Questions: Choose the correct values for A, B, C, and D that align like terms to find the sum vertically. 1.3 t^3 + 0.4 t^2 + (-24 t) + B + B + C + D A=(-0.6 t^2) B=(-8) C=18 t D=0 t^3 A=0 t^3 B=(-0.6 t^2) C=18 t D=(-8) A=0 t^3 B=(-0.6 t^2) C=(-8) D=18 t

Solution Steps

The first polynomial is: \[ 1.3 t^{3} + 0.4 t^{2} + (-24 t) \] The second polynomial is: \[ B + B + C + D \] We are given three options for the values of \( A, B, C, \) and \( D \).

To find the sum vertically, we need to align the terms of the same degree. The terms in the first polynomial are:

• \( 1.3 t^{3} \) (cubic term)
• \( 0.4 t^{2} \) (quadratic term)
• \( -24 t \) (linear term)

The second polynomial should have terms that align with these degrees. Therefore, we need to assign \( A, B, C, \) and \( D \) to the corresponding degrees:

• \( A \) should align with \( t^{3} \)
• \( B \) should align with \( t^{2} \)
• \( C \) should align with \( t \)
• \( D \) should align with the constant term

Let's evaluate each option to see which one aligns the terms correctly.

Option 1: \[ A = -0.6 t^{2}, \quad B = -8, \quad C = 18 t, \quad D = 0 t^{3} \]

• \( A = -0.6 t^{2} \) does not align with \( t^{3} \).
• \( B = -8 \) does not align with \( t^{2} \).
• \( C = 18 t \) aligns with \( t \).
• \( D = 0 t^{3} \) aligns with \( t^{3} \).

This option does not align the terms correctly.

Option 2: \[ A = 0 t^{3}, \quad B = -0.6 t^{2}, \quad C = 18 t, \quad D = -8 \]

• \( A = 0 t^{3} \) aligns with \( t^{3} \).
• \( B = -0.6 t^{2} \) aligns with \( t^{2} \).
• \( C = 18 t \) aligns with \( t \).
• \( D = -8 \) aligns with the constant term.

This option aligns the terms correctly.

Option 3: \[ A = 0 t^{3}, \quad B = -0.6 t^{2}, \quad C = -8, \quad D = 18 t \]

• \( A = 0 t^{3} \) aligns with \( t^{3} \).
• \( B = -0.6 t^{2} \) aligns with \( t^{2} \).
• \( C = -8 \) does not align with \( t \).
• \( D = 18 t \) aligns with \( t \).

This option does not align the terms correctly.

Final Answer