Essentials of Algebra for Secondary SchoolsD.C. Heath & Company, 1904 - 367 σελίδες |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 48
... satisfied by every set of values of these letters . Thus , the equation x + 2 = 5 is not satisfied by every value of x , but only by the value x = 3 . An equation of condition is usually called an equation . 67. If an equation contains ...
... satisfied by every set of values of these letters . Thus , the equation x + 2 = 5 is not satisfied by every value of x , but only by the value x = 3 . An equation of condition is usually called an equation . 67. If an equation contains ...
Σελίδα 138
... satisfied by an indefinitely great number of sets of value of these quantities . Consider , for example , the equation x + y = 5 . If x = 1 , we have 1 + y = 5 , or y = 4 . If x = 2 , we have 2 + y = 5 , or y - 3 ; and so on . Thus the ...
... satisfied by an indefinitely great number of sets of value of these quantities . Consider , for example , the equation x + y = 5 . If x = 1 , we have 1 + y = 5 , or y = 4 . If x = 2 , we have 2 + y = 5 , or y - 3 ; and so on . Thus the ...
Σελίδα 139
... satisfy the other . Consider , for example , the equations x + y = 5 , x - y = 3 . The first equation is satisfied by the set of values x = 3 , y = 2 , which does not satisfy the second . Therefore , the equations are independent . But ...
... satisfy the other . Consider , for example , the equations x + y = 5 , x - y = 3 . The first equation is satisfied by the set of values x = 3 , y = 2 , which does not satisfy the second . Therefore , the equations are independent . But ...
Σελίδα 224
... . 2 the values of x are imaginary ( § 248 ) ; it is impossible to find any real values of x which will satisfy the given equation . EXAMPLES . Solve the following equations : 3. 3x2 - QUADRATIC EQUATIONS Pure Quadratic Equations.
... . 2 the values of x are imaginary ( § 248 ) ; it is impossible to find any real values of x which will satisfy the given equation . EXAMPLES . Solve the following equations : 3. 3x2 - QUADRATIC EQUATIONS Pure Quadratic Equations.
Σελίδα 236
... satisfied when x has such a value that one of the factors of the first member is equal to zero ; for if any factor of a product is equal to zero , the product is equal to zero . Hence , the equation will be satisfied when x has such a ...
... satisfied when x has such a value that one of the factors of the first member is equal to zero ; for if any factor of a product is equal to zero , the product is equal to zero . Hence , the equation will be satisfied when x has such a ...
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9 x² a²b a²b² a³b ab² ab³ algebraic arithmetic means arithmetic progression ax² binomial Binomial Theorem cents change the sign coefficient cologarithm cube root decimal degree denominator digits Divide dividend divisor equal EXAMPLES exponent Extracting the square Find the H. C. F. Find the number Find the sum Find the value following rule formulæ geometric progression greater Hence highest common factor last term less logarithm mantissa miles an hour monomial Multiplying negative number Note number of dollars number of terms partial fractions perfect square polynomial positive integer positive number proportion quadratic equation quotient radical sign ratio Reduce remainder result second term Solve the equation Solve the following square root Subtracting Transposing trial-divisor unknown quantities Whence x²y x²y² xy²
Δημοφιλή αποσπάσματα
Σελίδα 280 - In any proportion,, the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 132 - At what time between 3 and 4 o'clock are the hands of a watch opposite to each other ? Let x = the number of minute-spaces passed over by the minutehand from 3 o'clock to the required time. Then, since the hour-hand is 15 minute-spaces in advance of the minute-hand at 3 o'clock, x — 15 — 30, or x — 45, will represent the number of minute-spaces passed over by the hour-hand.
Σελίδα 41 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Σελίδα 132 - How far can he ride in a coach which travels 41 miles an hour, so as to return in time, walking back at the rate of 3| miles an hour ? 44.
Σελίδα 22 - From §§36 and 37, we have the following rule: To subtract one number from another, change the sign of the subtrahend, and add the result to the minuend.
Σελίδα 281 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 59 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (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 two, plus the square of the second.
Σελίδα 280 - In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth.
Σελίδα 161 - A certain sum of money at simple interest amounts in m years to a dollars, and in n years to b dollars. Required the sum and the rate of interest. 47. A...
Σελίδα 140 - If necessary, multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities in the resulting equations of equal absolute value.