Calculus

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!

Well, honey, solving 3x + 4 is as easy as stealing candy from a baby. You just subtract 4 from both sides to isolate the 3x, then divide by 3 to get x. Voila! You've cracked the code and solved that little math puzzle.

6 x 2.25 equals 13.5. This calculation involves multiplying the whole number 6 by the decimal number 2.25. To find the product, you can multiply 6 by 225 (ignoring the decimal point) to get 1350, and then move the decimal point two places to the left to account for the two decimal places in 2.25, resulting in 13.5.

The graph of y = -x^2 + 3 crosses the x-axis when y = 0. To find the number of times it crosses the x-axis, we set -x^2 + 3 = 0 and solve for x. This equation has two solutions, so the graph crosses the x-axis twice. Therefore, the answer is C. Two.

This is a hard concept to understand, since infinity is not a definite number. It can keep carrying on forever, which makes it a surreal number.

However, 1 can be measured by infinity as well, due to the never ending amount of decimal places, for example, 1 x 10^-6 [0.000001], 1 x 10^-12 [0.000000000001] and so on.

So, since it is impossible to determine the boundary of infinity, for 1 and for infinity itself, it is most agreed that the result will still be infinity, for whatever sum or subtraction you do, excluding infinity - infinity (0).