It may seem difficult to measure the inside of a round object like a sphere or a cone in cubic units, but you can imagine filling the object with liquid and then pouring the liquid into a box to measure its volume.
We make a sketch and label the known dimensions, calling the unknown height . The ladder forms the hypotenuse of a right triangle, so we apply the Pythagorean theorem, substituting 25 for , 7 for , and for .
Multiply each term of the first binomial be each term of the second binomial. This gives four multiplications, often denoted by "FOIL," which stands for First terms, Outside terms, Inside terms, and Last terms.
For this example we must find two numbers and for which and . These two conditions tell us that and must both be negative. We start by listing all the ways to factor with negative factors:
andandand
We check for each possibility to see which one gives the correct middle term. Because , the factorization is
This time the product must be negative, so and must have opposite signs, one positive and one negative. There are only two ways to factor , either times or times . We just "guess" that the second factor is negative, and check for each possibility:
or
The middle term we want is , not , so we change the signs of and : we use and . The correct factorization is
We subtract the calories in three eggs from the total; the remainder is the number of calories in two slices of toast, so one slice has half that many calories:
SubsubsectionA.3.3.1Find the average of two numbers
The average of two numbers lies half-way between them on a number line. To find their average, we take one-half of their sum. That is, the average of and is
To multiply two fractions together, we multiply their numerators together, and multiply their denominators together. We can divide out any common factors in numerator and denominator before we multiply.