Prove that 53586077 is composite by finding a witness in the form of a positive integer a < 53586077 such that a^(53586077−1) is not equal to 1. Give any information necessary to show that your witness in fact witnesses. (Note: do not use a factor as a witness! Sure, 53586077 is small enough that you can exhaustively find a factor, but we want to test your knowledge of the primality-testing algorithm without using awkwardly-big numbers.)
(b) The number 294409 is a Carmichael number. Prove that it is composite by finding a witness in the form of a nontrivial square root of 1.

Answer:

1.25x + 1.5y=25

Step-by-step explanation:

let the number of lip balms that can be bought be x and the notebooks be y then their total cost is 1.25x + 1.5y. The total $25 there for the equation becomes 1.25x + 1.5y=25.

The required linear equation can be used to determine how many of each prize she can buy is 1.2x + 1.50y = 25.

Given that,
Jung-Soon has $25 to spend on prizes for a game at the school fair. Lip balm costs $1.25 each, and mini-notebooks cost $1.50 each. Write a linear equation that can be used to determine how many of each prize she can buy is ot be determined.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Let the number of lip balm that can be purchased be x,  and the number of mini notebooks purchased be y,
according to the question,
1.2x + 1.50y = 25

Thus, the required linear equation can be used to determine how many of each prize she can buy is 1.2x + 1.50y = 25.

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A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

Function: A(t) = (t+1)/(t-1)For the given function A(t), the following values are to be calculated: A(8), A(-5), A(3/1), and A(-71/1)A(8):We need to substitute t=8 in the function. A(8) = (8+1)/(8-1) = 9/7Therefore, A(8) = 9/7A(-5):We need to substitute t=-5 in the function. A(-5) = (-5+1)/(-5-1) = -1/3Therefore, A(-5) = -1/3A(3/1):We need to substitute t=3/1 in the function. A(3/1) = (3/1+1)/(3/1-1) = (4)/(2/1) = 4*1/2 = 2Therefore, A(3/1) = 2A(-71/1):We need to substitute t=-71/1 in the function. A(-71/1) = (-71/1+1)/(-71/1-1) = (-70/1)/(-72/1) = (-5/36)Therefore, A(-71/1) = -5/36Therefore, the respective answers for the given values of the function A(t) are as follows: A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

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(3x - 5y)(4x + 7y) =

3x × 4x + 3x × 7y - 5y × 4x - 5y × 7y =

12x² + 21xy - 20xy - 35y² =

12x² + xy - 35y²

Answer:

12x^2 + 1xy -35y^2

Step-by-step explanation:

12x^2 + 21xy -20xy -35y^2 becomes this simplified

The vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

To find a vector parallel to the line of intersection of the planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7, we first need to find the direction vector of the line of intersection.

We can find the direction vector by taking the cross product of the normal vectors of the two planes. The normal vector of the plane 2x - 3y + 5z = 2 is <2, -3, 5>, and the normal vector of the plane 4x + y - 3z = 7 is <4, 1, -3>. Taking the cross product of these two vectors, we get:

<2, -3, 5> × <4, 1, -3> = <-16, 22, 11>

This vector <-16, 22, 11> is the direction vector of the line of intersection of the two planes.

To find a vector parallel to this line, we can simply multiply the direction vector by a scalar. For example, we can choose a scalar of 2 to get:

2<-16, 22, 11> = <-32, 44, 22>

Therefore, the vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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The expression for G will be written as G = (-10x² + 100x + 44 ) / x.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is G = -10× + 100 + 44/×. The expression for G will be calculated as:-

G = -10× + 100 + 44/×

Take LCM of x and solve,

G = -10× + 100 + 44/×

G = (-10x² + 100x + 44 ) / x.

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Answer:

5 units

Step-by-step explanation:

Since The X coordinate of a point P on X axis is 4 and the y coordinate of a point Q on y axis is 3 the points are

P (4 , 0) and Q(0 , 3)

The formula to calculate distance between two points

\(PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\PQ=\sqrt{(0-4)^2+(3-0)}\\PQ=\sqrt{(4)^2+(3)^2}\\PQ=\sqrt{16+9} \\PQ=\sqrt{25} \\PQ=5\ units\ \\\)

IMPORTANT!

