What is a shape with 1 trillion sides called?

The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.

The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.

The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:

Divide a by b to get a quotient q and a remainder r

Replace a with b and b with r

Repeat the process until r is 0

If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:

GCD(11n+3, 2n+1)

As 11n + 3 = 3(2n + 1) + 5n

= GCD(2n+1, 5n )

As 2n + 1 = (2/5)(5n) + 1

= GCD(5n, 1)

= GCD(1, 0)

= 1

So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.

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a=11

Hope this Helped! :T

Answer:

B

Step-by-step explanation:

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Answer:

Top left quadrant (Quadrant 2)

Step-by-step explanation:

Answer:

Q1 : [tex]\frac{5}{8}[/tex]

Q2: [tex]\frac{2}{3}[/tex]

Q3: [tex]\frac{11}{12}[/tex]

Q4: [tex]\frac{4}{5}[/tex]

Q5:  [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Answer:

Q1. [tex]\frac{5}{8}[/tex]

Q2. [tex]\frac{2}{3}[/tex]

Q3. [tex]\frac{11}{12}[/tex]

Q4. [tex]\frac{4}{5}[/tex]

Q5. [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Q1.

[tex]\sqrt{\frac{25}{64}}[/tex] ⇒ [tex]\frac{\sqrt{25}}{\sqrt{64}}[/tex] = [tex]\frac{5}{8}[/tex]

Q2.

[tex]\sqrt{\frac{36}{81}}[/tex] ⇒ [tex]\frac{\sqrt{36}}{\sqrt{81}}[/tex] = [tex]\frac{6}{9} = \frac{2}{3}[/tex]

Q3.

[tex]\sqrt{\frac{121}{144}}[/tex] ⇒ [tex]\frac{\sqrt{121}}{\sqrt{144}} = \frac{11}{12}[/tex]

Q4.

[tex]\sqrt{\frac{64}{100}}[/tex] ⇒ [tex]\frac{\sqrt{64}}{\sqrt{100}} = \frac{8}{10} = \frac{4}{5}[/tex]

Q5.

[tex]\sqrt{\frac{4}{9}}[/tex] ⇒ [tex]\frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}[/tex]

Answer:

d). 4(9a - 3b)

Step-by-step explanation:

a). 4(6a-9b)

= 24a - 36b

b). 4(8a-3b)

= 32a - 12b

c). 4(9a+3b)

= 36a + 12b

d). 4(9a - 3b)

= 36a - 12b

Answer: Choice 2

Step-by-step explanation:

Step-by-step explanation:

8 × 10000 + 0×1000 + 2× 100 + n + 6 x 1=0

80000 + 0 + 200 + n + 6 =0

80206n = 0

n = -80206

The Additive inverse of 3/2 is -2/3.

Additive Reciprocal

An additive reciprocal is a number that is added to a given number to bring the sum to zero. For example, adding -3 to the number 3 will result in zero. So the additive reciprocal of 3 is -3. In our daily life, we come across situations where we cancel the value of a quantity by forming its additive reciprocal.

Additive Reciprocal in Fraction:

The additive reciprocal of the fraction a/b is -a/b and vice versa. This is because a/b + (-a/b) = 0. The additive reciprocal of a positive fraction is the same fraction with a negative sign, but for negative fractions the additive reciprocal is the same fraction without a negative sign.

Given, the number is 2/3

We have to find the additive inverse of the given number.

In mathematics, the additive inverse of a number ‘a’ is the number that, when added to ‘a’, yields zero.

So, 2/3 + (-2/3)= 0

Therefore, the additive inverse of 2/3 is -2/3.

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Answer:

f(6) = 182

Step-by-step explanation:

f(1) = 1

f(2) = 2

f(3) = 2f(2) + 3f(1) = 2(2) + 3(1) = 4 + 3 = 7

f(4) = 2f(3) + 3f(2) = 2(7) + 3(2) = 14 + 6 = 20

f(5) = 2f(4) + 3f(3) = 2(20) + 3(7) = 40 + 21 = 61

f(6) = 2f(5) + 3f(4) = 2(61) + 3(20) = 122 + 60 = 182

Answer:

-486

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

x² + 8² = 10²

x² + 64 = 100

x² = 36

x = 6

'The leangth of the shortcut is: '

guessing- '75'

Hope this helps!

Answer:

G.

Step-by-step explanation:

$12 is the flat fee and it costs 25 dollars per hour to rent a kayak. x is the number of hours, so 25x+12=y, the total cost for renting the kayak

The graph of y is a straight line parallel to the x−axis through the point (0,1)

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The equation is Y = 1

A straight line in slope (m) and intercept (c) form is:

y = mx + c

y is a straight line of slope 0 and y- intercept of 1

y = 0.x + 1

y = 1

Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)

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The correct answer is (D) 0.75. The probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%

We know that there are 8 possible outcomes when rolling the number cube (1, 2, 3, 4, 5, 6, 7, 8). Of these 8 outcomes, 5 of them are numbers greater than 4 (5, 6, 7, 8). So, the number of favorable outcomes is 5.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: P(number greater than 4) = 5/8. As a decimal, this is 0.625. However, the question asked for P(number greater than 4) which means we have to add 0.125 to 0.625, the answer is 0.75.

Therefore, the probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%. This means that if we roll the cube many times, we expect 75% of the rolls to be numbers greater than 4.

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Answer:

25 [tex]cm^{2}[/tex]

Step-by-step explanation:

The others are squares as well, meaning each of the sides are equal.

