AlgebraVery hardRange of a coordinate inside a region
Algebra practice question
In the xy-plane, the point (k, 3) lies in the region where y > x and y < 2x. Which of the following gives all possible values of k?
- A. 1.5 < k < 3Correct
- B. k < 3
- C. k > 1.5
- D. 3 < k < 6
Answer: A. 1.5 < k < 3
y > x gives 3 > k, and y < 2x gives 3 < 2k, so k > 1.5. Together: 1.5 < k < 3.
Why the other answers are wrong
- B. k < 3
- Ignores the second inequality.
- C. k > 1.5
- Ignores the first inequality.
- D. 3 < k < 6
- Reverses both inequalities.
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.