(i) 4p+7 = 4(-2)+7 = -8+7 = -1 [putting p = -2]
(ii) -3p2 + 4p+7 = -3(-2)2+4(-2)+7 = -3×4-8+7 = -12-8+7 = -20+7 = -13 [putting p = -2]
(iii) -2p3-3p2+4p+7 = -2(-2)3-3(-2)2+4(-2)+7 = -2×(-8)-3×4-8+7 = 16-12-8+7 = -20+23 = 3 [putting p = -2]
If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)
Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30