In the following expression, both A and B are variables that can take positive values.A(B)(B+2)Which of these actions will cause the expression's value to increase?Choose 2 answers:A). Keeping A constant and increasing BB). Keeping A constant and decreasing BC). Increasing A and keeping B constantD). Decreasing A and keeping B constant
Q. In the following expression, both A and B are variables that can take positive values.A(B)(B+2)Which of these actions will cause the expression's value to increase?Choose 2 answers:A). Keeping A constant and increasing BB). Keeping A constant and decreasing BC). Increasing A and keeping B constantD). Decreasing A and keeping B constant
Analyze Expression AB(B+2): First, let's analyze the expression AB(B+2). This expression means A raised to the power of B, multiplied by (B+2). To understand how changes in A or B affect the expression, we need to consider how each component behaves.
Option A: Increase B: Consider option A: Keeping A constant and increasing B. Increasing B will increase the exponent B in AB, making AB larger since A > 1. Also, (B+2) increases as B increases, thus the entire expression A(B)(B+2) increases.
Option B: Decrease B: Now, look at option B: Keeping A constant and decreasing B. Decreasing B will decrease the exponent in AB, making AB smaller since A > 1. Also, (B+2) decreases as B decreases, thus the entire expression AB(B+2) decreases.
Option C: Increase A: Consider option C: Increasing A and keeping B constant. Increasing A while B remains constant will increase the value of AB, as the base of the exponentiation is getting larger. Since (B+2) remains constant, the overall expression A(B)(B+2) increases.
Option D: Decrease A: Finally, examine option D: Decreasing A and keeping B constant. Decreasing A while B remains constant will decrease the value of AB, as the base of the exponentiation is getting smaller. Since (B+2) remains constant, the overall expression A(B)(B+2) decreases.