write the following using numbers, literally and signs of basics operations (1) 3 taken away from the quotient of x and y (2) 4 times x subracted from y
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Answer:
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Step-by-step explanation:
Write the following using literals, numbers and signs of basic operations:
(i) x increased by 12
(ii) y decreased by 7
(iii) The difference of a and b, when a > b
(iv) The product of x and y added to their sum
(v) One-third of x multiplied by the sum of a and b
(vi) 5 times x added to 7 times y
(vii) Sum of x and the quotient of y by 5
(viii) x taken away from 4
(ix) 2 less than the quotient of x by y
(x) x multiplied by itself
(xi) Twice x increased by y
(xii) Thrice x added to y squared
(xiii) x minus twice y
(xiv) x cubed less than y cubed
(xv) The quotient of x by 8 is multiplied by y
ANSWER:
(i) x increased by 12 is (x+12).
(ii) y decreased by 7 is (y-7).
(iii) The difference of a and b, when a>b is (a-b).
(iv) The product of x and y is xy.
The sum of x and y is (x+y).
So, product of x and y added to their sum is xy+(x+y).
(v) One third of x is
x
3
.
The sum of a and b is (a+b).
∴ One-third of x multiplied by the sum of a and b =
x
3
×(a+b)=
x(a+b)
3
(vi) 5 times x added to 7 times y = (5×x)+(7×y), which is equal to 5x+7y.
(vii) Sum of x and the quotient of y by 5 is x+
y
5
.
(viii) x taken away from 4 is (4-x).
(ix) 2 less than the quotient of x by y is
x
y
-2.
(x) x multiplied by itself is x×x=x2.
(xi) Twice x increased by y is (2×x)+y = 2x+y.
(xii) Thrice x added to y squared is (3×x)+(y×y)=3x+y2.
(xiii) x minus twice y is x-(2×y)=x-2y.
(xiv) x cubed less than y cubed is (y×y×y)-(x×x×x)=y3-x3.
(xv) The quotient of x by 8 is multiplied by y is
x
8
×y=
xy
8
.