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according added algebraic angle answer arithmetic arranged binomial called CHAPTER Check coefficient common consider contains cube denominator Determine diagram difference digits divided division divisor dollars equal equation examples exceeds EXERCISE Expand exponents expressions Extract factors feet Find the number formula four fraction function given gives graph graphically greater Hence inches increased integral interest less letter means method miles multiplied negative Note obtain points polynomials positive preceding problem proportional prove quadratic equation quotient radical ratio reduced remainder represented respectively result satisfied sides Simplify smaller solution Solve square root statements Substituting subtract surd symbols temperature term third Transposing triangle true twice units unknown quantities walk written yards zero
Página 164 - The sum of the three angles of any triangle is equal to 180°.
Página 47 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Página 135 - A fraction may be reduced by division to an integral or mixed expression, if the degree of the numerator is equal to, or greater than, that of the denominator.
Página 170 - If the product of two numbers is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Página 104 - A trinomial belongs to this type, ie it is a perfect square, when two of its terms are perfect squares, and the remaining term is equal to twice the product of the square roots of these terms.
Página 299 - Or ж2 + 2x-24 = 0. 325. If both members of an equation are divided by an expression involving the unknown quantity, the resulting equation contains fewer roots than the original one. In order to obtain all roots of the original equation, such a common divisor must be made equal to zero, and the equation thus formed be solved. Eg let it be required to solve If we divide both members by x — 3, we obtain ж + 3 = 5 or x = 2.
Página 105 - We have seen that the product of the sum and the difference of two numbers is equal to the difference of the squares of these numbers. Conversely, the difference of the squares of any two numbers is equal to the product of the sum and the difference of these numbers.
Página 77 - Uniting, - 2 x = - 30. Dividing, x — 15. Check. In 15 years A will be 30 ; 5 years ago he was 10 ; but 30 = 3 x 10. Ex. 3. To a quantity of water contained in a vessel., 56 gallons were added, and there was then in the vessel 8 times as much as at first. How many gallons did the vessel contain at first ? Let x = the number of gallons contained in the vessel at first. The verbal statement expressed in letters gives x + 66 = 8 x.
Página 55 - To divide a polynomial by a monomial, divide each term of the dividend by the divisor and add the partial quotients.