As we take the square root of 25 we get two values +5 and -5 we always take the positive value because distance can never be negative.

Answer:

3

Step-by-step explanation:

The solution to the given integral is:

∫ 1/√x(1+√x)^4 dx = 2ln|1 + √x| + 2(1 + √x)^(-1) + C.

Let u = 1 + √x

Then, we can write x = (u - 1)^2 and dx = 2(u - 1) du

Substituting these expressions into the integral, we get:

∫ 1/√x(1+√x)^4 dx = ∫ 1/u^2 * u^4 * 2(u - 1) du

= 2∫ (u-1)/u^2 du

= 2∫ (u/u^2) - (1/u^2) du

= 2∫ u^(-1) du - 2∫ u^(-2) du

= 2ln|u| + 2u^(-1) + C

Substituting back for u, we get:

2ln|1 + √x| + 2(1 + √x)^(-1) + C

Therefore, the solution to the given integral is:

∫ 1/√x(1+√x)^4 dx = 2ln|1 + √x| + 2(1 + √x)^(-1) + C.

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Answer:

\(x^{2} -121\) goes with (x+11)(x-11)

\(x^{2} +121\) does not have a solution/answer

\(16x^{2} -25\) goes with (4x+5)(4x-5)

\(25x^{2} -16\) goes with (5x+4)(5x-4)

\(x^{2} -50\) does not have a solution/answer

\(x^{4}-64\) goes with \((x^{2} +8) (x^{2} -8)\)

\(x^{2} -144\) goes with (x+12) (x-12)

Step-by-step explanation:

its factoring

Answer to the question:

112 bags.

Step-by-step explanation:

\(one \: bag \: of \: rice \: = \frac{5}{8} \)

\(70 \div \frac{5}{8} = 112\)

So 112 bags that weight 5/8kg can be contained in a bag of 70kg.

Hope this helps!

Answer:

B

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

but plsdoble check it

Answer:

The last expression.

Step-by-step explanation:

The last expression is not a polynomial because x is in the denominator of the second term.

Answer:

\(4x^2+\frac{5}{x} -6\)

Step-by-step explanation:

A rule for polynomials, is that if they have variables, the powers should be positive whole numbers. Basically, this means you cannot divide by a variable, but in option 4, second term, you are dividing 5 by x, which is the same as\(5*x^{-1}\). This means you are not raising the variable to a positive power, which means the whole 4th option is not a polynomial.

Answer:

27.5 mm

Step-by-step explanation:

The game piece has the shape of two identical square pyramids attached at their bases. Given that the perimeters of the square bases are 80 millimeters, and the slant height of each pyramid is 17 millimeters.

Let the side length of each of the side of the base of the pyramid be b, hence:

perimeter = 4b

80 = 4b

b = 20 mm. half of the side length = b/2 = 20 / 2 = 10 mm

The slant height (l) = 17 mm, Let h be the height of one of the pyramid, hence, using Pythagoras theorem:

(b/2)² + h² = l²

17² = 10² + h²

h² = 17² - 10² = 189

h = √189

h = 13.75 mm

The length of the game piece = 2 * h = 2 * 13.75 = 27.5 mm.

Answer:

B

Step-by-step explanation:

Is the correct answer

Answer:

$3

Step-by-step explanation:

The System of Equation to represent the situation is:

x+ y = 28

x - y =4

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The sum of ages of two siblings add up to 28 years.

and, the difference of their ages is 4.

If "x" the older brother age and with "y" the younger brother age.

then, the system of equations are

x+ y = 28

x - y =4

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The Translation of Question attached here:

The ages of two siblings add up to 28 years and their difference is four years. What would be the system of equations that represents the problem? Suggestion represent with "x" the older brother and with "y" the younger brother

Answer:

Option 2

Step-by-step explanation:

Using the quadrstic formula,

\(\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}\)

Case 1

\(\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}\)

Case 2

\(\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}\)

Answer:false

Step-by-step explanation:

Given that the triangle are similar  the values of x and y ​are;

x = 3.75

y = 9.8

To solve, we need to use ratio

Since Triangles ABC and DEF are similar, their corresponding sides will be of the same ratio.

x/5 = 9/12 = y/b

x = (5 x 9) /12 = 15/4 = 3.75

From Pythagoras' theorem,

y² = x² + 9²

= (15/4)² + 9²

= 95.0625

y = √95.0625

y ≈ 9.8

thus, it is correct to state that x = 3.75 while, y = 9.8

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Full question:

Given the similar right triangles in the figure. Find the exact values of x and y?

