Answer: The expression is 2x² - p³.
To find the values of x and y for which the expression is less than 30, we need to substitute the given values of x and y into the expression and then solve for p.
Let's consider each option:
A. x = 9 and y = 5
Expression = 2(9)² - p³ = 2(81) - p³ = 162 - p³
B. x = 4 and y = 1
Expression = 2(4)² - p³ = 2(16) - p³ = 32 - p³
C. x = 7 and y = 4
Expression = 2(7)² - p³ = 2(49) - p³ = 98 - p³
D. x = 5 and y = 3
Expression = 2(5)² - p³ = 2(25) - p³ = 50 - p³
We need the value of the expression to be less than 30, so we have the inequality:
Expression < 30
Now, let's compare each expression to 30:
A. 162 - p³ < 30
B. 32 - p³ < 30
C. 98 - p³ < 30
D. 50 - p³ < 30
To find the values of p that satisfy each inequality, we need to rearrange them and solve for p:
A. - p³ < 30 - 162
p³ < -132
p³ > 132
Since p³ is positive, we have: p > (132)^(1/3)
B. - p³ < 30 - 32
p³ < -2
p³ > 2
Since p³ is positive, we have: p > (2)^(1/3)
C. - p³ < 30 - 98
p³ < -68
p³ > 68
Since p³ is positive, we have: p > (68)^(1/3)
D. - p³ < 30 - 50
p³ < -20
p³ > 20
Since p³ is positive, we have: p > (20)^(1/3)
Now, let's find the values of (132)^(1/3), (2)^(1/3), (68)^(1/3), and (20)^(1/3):
(132)^(1/3) ≈ 5.282
(2)^(1/3) ≈ 1.260
(68)^(1/3) ≈ 4.132
(20)^(1/3) ≈ 2.714
So, the values of p satisfying each inequality are:
A. p > 5.282
B. p > 1.260
C. p > 4.132
D. p > 2.714
To summarize, for the expression 2x² - p³ to be less than 30, the value of p must be greater than 5.282, 1.260, 4.132, and 2.714. None of the given options satisfy all of these conditions, so none of the provided options are correct.