imagine that 1 unit on the drawing is equal to 2 units on the object. You can enlarge small objects and draw them on paper 2:

1 scale. This means that the drawing of the object is twice the size of the object itself.

Starting from the top right corner of the paper, draw five parallel diagonal lines towards the bottom left corner.

Step 2 - Create a diagonal cross pattern. ... Step 3 - Put the scales into the diamond shaped box. ...

Step 4 - Draw the scales in the middle part.

A full-size drawing will be 1.

1 (or sometimes 1/1 or "one to one"). A half-sized drawing will be 1.

2. A 10th grade drawing will be 1.

10. A double size drawing will be 2.

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The smallest y - intercept for the given equations is, (0, -6).

What is y - intercept?

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

There are four function are given.

We have to find which function having smallest y - intercept.

Since, to find y - intercept we have to plug x = 0 in each equation.

Consider, the functions

1. g(x) = 2x - 6

Plug x = 0

g(0) = 0 - 6

g(0) = -4

⇒  The y - intercept is (0, -4).

2. f(x) = √x - 2

Plug x = 0

f(0) = 0 - 2

f(0) = -2

⇒  The y - intercept is (0, -2).

3. For 3 we get the equation, y = 2x + 1

Plug x = 0

y = 0 + 1

⇒  The y - intercept is (0, 1).

4. From graph the y - intercept is (0, -2).

Hence, the smallest y - intercept for the given equations is, (0, -6).

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Answer:

Step-by-step explanation:

6-2^x=1

-2^x+6=1

-2^x+6-6=1-6

-2^x=1-6

-2^x=-5

x=-5

The formula to find the resolution of an image, also known as its pixel density, is Pixels per Inch (PPI) or Pixels per Centimeter (PPCM). This formula is used to determine the number of pixels in a given area of an image.

The higher the PPI or PPCM, the greater the resolution of the image.

To calculate PPI, you need to know the total number of pixels in the image (width x height) and the physical size of the image (width x height in inches or cm). Once you have this information, you can use the following formula: PPI = (pixels / physical size) x (inches/cm).

For example, if an image has a resolution of 1920 x 1080 pixels and is printed at a size of 8 x 6 inches, the PPI would be (1920 x 1080) / (8 x 6) = 240 PPI.

In conclusion, PPI or PPCM is the formula used to find the resolution of an image, also known as its pixel density. It is calculated by dividing the total number of pixels in the image by its physical size and multiplying it by inches/cm.

The higher the PPI or PPCM, the greater the resolution of the image. It is important to consider the PPI or PPCM when choosing an image to print or display in order to ensure that it will be of high quality and have a high resolution.

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The function that represents the vertical compression of function f(x) = x² by a factor of 1/2 is given as follows:

f(x) = x²/2.

The parent function for this problem is defined as follows:

f(x) = x².

For a vertical compression by a factor of a, the function is multiplied by the constant a with absolute value less than 1, that is:

g(x) = a x f(x), |x| < 1.

The factor of the compression for this problem is of a = 1/2, hence the function that represents the vertical compression of function f(x) = x² by a factor of 1/2 is given as follows:

f(x) = x²/2.

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Answer:

24 pens

Step-by-step explanation:

Answer: the answer is actually 288

Step-by-step explanation:

you multiple 12 by 12 to get 144 then you multiply that by 2 to get 288

Therefore ,when the problem of expression is solved, we may state that the necessary inequality statement is 4.50x+1.75y 50.

An expression in mathematics consists of a statement, two or more variables or integers, but one or more mathematical functions. Numbers can be multiplied, divided, added, or subtracted using this mathematical operation. The construction of an expression is as follows: Expression: Math operator, variable or number, and math operator.

Here,

Cost per assignment is $4.50.

Therefore, "x" assignment cost equals 4.50x.

Cost per assignment: $1.75

Assignment "Y" cost is therefore 1.75Y.

Consequently, the sum of 4.50x+1.75y must be $50 or less.

Therefore, 4.50x+1.75y ≤ 50 is the necessary inequality statement.

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A z-score is used to measure how many standard deviations an individual value is from the mean of a given set of data.

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The value of the variable, n is 5

An algebraic expression can simply be defined as an expression that is composed of variables, coefficients, factors, constants and terms.

These mathematical expression called algebraic expressions are also composed of arithmetic operations, such as;

Examples of algebraic expressions are;

2x + 18

2x² + 4

3y + 6

From the information given, we have that;

7n - 4 = 31

collect like terms

7n = 31 + 4

Add like terms

7n = 35

Make 'n' the subject of formula

n = 35/7

n = 5

Thus, the value is 5

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[nΣk=1]k/(k+1)! is the notation of the summation .

The summation notation is a compact way of expressing the sum of a series of terms. In this case, the series of terms is the expression "1/2! + 2/3! + 3/4! + ...+ n/(n+1)!" which can be represented using the summation notation as [nΣk=1]k/(k+1)!. It is saying the sum of all k/(k+1)! where k = 1, 2, 3, ...., n. The summation notation consists of three parts, the n, Σ and the k=1. The n represents the upper limit of the summation, the Σ (sigma) represents the summation operator and the k=1 represents the lower limit of the summation.

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Enter the data value to be searched for in the Search text area. Choose the database to search in from the Database drop-down menu.

The length of the sequence is the number of ordered elements (which could be infinite). Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of sequences you need to be familiar with. A list of numbers connected by a rule is known as a number sequence. You can determine the subsequent numbers in the sequence if you figure out the rule. The difference in this instance between each number is 6.

given

Enter the data value to be searched for in the Search text area.

Choose the database to search in from the Database drop-down menu.

Select the tables and views you want to search in from the Select objects to search tree, or leave them all checked.

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