AlgebraVery hardArea of a region defined by three inequalities
Algebra practice question
In the xy-plane, the region satisfying y ≥ 2x − 4, y ≤ 4, and x ≥ 0 is a triangle. What is its area?
Answer: 16
The vertices are (0, −4), (0, 4), and (4, 4). The vertical side has length 8 and the horizontal side has length 4, so the area is (1/2)(8)(4) = 16.
Common wrong answers
- If you answered 8
- 8 uses a base of 4 and a height of 4.
- If you answered 12
- 12 uses a height of 3.
- If you answered 32
- 32 forgets the half.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.