Calculus

2x2 ÷ x = 2x

To solve for x when z equals y divided by x, you can rearrange the equation to isolate x. Start by multiplying both sides by x to get xz = y. Then, divide both sides by z to solve for x, giving you x = y/z. This is the solution for x when z equals y divided by x.

Well, honey, if you're counting one number per second without any breaks, it would take you about 31.7 trillion years to count to one sextillion. So, grab a comfy chair, a good book, and maybe a snack because you'll be at it for a while. Good luck with that counting marathon!

Well, isn't that just a happy little math problem we have here! To find n, we can simply divide 450 by 15. When we do that, we find that n equals 30. Just like painting a beautiful landscape, sometimes all we need is a little bit of math to reveal the hidden beauty in numbers.

24.5

Well, isn't that a lovely little equation we have here! To simplify 2x squared minus 2x, we can factor out the common factor, which is 2x. So, the expression simplifies to 2x(x - 1). Just like painting a happy little tree, it's all about finding the beauty in the simplicity of things.

Several equations do. You need to be more specific.

It could be anything including 20 + 8, 30 - 2, 4 x 7, etc.

1 hour = 60 minutes

2/5 hour = 2/5 x 60 = 24 minutes

Oh honey, irrational numbers are used in all sorts of fun ways! From calculating the diagonal of a square to measuring the circumference of a circle, these quirky numbers pop up everywhere in math and science. So next time you come across a pesky square root or a never-ending decimal, just remember that irrational numbers are here to keep things interesting.

56

To find the values of x and y that satisfy the system of equations x + y = 4 and y = 2x + 1, you can substitute the expression for y from the second equation into the first equation. This gives you x + (2x + 1) = 4. Simplifying, you get 3x + 1 = 4, which leads to 3x = 3 and x = 1. Substituting x = 1 back into the second equation, you find y = 2(1) + 1, so y = 3. Therefore, the solution to the system of equations is x = 1 and y = 3.

Oh, dude, branches of mathematics? Like, there's algebra, where you solve for X and make numbers play nice. Then there's geometry, where you're all about shapes and angles, like a math Picasso. And don't forget calculus, where you're basically doing math gymnastics with curves and slopes. Math, man, it's like a whole forest of numbers and stuff.

Absolutely, friend! 3 times 1 is simply 3. Just like painting a happy little tree, sometimes the simplest things can bring the most joy. Keep up the good work!

The expression 3x + 3y is a linear combination of two variables, x and y, with coefficients 3. The answer to this expression depends on the specific values of x and y. If x = 2 and y = 4, then the answer would be 3(2) + 3(4) = 6 + 12 = 18. In general, the answer to 3x + 3y is 3 times the sum of x and y.

To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS). First, we perform multiplication and division before addition and subtraction. So, we start by multiplying 3 by 3, which equals 9. Then, we add and subtract in order from left to right: 3 + 9 - 3 + 3 = 12. Therefore, the answer is 12.

When you multiply two terms with the same base, you add their exponents. In this case, y to the power of 4 multiplied by y to the power of 5 is equal to y to the power of (4+5), which simplifies to y to the power of 9.

If you want to work with real numbers, there is no answer. the square of any number, whether positive or negative, is a positive number, so x2 cannot be -3.

If you accept complex numbers as a solution, the square root of minus 1 is called i (when squared, both i and -i give -1); the square root of -3 is equal to the square root of 3 times i, the square root of -4 is 2i, etc.

Complex numbers are frequently used in some areas of science (electricity, quantum mechanics, and others); in other areas, it just doesn't make sense to use them. Similarly, for some problems fractional solutions, or negative solutions, may be acceptable, for others, not.

To solve the equation 5^x = 15, you can take the logarithm of both sides. By taking the natural logarithm of both sides, you get x * ln(5) = ln(15). Then, you can solve for x by dividing both sides by ln(5), giving you x = ln(15) / ln(5), which is approximately 1.682.

To solve the equation 3log5 125 - log2 8 = x, you can use the properties of logarithms. First, simplify the logarithmic expressions: 3log5 125 simplifies to log5 (125^3), and log2 8 simplifies to log2 (2^3). This gives you log5 15625 - log2 8 = x. Then, you can combine the logarithms using the quotient rule to get log5 (15625/8) = x. Finally, simplify the expression inside the logarithm to get x = log5 1953.125.

An obtuse angle.

In the expression 8 - x, "8" is the minuend and "x" is the subtrahend. When you subtract x from 8, you are finding the difference between the two values. The result will vary depending on the value of x.

Oh, dude, x times y equals the product of x and y. It's like when you have x groups of y things, and you're too lazy to count them all out individually, so you just multiply them together and call it a day. Math, man, it's wild.

2

Well, isn't that a happy little question! When y equals 0, it means that the point is right on the x-axis. So, the value of x at that point is also 0. Just like painting, math can be a beautiful and peaceful experience when we take our time to understand it.

Oh, what a happy little question! Let's gently divide 2 into the polynomial -3x^2 + 7x - 9. When we do that, we find that the remainder is -6x - 21. Just remember, there are no mistakes, only happy little accidents in math!