Elementary AlgebraMacmillan, 1905 - 373 páginas |
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Términos y frases comunes
a+b)² a+b+c a²b a²b² a²b³ a³b ab+b² ab² ab³ angle arithmetic arithmetic means ax² B's age binomial binomial theorem Check coefficient consecutive numbers contain cube denominator difference digits divided dividend division divisor examples exceeds EXERCISE exponents feet Find the H. C. F. Find the number Find the sum Find the value following expressions graph Hence inches method miles per hour monomial multiplied negative number of dollars numerical value obtained polynomial problem proportional quadratic equation quotient ratio reduced remainder Simplify simultaneous equations Solve the equation Solve the following square root Substituting subtract surd third Transposing triangle trinomial twice unknown number unknown quantities x²y x²y² x²y³ xy² yards zero
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Página 164 - Thus when it is said that the sum of the three angles of any triangle is equal to two right angles, this is a theorem, the truth of which is demonstrated by Geometry.
Página 47 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers 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 - If the degree of the numerator is equal to, or greater than, that of the denominator, the preceding methods are inapplicable.
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. (Converse of § 181.) If mn = pq, and we divide both members by nq, we have m_p. qn Ex.1. Findíc, if 6:
Página 7 - ... principle : The square root of a fraction is equal to the square root of its numerator divided by the square root of its denominator...
Página 205 - A man rows down a stream, whose rate is 3% miles per hour, for a certain distance in 1 hour and 40 minutes. In returning, it takes him 6 hours and 30 minutes to arrive at a point 2 miles short of his starting-place. Find the distance which he rowed down stream, and his rate of pulling. 50. If a certain number be divided by the sum of its two digits, the quotient is 6 and the remainder 1. If the digits be inverted, the quotient of the resulting number increased by 8, divided by the sum of the digits,...
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 47 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Página 215 - The number of terms is greater by 1 than the exponent of the binomial. 2. The exponent of a in the first term is the same as the exponent of the binomial, and decreases by 1 in each succeeding term.