See attached image

If JK║LM, all of the statements that are true include the following:

A. JK and LM do not intersect.

B. JK and LM are parallel.

D. JK and LM lie in the same plane.

In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Based on the information provided about line segment JK and line segment LM, we can reasonably infer and logically deduce the following true statements:

In conclusion, line segments JK and LM are both parallel lines.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

−3^2−13+68

Step-by-step explanation:

The convergence set of the given power series is the set of all values of x in the interval (-|x-7|, |x-7|).

In order to determine the convergence set of the given power series, we can use the ratio test.

The ratio test states that if the limit as n goes to infinity of the absolute value of aₙ₊₁ / aₙ is less than 1, then the series converges for all x in the interval (-R, R) where R is the reciprocal of the limit.

The given power series is:

sigma n = 1 to infinity (17/ (n² + 5n))×(x - 7)ⁿ

We can apply the ratio test as follows:

aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))×(x - 7)⁽ⁿ⁺¹⁾ | / |(17/ (n² + 5n))×(x - 7)ⁿ|

aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))/(n² + 5n) × |(x - 7)|⁽ⁿ⁺¹⁾ | / |(x - 7)|ⁿ

As we can see the limit as n goes to infinity of the absolute value of

aₙ₊₁ / aₙ = |(x - 7)|

Let R = |x - 7|, therefore, the series converges for all x in the interval (-R, R)

So the series converges for all values of x in the interval (-|x-7|, |x-7|).

--The given question is incomplete, answering to the question below--

"Determine the convergence set of the given power series.

sigma n = 1 to infinity ( 17/ (n² + 5n))×(x - 7)ⁿ"

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Answer:

the answer is 4 i believe

Step-by-step explanation:

Answer:

it's AAAAAAAAAAAAAAAAAAA

Answer:

It's A <3

I took the test. ^^

C. size

because when things dilate they change in size but not shape, orientation or betweenness

Given:

Two dice are rolled together.

Total number of possible outcomes.

To find:

The list of total possible outcomes.

The probability of getting a sum of 11 in these outcomes.

The probability of getting a sum less than or equal to 4.

The probability of getting a sum of 13 or more.

Solution:

If two dice are rolled together, then the total number of possible outcomes is 36 and list of total possible outcomes is

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Sum of 11 in these outcomes = {(5,6),(6,5),(6,6)} = 3

The probability of getting a sum of 11 in these outcomes is

\(P(\text{sum=11})=\dfrac{3}{36}\)

\(P(\text{sum=11})=\dfrac{1}{12}\)

Therefore, the probability of getting a sum of 11 in these outcomes is \(\dfrac{1}{12}\).

Sum less than or equal to 4 = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)} = 6

The probability of getting a sum less than or equal to 4 is

\(P({sum\leq 4})=\dfrac{6}{36}\)

\(P({sum\leq 4})=\dfrac{1}{6}\)

Therefore, the probability of getting a sum less than or equal to 4 is \(\dfrac{1}{6}\).

Sum of 13 or more = empty set because maximum sum is 12.

The probability of getting a sum of 13 or more is

\(P(sum\geq 13)=\dfrac{0}{36}\)

\(P({sum\geq 13})=0\)

Therefore, the probability of getting a sum of 13 or more is 0.

x is greater than eleven thirds.

Inequality are expression that have <, > , ≤ and ≥ .

Therefore,

1 / 5 (5x) + 10 + 5x > 32

Hence,

1 / 5 × 5x + 10 + 5x > 32

x + 10 + 5x >32

combine like terms

x + 10 + 5x >32

x + 5x + 10 > 32

Therefore,

x + 5x + 10 > 32

6x + 10 > 32

subtract 10 from both sides

6x + 10 - 10 > 32 - 10

6x > 22

divide both sides by 6

x > 22 / 6

x > 11 / 3

Therefore, x is greater than eleven thirds.

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