How do you convert this equation into vertex form?

Among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.

For the first part of the problem, we can prove that the game must end after at most n(n+1)/2 turns by induction. Base case: When there is only one bowl, Marvin can remove the single marble in one turn, so the game ends after one turn.

Inductive step: Suppose the game ends after at most k(k+1)/2 turns when there are k bowls. We will show that the game ends after at most (k+1)(k+2)/2 turns when there are k+1 bowls. If Marvin removes a marble from a bowl, then the number of bowls decreases by one and the game must end after at most k(k+1)/2 turns by the inductive hypothesis.

If Marvin moves a marble from bowl A to bowl B, where bowl A has at least one marble and bowl B has at least as many marbles as bowl A, then the number of marbles in bowl A decreases by one and the number of marbles in bowl B increases by one. Since bowl B has at least as many marbles as bowl A, the number of bowls remains unchanged. Thus, the game must still end after at most k(k+1)/2 turns.

In either case, the game ends after at most k(k+1)/2 turns, so the game must end after at most (k+1)(k+2)/2 turns when there are k+1 bowls, as desired.

For the second part of the problem, we can prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns by constructing a strategy.

Suppose Marvin wants to make the n-bowl game last for at least kn turns. He can do this by making sure that there are always at least k marbles in each bowl. To do this, Marvin can start by placing k marbles in the first bowl, k-1 marbles in the second bowl, and so on, down to 1 marble in the nth bowl.

On each turn, Marvin can choose a bowl with at least k marbles and move one marble to a bowl with fewer than k marbles. For example, if there are k+1 marbles in the first bowl and k marbles in the second bowl, Marvin can move one marble from the first bowl to the second bowl. This keeps the number of marbles in each bowl at least k. Since Marvin can take at least one turn per bowl, the game will last for at least kn turns.

For the third part of the problem, we can prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.

Let n be a positive integer. We will show that either Marvin has a winning strategy for the n-bowl game or Marisa has a winning strategy for the (n+1)-bowl game.

If Marvin has a winning strategy for the n-bowl game, then he can win the n-bowl game by following his winning strategy.

If Marvin does not have a winning strategy for the n-bowl game, then Marisa has a winning strategy for the n-bowl game. In this case, Marvin can adopt Marisa's winning strategy for the n-bowl game as his own winning strategy for the (n+1)-bowl game.

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Answer:

Step-by-step explanation:

you will need a 10ft tall ladder

i hope that helped

Answer:

They are both irrational

Step-by-step explanation:

so the square root of 8 is 2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

the square root of 98 is also irrational for the same reason but the square root is 9.89949493661.

The product of two √8 and √98 irrational number is irrational.

A rational number is any number that can be expressed as a ratio (or fraction) of two integers.

Any real number that cannot be represented as the quotient of two integers is irrational.

Given:

The rational number are : √8 and √78

As, the √8=  2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

and, √98 = 9.89949493661 is also irrational.

Hence, the product of two irrational number is irrational.

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We can find the domain and range of the function without the help of graphing calculator by the following steps mentioned below.

The domain of a function is the set of values that we are allowed to enter into our function.

This set consists of the x values for a function like f. (x).

The set of values that a function can accept as input is known as its range.

The function outputs this list of values once we enter an x value.

The domain of a function refers to the set of input values.

These numbers, which stand in for the independent variable, are corresponding to the x-axis value.

The range of a function refers to the set of output values.

These values, which indicate the dependent variable, are corresponding to the y-axis value.

Find a function's domain and range without graphing as follows:

(A) Place y = f(x)

(B) In terms of y, solve the equation y = f(x) for x. Let x = g (y)

(C) Discover the values of y and its domain of f for which the values of x, as determined by x = g(y), are real.

(D) The range of the supplied function is the collection of y values produced in step 3.

Therefore, we can find the domain and range of the function without the help of graphing calculator by the following steps mentioned above.

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The correct answer to the expression is 10.

By using BODMAS rule,

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction in its entire form. Therefore, in BODMAS, the orders or exponents are given the second choice here (x n ) A method or sequence called the BODMAS rule is used in mathematics to simplify arithmetic expressions with many operators. When there are several operators in an equation, we must first determine the correct sequence in which to solve the equation. The BODMAS rule assists in the solution of this issue.

Given expression,

2+5*4-8/⅘

=2+20- 40/4    

= 22-10

= 10

Hence, the correct answer to the expression is 10.

