Algebra for BeginnersMacmillan, 1895 - 188 σελίδες |
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Σελίδα 51
... expression 2a3b2 + 3ab1 + 3a2b2x − x5 + 20a2b3 - 11a1 + 7a3b2 , which terms are like , and which are homogeneous ? 18. In each term of the expression ... SIMPLE EQUATIONS . 71. AN equation asserts VIII . ] 51 REVISION OF ELEMENTARY RULES .
... expression 2a3b2 + 3ab1 + 3a2b2x − x5 + 20a2b3 - 11a1 + 7a3b2 , which terms are like , and which are homogeneous ? 18. In each term of the expression ... SIMPLE EQUATIONS . 71. AN equation asserts VIII . ] 51 REVISION OF ELEMENTARY RULES .
Σελίδα 52
... equation , The value so found is called the root or the solution of the equation . 74. An equation which involves the unknown quantity in the first degree is called a simple equation . It is usual to denote the unknown quantity by the ...
... equation , The value so found is called the root or the solution of the equation . 74. An equation which involves the unknown quantity in the first degree is called a simple equation . It is usual to denote the unknown quantity by the ...
Σελίδα 53
... equation . Dividing both sides by 7 we get Similarly , if x = 2 , - = - 6 , х 2 multiplying both sides by 2 , we get x = -12 , [ Axiom 4 ] . [ Axiom 3 ] . Again , in the equation 7x - 2x - x = 23 + 15-10 , by ... SIMPLE EQUATIONS .
... equation . Dividing both sides by 7 we get Similarly , if x = 2 , - = - 6 , х 2 multiplying both sides by 2 , we get x = -12 , [ Axiom 4 ] . [ Axiom 3 ] . Again , in the equation 7x - 2x - x = 23 + 15-10 , by ... SIMPLE EQUATIONS .
Σελίδα 54
... equation of fractional coefficients . This can always be done by multiplying both sides of the equation by the least ... simple equations we have only to show that when we substitute the value of x in the two sides of the equation we ...
... equation of fractional coefficients . This can always be done by multiplying both sides of the equation by the least ... simple equations we have only to show that when we substitute the value of x in the two sides of the equation we ...
Σελίδα 55
... equation ( x + 1 ) ( 2x - 1 ) - 5x = ( 2x - 3 ) ( x − 5 ) +47 . When x = 7 , the left side ( x + 1 ) ( 2x − 1 ) − 5x - = ( 7 + 1 ) ( 14-1 ) -35 = ( 8 x 13 ) - 35 = 69 . The right side ( 2x - 3 ) ( x - 5 ) +47 = ( 14 ... SIMPLE EQUATIONS .
... equation ( x + 1 ) ( 2x - 1 ) - 5x = ( 2x - 3 ) ( x − 5 ) +47 . When x = 7 , the left side ( x + 1 ) ( 2x − 1 ) − 5x - = ( 7 + 1 ) ( 14-1 ) -35 = ( 8 x 13 ) - 35 = 69 . The right side ( 2x - 3 ) ( x - 5 ) +47 = ( 14 ... SIMPLE 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.