Algebra for BeginnersMacmillan, 1895 - 188 σελίδες |
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Σελίδα 25
... substitution where some of the symbols denote negative quantities . Example 1. If a = -4 , find the value of a3 . Here a3 = ( -4 ) 3 = ( − 4 ) × ( − 4 ) × ( − 4 ) : - 64 . - = By repeated applications of the rule of signs it may ...
... substitution where some of the symbols denote negative quantities . Example 1. If a = -4 , find the value of a3 . Here a3 = ( -4 ) 3 = ( − 4 ) × ( − 4 ) × ( − 4 ) : - 64 . - = By repeated applications of the rule of signs it may ...
Σελίδα 54
... . In the case of simple equations we have only to show that when we substitute the value of x in the two sides of the equation we obtain the same result . Example . To show that x = 7 satisfies the 54 [ CHAP . ALGEBRA .
... . In the case of simple equations we have only to show that when we substitute the value of x in the two sides of the equation we obtain the same result . Example . To show that x = 7 satisfies the 54 [ CHAP . ALGEBRA .
Σελίδα 78
... substitute this value of y in either of the given equations . Thus from ( 1 ) , and 3x + 21 = 27 ; .. x = 2 , y = 3. √ Note . When one of the unknowns has been found , it is immaterial which of the equations we use to complete the ...
... substitute this value of y in either of the given equations . Thus from ( 1 ) , and 3x + 21 = 27 ; .. x = 2 , y = 3. √ Note . When one of the unknowns has been found , it is immaterial which of the equations we use to complete the ...
Σελίδα 79
... Substitute this value in ( 1 ) , :: 35 + 2y = 47 ; .. y = 6 , Note . Add when the coefficients of one unknown are equal and unlike in sign ; subtract when the coefficients are equal and like in sign . Elimination by Substitution ...
... Substitute this value in ( 1 ) , :: 35 + 2y = 47 ; .. y = 6 , Note . Add when the coefficients of one unknown are equal and unlike in sign ; subtract when the coefficients are equal and like in sign . Elimination by Substitution ...
Σελίδα 83
... ( 2 ) and ( 3 ) , we have and from ( 1 ) 21x + 4y = 282 ; 12x - 4y = 48 ; ( 1 ) . ( 2 ) . ( 3 ) . whence x = 10 , y = 18. Also by substitution in ( 2 ) we obtain z = 14 . EXAMPLES XIII . c . 10 . = x - XIII . ] 83 SIMULTANEOUS EQUATIONS .
... ( 2 ) and ( 3 ) , we have and from ( 1 ) 21x + 4y = 282 ; 12x - 4y = 48 ; ( 1 ) . ( 2 ) . ( 3 ) . whence x = 10 , y = 18. Also by substitution in ( 2 ) we obtain z = 14 . EXAMPLES XIII . c . 10 . = x - XIII . ] 83 SIMULTANEOUS EQUATIONS .
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+b² acres algebraical sum Arithmetic arranged beginner cents CHAPTER coefficient Completing the square compound expressions convenient cube root descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII exceeds Find the highest Find the lowest find the number Find the product Find the square Find the sum find the value following expressions given expressions half-dollars Hence highest common factor lowest common denominator lowest common multiple lowest terms miles an hour miles per hour minute-hand Multiply negative numerator and denominator obtain quadratic equation quotient Reduce to lowest remainder removing brackets Resolve into factors result rule of signs side simple equation simultaneous equations Solve the equations square root Subtract Transposing trinomial unknown quantities walk whence write yards α α
Δημοφιλή αποσπάσματα
Σελίδα 91 - The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal to the square of the first plus twice the product of the first by the second, plus the square of the second.
Σελίδα 107 - Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Σελίδα 89 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Σελίδα 54 - Transpose all the terms containing the unknown quantity to one side of the equation, and the "known quantities to the other.