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The slope of the linear equation y = -3x + 4 is -3, and the y-intercept is 4.

To calculate the slope of a linear equation, the formula is m = (y2 - y1) / (x2 - x1). The slope is calculated by selecting two points on the line, (x1, y1) and (x2, y2), and then subtracting the first point's y-value from the second's and dividing the result by the first point's x-value minus the second's. For the equation y = -3x + 4, the y-intercept is 4, which is the b-value in the equation y = mx + b. The y-intercept is the point where the line crosses the y-axis. To calculate the y-intercept, set x = 0 and solve for y. For the equation y = -3x + 4, when x = 0, y = 4. Therefore, the y-intercept is 4.

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Answer:

Step-by-step explanation:

If Z1 = (x1, y1) and Z2 = (x2, y2) are complex numbers, then their sum is given by:

Z1 + Z2 = (x1 + x2, y1 + y2)

For example, if Z1 = (3, 4) and Z2 = (-2, 5), then their sum is:

Z1 + Z2 = (3 + (-2), 4 + 5) = (1, 9)

In general, to add two complex numbers, we add their real parts and their imaginary parts separately.

The value of  [tex]z_1[/tex] +  [tex]z_2[/tex]  = ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Complex Numbers. Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a imaginary number called a "iota."

Given:

[tex]Z_1=(x_1,y_1)[/tex] and [tex]Z_2=(x_2,y_2)[/tex]

Also, we know by Complex number

[tex]z_1[/tex] = [tex]x_1[/tex] + i [tex]y_1[/tex]

and, [tex]z_2[/tex] = [tex]x_2[/tex] + i [tex]y_2[/tex]

Then, [tex]z_1[/tex] +  [tex]z_2[/tex]

= ( [tex]x_1[/tex] + i [tex]y_1[/tex]) + ( [tex]x_2[/tex] + i [tex]y_2[/tex])

= ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Hence, the addition gives  ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex]).

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Yes, the given equation is quadratic equation.

Here it has been given that,

3x² - 5x + 9 = x² - 7x + 3

Now, after solving  above equation further we obtain,

2x² + 2x + 6 = 0

From the above equation the factor 2 is taken out as it is common and now the equation looks like : x² + x + 3 = 0

The coefficients of the quadratic equation are compared  and if it meets the criteria then it is quadratic equation otherwise not.

Now as we can see, the above equation clearly represents a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 1 and c = 3.

Hence, the above given equation is a algebraic quadratic equation.

Which of the following is quadratic equation 3x² - 5x + 9 = x² - 7x + 3 ?

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The reasons and statements that completes the two-column table method used to prove that triangle ΔRVX is congruent to ΔTWU (ΔRVX ≅ ΔTWU) are as follows;

Statement                                   [tex]{}[/tex]         Reason

12. UW = VX                   [tex]{}[/tex]                   Transitive Property of Equality

13. ΔRVX ≅ ΔTWU [tex]{}[/tex]                           SSS

Two triangles are congruent if the lengths of the three sides of one triangle are the same as the lengths of the three sides of the other triangle.

The details and reasons for the statements used to prove the congruency of the ΔRVX and ΔTWU are as follows;

RV = RS + SV; Additive property of length

The additive property of length states that a point B can be located on a segment AC only if, we get; AC = AB + BC

RV = ST + SW Substitution

The substitution property states that if a = b then a can substitute b in equations and expressions, such that the values of the expressions and equations remain the same.

RV = TW Transitive Property of Equality

The transitive property of equality states that if a = b and b = c, then a = c

ΔRVX ≅ ΔTWU SSS

The SSS (Side-Side-Side) congruency postulate states that two triangles are congruent if the lengths of all three sides of one triangle are congruent to the lengths of the sides of the other triangle.

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The measures of the angles are 72°, and 108°.

What is Angle Sum Property?

The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.

We have,

two angles form a linear pair. one angle measure is 36° more than the other.

If two angles form a linear pair, then the sum of the degree measure of the angles is 180°.

Let x be the measure of the smaller angle.

Then,

36° + x is the measure of the other angle.

So,

36° + x  + x = 180°

2x = 180° - 36°

2x = 144°

x = 144°/2

x = 72°

the measure of the smaller angle is  x = 72°,

the measure of the other angle is

36° +  72° = 108°

Hence, the measures of the angles are 72°, and 108°.

