The student's algebra |
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Σελίδα 84
... lues of x and y . 4 Multiplying the first equation by 20 , 8x - 4y + 150 = 5x + 10y + 10 + 120 ; by transposition , 8x - 5x - 4y - 10y = 10 + 120-150 , or 3x - 14y = -20 . Multiplying the second equation by 12 , 144-3x - 3y = 2x + 6y + ...
... lues of x and y . 4 Multiplying the first equation by 20 , 8x - 4y + 150 = 5x + 10y + 10 + 120 ; by transposition , 8x - 5x - 4y - 10y = 10 + 120-150 , or 3x - 14y = -20 . Multiplying the second equation by 12 , 144-3x - 3y = 2x + 6y + ...
Σελίδα 87
... lues of x and y . 7 x + y 9. Given 3 ± y + 6 = 12 — y , 4 and + y + 13 = 2 + 13 = x + y + 4 , 3x + 2y 3x + 6 10. Given = 11 2x + 3y + 4 9 and 3 , S Ans . { x = 4 . y = 9 . Ans . { x = 9 . y = 3 . x = 4 . Ans . y = 5 . 11. Given 3x + 3 3x ...
... lues of x and y . 7 x + y 9. Given 3 ± y + 6 = 12 — y , 4 and + y + 13 = 2 + 13 = x + y + 4 , 3x + 2y 3x + 6 10. Given = 11 2x + 3y + 4 9 and 3 , S Ans . { x = 4 . y = 9 . Ans . { x = 9 . y = 3 . x = 4 . Ans . y = 5 . 11. Given 3x + 3 3x ...
Σελίδα 102
... = ± 4 , and y == ± 6 . 2 L2 8. Given x + y : x — y | :: 36 : 1 , and x2 - y2 = 24 , to find the va- lues of x and y . From the first equation , by Theorem 12 , x + y : g :: 6 : 1 ; Theorem 5 , 2x : 2y 7 : 5 ; 102 PURE QUADRATICS , & c .
... = ± 4 , and y == ± 6 . 2 L2 8. Given x + y : x — y | :: 36 : 1 , and x2 - y2 = 24 , to find the va- lues of x and y . From the first equation , by Theorem 12 , x + y : g :: 6 : 1 ; Theorem 5 , 2x : 2y 7 : 5 ; 102 PURE QUADRATICS , & c .
Σελίδα 105
... lues of x and y . Ans . { x = 3 . y = 2 . 9. Given x3 - y3 : x2y — xy2 :: 7 : 2 , to find the va- and x + y = 6 , lues of x & y . Ans . Sx = 4 or 2 . 10. Given 3 - y3 = 274 , 35 to find the values of x and xy - xy2 = 4 , and y Ans . ( x ...
... lues of x and y . Ans . { x = 3 . y = 2 . 9. Given x3 - y3 : x2y — xy2 :: 7 : 2 , to find the va- and x + y = 6 , lues of x & y . Ans . Sx = 4 or 2 . 10. Given 3 - y3 = 274 , 35 to find the values of x and xy - xy2 = 4 , and y Ans . ( x ...
Σελίδα 122
... lues of x . Ans . x = 9 , or -2 . 19. Given x2 - 6x + 2 = 3 , to find the values of x . Ans . x = 7 , or —1 . 1 20. Given lues of x . 3x + 1 × / 2x − 1 = 12 , to find the va- Ans . x = 5 , or 58 12 ' 5.x2-12 3x2 14x - 2x2 21. Given x + ...
... lues of x . Ans . x = 9 , or -2 . 19. Given x2 - 6x + 2 = 3 , to find the values of x . Ans . x = 7 , or —1 . 1 20. Given lues of x . 3x + 1 × / 2x − 1 = 12 , to find the va- Ans . x = 5 , or 58 12 ' 5.x2-12 3x2 14x - 2x2 21. Given x + ...
Συχνά εμφανιζόμενοι όροι και φράσεις
5th power added Algebra Algebraist answer the conditions arithmetical progression axiom bushels coefficient completing the square compound quantity cube root denominator difference digits dividend divisor equa EXAMPLES FOR PRACTICE extracting the root extracting the square find the values Find two numbers four numbers four quantities fourth power gained gallons geometrical progression given equation hence least common multiple lues miles multiplying this equation number of yards Pure Quadratics QUADRATIC EQUATIONS quan quantities be proportionals question quired quotient radical sign ratio remainder Required each person's Required the cube Required the length Required the number Required the price Required the sides Required the square second equation second term shillings Simple Equations simple quantity sold solution square root squaring each side substituting this value subtracted surd quantity Theorem third three numbers transposing transposition unknown quantity values of x vulgar fraction whence whole number yards of silk
Δημοφιλή αποσπάσματα
Σελίδα 13 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 11 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Σελίδα 14 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 79 - Prob. 3. Find two numbers, the greater of which shall be to the less, as their sum to 42 ; and as their difference to 6.
Σελίδα 13 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth...
Σελίδα 40 - Sib., his head weighs as much as his tail and half his body, and his body weighs as much as his head and his tail ; what is the whole weight of the fish ? . Aas.
Σελίδα 13 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 13 - Composition, when the sum of the first and second is to the second as the sum of...
Σελίδα 80 - A farmer with 28 bushels of barley at 2s. 4d. per bushel, would mix rye at 3 shillings per bushel, and wheat at 4 shillings per bushel, so that the whole mixture may consist of 100 bushels, and be worth 3s. 4d. per bushel. How many bushels of rye, and how many of wheat must he mix with the barley ? Ans.