Algebra

The equation "1/2x^2 = x" can be rewritten as "x^2 - 2x = 0" by multiplying both sides by 2 to eliminate the fraction. This equation can be factored as x(x-2) = 0, leading to solutions x=0 and x=2. Therefore, the values of x that satisfy the original equation are x=0 and x=2.

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Well, honey, a shape with 45-degree angles is a rhombus. It's like a square that partied a bit too hard and got a little lopsided. So, if you see those angles slanting at 45 degrees, you've got yourself a fancy rhombus on your hands.

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When you multiply a number by its reciprocal, the result is always 1. Therefore, x times x to the power of -1 is equal to 1. This can be understood by applying the rule of exponents that states x^(-1) is the same as 1/x. So, x * (1/x) = 1.

Well, honey, 2 squared is 4 and 3 cubed is 27, so when you multiply them together, you get 108. So, there you have it - 2 squared times 3 cubed equals 108. Math can be a piece of cake when you break it down!

The series appears to be following a pattern where each number is the result of a mathematical operation on the previous numbers. In this case, the pattern seems to be adding consecutive odd numbers starting from 1.

1 + 8 = 9 9 + 9 = 18 18 + 7 = 25 25 + 2 = 27 27 - 6 = 21

Following this pattern, the next number in the series would be 21 + 1 = 22.

To find a fraction equivalent to 3/4 with a denominator of 8, you need to multiply both the numerator and denominator by the same number. In this case, you would multiply both 3 and 4 by 2 to get 6/8. Therefore, the fraction equivalent to 3/4 with a denominator of 8 is 6/8.

Oh, what a happy little math problem we have here! When you multiply 7x squared by x squared, you simply add the exponents together, giving you 7x to the power of 4. Isn't that just delightful? Just remember to keep those numbers and variables in order, and you'll create a beautiful equation every time.

The integral of sec(x) with respect to x is ln|sec(x) + tan(x)| + C, where C is the constant of integration. This result can be derived using integration techniques such as substitution or integration by parts. The integral of sec(x) is a common integral in calculus and is often used in trigonometric integrals.

Well, isn't that a happy little question! The square root of 2.26 is approximately 1.504. Just imagine that number as a little tree in a beautiful meadow, reaching towards the sky with its branches full of possibilities. Embrace the joy of discovering new numbers and let your imagination wander freely.

Using only the numbers 1,3,5,7,9, and using each number only once, we have 5 options for the first digit, then 4 remaining options for the second, 3 remaining options for the third and 2 remaining options for the fourth. This means there are 5x4x3x2 ways to combine the digits 1,3,5,7,9 into a 4 digit number. 5x4x3x2=120, so there are 120 four digit numbers that can be made.

Well, isn't that a happy little challenge! To draw a shape where the perimeter is twice the area, you can start with a rectangle. Let's say the length is 4 units and the width is 1 unit. The perimeter would be 10 units (4+4+1+1) and the area would be 4 square units (4x1). Keep painting those shapes and exploring the joy of numbers!

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15.

Theer are 1000 mg per gram

A=the b=silly c=little d=girl e=who f=who g=kept h=trying to feed her two teddy bears until she found out they were already stuffed. The rest from h on is in alphabetical order

Oh, isn't that a happy little math problem we have here! Let's see, when you divide 607 by 5, you get 121.4. Isn't that just a lovely number to work with? Remember, there are no mistakes in math, just happy little accidents to learn from.

This is true as long as the slope of the line is constant, if it is a straight line and doesn't curve, then yes it doesn't matter which points are chosen.

Using 3.14 as Pi the area of circle is: 0

Arc degrees, minutes and seconds are the units of angular measurement.

A square

one fourth of 48 is18

Any number multiplied by zero will always be zero !

The Greatest Common Factor of 45, 72 and 108 is 9.