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a sampling plan in which an initial sample is selected and the audit team either draws a final conclusion or selects additional items before drawing a final conclusion is known as Sequential sampling

Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary. This sampling strategy offers the researcher limitless opportunities to adjust his research procedures and obtain a keen understanding of the study he is currently conducting.

Sequential sampling has a number of benefits, including limitless options for sample size selection and sampling schedule, little cost and labor requirements, and the ability to make minor alterations and modifications to the primary research even during the early stages of the project.

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The four fundamental translations or transformations in geometry are translation, reflection, rotation, dilation, and resizing.

For a function graph, four different transformations are feasible (and translation in math is one of them). When we translate, we move a figure in any direction. When we reflect, we turn a figure or a line over. The act of rotating a figure around a point is known as rotation.

In mathematics, a translation merely moves a shape up, down, left, or right without turning it. The image or the translated shapes seem to be the same size as the original shape, proving that they are congruent. Simply said, they have changed their path or directions.

Three types of translation are described in Jakobson's On Linguistic Aspects of Translation (1959, 2000): intralingual (inside one language, such as rewording or paraphrasing), interlingual (between two languages), and intersemiotic (between sign systems).

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Step-by-step explanation:

A number is divisible by 11 if and only if the difference between sum of alternate digits is divisible by 11.

Here the number is x557x55. The difference between the sum of alternate digits is,

[tex]\longrightarrow S=(x+5+x+5)-(5+7+5)[/tex]

[tex]\longrightarrow S=2x-7[/tex]

By statement, the number x557x55 is divisible by 11 if and only if [tex]S=2x-7[/tex] is divisible by 11.

Let,

[tex]\longrightarrow 2x-7=11a[/tex]

[tex]\longrightarrow 2x=11a+7\quad\dots(1)[/tex]

We separate the RHS as the following.

[tex]\longrightarrow 2x=10a+a+6+1[/tex]

[tex]\longrightarrow 2x=10a+6+a+1[/tex]

[tex]\longrightarrow 2x=2(5a+3)+(a+1)[/tex]

In this question, the LHS is an even integer since x is a digit, i.e., integer. So RHS should also be an even integer.

Since [tex]2(5a+3)[/tex] is even, [tex]a+1[/tex] must be even. So let,

[tex]\longrightarrow a+1=2k[/tex]

[tex]\longrightarrow a=2k-1[/tex]

Then (1) becomes,

[tex]\longrightarrow 2x=11(2k-1)+7[/tex]

[tex]\longrightarrow 2x=22k-4[/tex]

[tex]\longrightarrow x=11k-2\quad\dots(2)[/tex]

So this is expression for x, for any integer k.

As x is a digit of x557x55, x is a single digit integer, so its value lies in between 1 and 9 [x ≠ 0 because it is also the left most digit of x557x55], i.e.,

[tex]\longrightarrow 1\leq x\leq 9[/tex]

From (2),

[tex]\longrightarrow 1\leq 11k-2\leq 9[/tex]

Adding 2,

[tex]\longrightarrow 3\leq 11k\leq 11[/tex]

Dividing by 11,

[tex]\longrightarrow\dfrac{3}{11}\leq k\leq 1[/tex]

Since k is an integer, we get,

[tex]\longrightarrow k=1[/tex]

Then from (2),

[tex]\longrightarrow x=11(1)-2[/tex]

[tex]\longrightarrow\underline{\underline{x=9}}[/tex]

Hence the value of x is 9.

The ordered pair for Point N is (6,9).

What is the ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.

Here, we have

Given the graph and we have to find the coordinates of all points.

N = (6,9)

M = (5,7)

R = (9,8)

D = (2,6)

C = (1,4)

B = (2,1)

A = (6,2)

Q = (7,5)

Hence, the ordered pair for Point N is (6,9).

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Yes, this equation is a quadratic equation.

What is a quadratic equation?

Quadratic equation are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx  + c = 0 where a, b, c ∈ R and a ≠ 0.

The given equation 3x² + 5x + 9x² + 7x + 3 = 0 can be written as 12x² + 12x +3 = 0, which is a general form of quadratic equation where a = 12, b = 12 and c =3.

Hence, the equation is a quadratic equation.