The square root of 144 is 12, meaning the side of the red square is 12.

169's square root is 13, meaning the hypotenuse of the center triangle is 13.

Now that we have a side and the hypotenuse, we can use Pythagorean theorem to find out the final side.

12^2 + x = 13^2

[tex]12^{2} + x^{2} =13^{2} \\144 + x^{2} = 169\\x^{2} = 25\\x = 5[/tex]

Now that we have the side, let's just square it to find the area.

[tex]5 * 5 = 25[/tex]

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the location of this point.

The result of the first equation is

x + 6y = 25

we can easily solve for x by subtracting 6y from both sides we have  

x + 6y - 6y = 25 - 6y

x - 25 - 6y

So, the first equation's x term can be simply solved.

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

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5 is not an algebraic expression.

Since it is obvious that 5 is a constant, even if constants constitute a component of the algebraic equation, they do not finish it. A variable and an operator are also necessary for an expression to qualify as an algebraic expression. Any unknown term, such as x, y, or z, can be a variable, and the operators + and - can be used. Terms with no associated variables are known as constants. A variable and an operator are also necessary for an expression to qualify as an algebraic expression.

It follows that 5 cannot be an algebraic expression.

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Answer:

A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

Given the pictorial equations, you want to know the single-digit values of each of the images.

There are 6 equations in 5 unknowns, but no numerical values are assigned. Solving the equations will only give ratios of values. From those, we need to determine the numerical values that will keep all numbers in the range 1–9.

Let the icons be represented by letter variables as follows:

Rewriting the equations to standard form, we have ...

  h +b -m -s = 0 . . . . . [eq1]

  h -b +t = 0 . . . . . . . . [eq2]

  b -3s = 0 . . . . . . . . . [eq3]

  h -s -t +m = 0 . . . . .  [eq4]

  h +2s -m = 0 . . . . . . [eq5]

  h +b +s -2t = 0 . . . . . [eq6]

We can add [eq4] to [eq1] and [eq5] to eliminate the m variable.

  (h +b -m -s) +(h -s -t +m) = 0   ⇒   2h +b -2s -t = 0 . . . . [eq7]

  (h +2s -m) +(h -s -t +m) = 0   ⇒   2h +s -t = 0 . . . . . . . . . [eq8]

Adding [eq2] to [eq6], and [eq7] will eliminate the b variable.

  (h +b +s -2t) +(h -b +t) = 0   ⇒   2h +s -t = 0 . . . . same as [eq8]; no help

  (2h +b -2s -t) +(h -b +t) = 0   ⇒   3h -2s = 0 . . . . . [eq9]

Now, we have 3 equations in 4 unknowns:

  b -3s = 0 . . . . . . . [eq3]

  3h -2s = 0 . . . . . . [eq9]

  2h +s -t = 0 . . . . . [eq8]

The smallest positive integer values that will satisfy [eq9] are ...

  h = 2, s = 3

Using these in the remaining equations gives ...

  b -3·3 = 0   ⇒   b = 9

  2·2 +3 -t = 0   ⇒   t = 7

And we can find m using [eq5]:

  m = h +2s = 2 +2·3 = 8

Then the solution is ...

Answer:

-1.256165295×10×10×10×10×10×10×10×10×10×10×10

Step-by-step explanation:

negative changes everything

Part (i)

The square has area of 12*12 = 144 square meters. From that, we carve out four quarter-circles from each corner, as the diagram shows. Imagine that we rearranged the quarter circles so that they would then form a full circle. This circle would have radius 6 (half of the 12 meters), so the area of the circle is pi*r^2 = pi*6^2 = 36pi exactly

The four white sections combine to an exact area of 36pi, which approximates to 36*3.14 = 113.04 square meters. Use more decimal digits in pi to get a better approximation.

Exact answer: 36pi square meters

Approximate answer: 113.04 square meters (when using pi = 3.14)

=======================================================

Part (ii)

Once we know what the white sections combine to, we can subtract that area from the total overall area of 144 m^2

We end up with 144 - 36pi as the exact area of the red section

This approximates to 144 - 36*3.14 = 30.96 m^2

Exact answer:  144 - 36pi square meters

Approximate answer: 30.96 square meters (when using pi = 3.14)

Truncation error for S4 is 0.037.

Truncation errors are defined as the errors formed when we use approximation instead of actual procedures.

Given is a series.

S4 means,

6/(3¹) + 6/(3²) + 6/(3³) + 6/(3⁴)

The actual sum of these values gives,

2 + 0.6666..7 + 0.2222.. + 0.074074...

= 2.962962..

≈ 2.963

Truncation error = 3 - 2.963 = 0.037

Hence the truncation error is 0.037.

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Answer:

B

Step-by-step explanation:

since the value is above 1 and your subtracting 1 to drop the value below the 0 point below making it negative.

Answer:

25.12 kilometers

Step-by-step explanation:

[tex]c = 2\pi \: r[/tex]

C = 2 × 3.14 × 4

C = 25.12

Answer:

74

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Your answer is D

Step-by-step explanation:

Your base is 7cm. The hypotenuse is 2x or 2(7)=14 and the height is x[tex]\sqrt{3[/tex] or 7[tex]\sqrt3[/tex]

The statement that correctly describes the graph is given as follows:

C. The graph represents a linear function with a constant rate of change.

A function is classified as linear or non-linear depending on the rate of change of the function.

If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.

Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.

As the graph presented at the end of the answer shows a linear function with constant slope, it has a constant rate of change, thus it is linear and option c is correct.

The graph is given by the image presented at the end of the answer.

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