Calculus

No, a kite does not tessellate. In geometry, tessellation refers to the repeated use of one or more shapes to completely fill a surface without any gaps or overlaps. A kite shape has two pairs of adjacent sides that are equal in length but do not meet at right angles, making it impossible to tessellate without leaving gaps between the shapes.

To simplify x divided by the square root of x, we can rewrite the square root of x as x^(1/2). Dividing x by x^(1/2) is equivalent to multiplying x by x^(-1/2), which simplifies to x^(1-1/2). Therefore, x divided by the square root of x simplifies to x^(1/2), which is the square root of x.

Well, isn't that a happy little math problem we have here? To solve 9 to the power of x equals 243, we can rewrite 243 as 3 to the power of 5. Since 9 is 3 squared, we can rewrite 9 as 3 to the power of 2. Now we have 3 to the power of 2x equals 3 to the power of 5. So, setting the exponents equal to each other, we get 2x equals 5. Therefore, x equals 5 divided by 2, which simplifies to x equals 2.5. Happy solving!

The first quadrillion digits of pi are not practically computable or known. As of now, the most extensive calculation of pi includes trillions of digits, but calculating a quadrillion digits would require immense computational power and time. Pi is an irrational number, meaning it has an infinite and non-repeating decimal expansion, making it a challenging task to calculate such a vast number of digits.

6x times x equals 6x^2. It's just math, honey, not rocket science. So put on your big girl pants and go solve that equation.

The metric prefix that represents 1 x 10^6 is "mega-." In scientific notation, "mega-" is denoted by the symbol "M." Therefore, 1 x 10^6 meters would be equivalent to 1 megameter (1 Mm). This prefix is commonly used in various fields such as physics, engineering, and technology to denote large quantities or measurements.

Oh, dude, so, like, when you multiply 8 by 0, you get 0, not 4n. It's like trying to make a sandwich with just bread - you're missing the filling! Maybe check your math or see if there's more to the equation that got lost along the way.

Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.

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Standard form requires a single non-zero digit before the decimal point and a multiplier of a power of 10 which gets the decimal point back to where it was in the original number. To calculated the power of the ten count how many digits the decimal point needs to move; if it needs to move to the left make it negative:

59 = 5.9 × 10¹

The inverse function is obtained by interchanging corresponding values of x and y and then transposing the resulting equation to make y the subject.

f(x) = y = 8x + 5 therefore f-1(x) = x = 8y + 5 : 8y = x - 5 : y = (x - 5)/8

The inverse function of y = 8x + 5 is y = (x - 5)/8

To find the product of 8x and 2x, you multiply the coefficients (8 and 2) to get 16, and then multiply the variables (x and x) to get x^2. Therefore, 8x * 2x equals 16x^2.

The expression 2x + 4 represents a linear equation where x is a variable. To simplify this expression, you would combine the like terms, which in this case are the 2x and the 4. Therefore, the simplified form of 2x + 4 is 2x + 4.

The algebraic expression for "7 increased by x" is 7 + x. In this expression, the variable x represents the amount by which 7 is being increased. Adding x to 7 results in the total value after the increase.

To find the population density of a country, you divide the amount of people in the country by the amount of squared kilometres. For example, Bangladesh has the highest population density; it is 1000 people per squared km!

When a number is raised to the power of 2, it means that the number is multiplied by itself. In mathematical terms, X to the power of 2 is written as X^2, or X * X. This is equivalent to X squared, and represents the area of a square with sides of length X.

Counting to 1000 in 6 minutes means counting at a rate of 1000/6 = 166.67 numbers per minute. To count to 100,000 at this rate, you would divide 100,000 by 166.67 to get approximately 600 minutes. Therefore, it would take around 600 minutes or 10 hours to count to 100,000 at the same rate as counting to 1000 in 6 minutes.

Well, isn't that just a happy little math question! When you see "log base 81 of 9," you're looking for the power you need to raise 81 to get 9. Since 81 to the power of 1/2 equals 9, the answer is 1/2. Just a little mathematical magic to brighten your day!

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Oh, what a happy little question! When you multiply 500 by 100, you get 50,000. Isn't that just a lovely number to work with? Just imagine all the wonderful things you could do with 50,000 - maybe paint a beautiful landscape or spread some joy to others.

Well, honey, if Y divided by 5 equals 3, then Y must equal 15. It's simple math, darling. Just plug 3 back into the equation and see for yourself. Math doesn't have to be a headache, dear, just embrace the numbers and move on with your fabulous self.

The property you are referring to is the multiplicative identity property. This property states that any number multiplied by 1 will result in the original number. In this case, 1 multiplied by n will always equal n, no matter the value of n. This property is fundamental in multiplication and plays a crucial role in various mathematical operations.

Solving a system of equations by graphing involves plotting the equations on the same coordinate plane and finding the point(s) where the graphs intersect, which represents the solution(s) to the system. Each equation corresponds to a line on the graph, and the intersection point(s) are where the x and y values satisfy both equations simultaneously. This method is visually intuitive but may not always provide precise solutions, especially when dealing with non-linear equations or when the intersection point is not easily identifiable due to the scale or nature of the graphs.

10 x 10 x 10 x 10 x 10 x 10 =

100 x 100 x 100 =

10,000 x 100 = 1,000,000 ( one million).

The above multiplication is usually written as '10^(6).

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