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Answer:

y=1/2x+-2

Step-by-step explanation:

The solution to both inequality is 2 ≥  -x and -x≥ 14

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have the equation 1≥-x-1 and -x-1≥ −13

Let us solve the inequality

1 ≥ - x - 1

1 + 1 ≥ -x

2 ≥  -x

Now, let us solve the inequality

-x-1≥ −13

-x+13 ≥ -1

-x≥ 14

Therefore the solution to both inequality is 2 ≥  -x and -x≥ 14

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Answer:

Number 5

Step-by-step explanation:

When the net is folded, 3 will be folded left and up, with 4 being the base. 6 will be folded right, with 2 being the top of the cube.

So, we have pairs

2 and 4

6 and 3

1 and 5

So, the opposite of the number 1 is the number 5

The pool holds about 245,000 gallons. Therefore, option (c) 244,596 gal is correct.

To find the number of gallons of water the pool holds, we need to convert the volume in cubic feet to gallons.

One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.

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One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself, so 1 is not consider as a prime number.

Therefor 1 is not the biggest 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 and not a decimal or fraction.

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Three parameters, start value, stop value, and step value, are required for the range() method in Python to function. After incrementing the values by the amount specified in the step value .

The range of values between a given data collection's top and lowest values is known as the statistical range. The difference between the highest and lowest observation is another method of expressing the range. By deducting the highest value from the lowest, one may calculate the sample interval. A crucial indicator of variability for continuous variables is the sample range.

here

startNumber (optional): The series of integers that are returned begins with this number.

stopNumber: The list of integers that range() provides comes to an end before this one.

stepValue (opportunity): a number that is an integer and represents the difference between each integer in the series.

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The equation that shows the number of plates that is remaining would be = Y = (Total salad plate/X) - 4.

A banquet hall is a building constructed is a way that various celebrations and functions can be held in such a place such as wedding receptions.

The total number of salad plates available = 144

The number of salad plate per every table set = 10

The number of salad plates remaining = y

The number of tables set by Duncan = x.

If 1 table = 10

X tables = 144

make X tables the subject of formula;

X tables = 144/10

X tables = 14 tables (approximately)

But 14 × 10 = 140 salad for the 14 tables

The remaining salad plates is 4 plates.

Y = (Total salad plate/X) - 4

Therefore, the number of salad plates remaining which is 4 depends on the number of tables Duncan sets which is 10.

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this was an accident how do I delete?

The rule of reflection for the points (x, y) for the graph is (y, - x).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the given line has points(x, y), B(2, 3) and C(1, 6).

Now, The graph has been translated down 2 units and reflected 180° along the x-axis so the image of the graph has points(y, - x) B'(3, - 2) and C'(6, - 1).

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No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

Rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

Rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre to centre distance(C).

Solution:

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP  

Pittiong the values in above eq.

8 teeth/in =17/DP    =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

=>(NP/NG)=(TG/TP)

=>1120/544 =TG/17 =>TG=35

No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

=>1120/544=DG/2.125

=>DG=4.375 in.

In the next fig. I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre to centre distance(C)

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

=>C=(DP+DG)/2

Diameter =2*radius}

=>C=(2.125+4.375)/2 in. =3.25 in.

Theoretical centre to centre distance (C)=3.25 in.

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Answer:

Step-by-step explanation:

D?

10 more than 37 will be Addition of 10 and 37 which is supposed to be 10 plus 37 = 47.

Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.

We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 37 to add 10 to 37. Therefore, the answer is 47 once more.

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The mean of the given observation is 9.

What are the mean, median, and example?

The ratio between the total number of observations in a data set and the sum of all observations is known as the mean in statistics. The most frequent number, or the one that happens the most frequently, is known as the mode.

                   Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

Mean = Sum of all the observations/Number of observations

Mean = 4+6+8+10+12+14/6

Mean = 54/6

Mean = 9

Hence, the mean of the given observation is 9.

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The zeros of the polynomial are 1/2√2 and -3/√2.

The zeros of a polynomial are all the x-values that make the polynomial equal to zero.

Given, the polynomial is 4x² + 5√2x - 3.

We have to find the zeros of the polynomial,

Let 4x² + 5√2x - 3 = 0

On factoring,

= 4x² + 6√2x - √2x - 3

= 2√2x(√2x + 3) - (√2x + 3)

= (2√2x - 1)(√2x + 3)

Now, 2√2x - 1 = 0

2√2x = 1

x = 1/2√2

Also, √2x + 3 = 0

√2x = -3

x = -3/√2

Therefore, the zeros of the polynomial are 1/2√2 and -3/√2.

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