Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker needs to pass

Question

Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker needs to pass two checkpoints before completing a race. The total distance for the race is 120 miles. The distance from the starting point to checkpoint 1 is 35 miles more than half the distance from checkpoint 1 to checkpoint 2. The distance from checkpoint 2 to the finish line is 20 miles less than twice the distance from checkpoint 1 to checkpoint 2. Let x represent the distance from the starting point to checkpoint 1, y represent the distance from checkpoint 1 to checkpoint 2, and z represent the distance from checkpoint 2 to the finish line. Complete the matrix equation that models this situation, A-1B = X.

in progress 0
Savannah 1 week 2021-10-11T20:10:42+00:00 2 Answers 0

Answers ( )

    0
    2021-10-11T20:11:47+00:00

    These are the options:

    0
    2021-10-11T20:11:59+00:00

    Answer:

    The matrix equation is \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

    Step-by-step explanation:

    * Lets change the story problem to equations

    – The distance between the starting point and checkpoint 1 is x

    – The distance between checkpoint 1 to checkpoint 2 is y

    – The distance between checkpoint and the finish line is z

    – The total distance for the race is 120 miles

    ∴ x + y + z = 120 ⇒ (1)

    -The distance from the starting point to checkpoint 1 is 35 miles

     more than half the distance from checkpoint 1 to checkpoint 2

    ∵ The distance from the starting point to checkpoint 1 is x

    ∵ The distance from checkpoint 1 to checkpoint 2 is y

    – x is more than half y by 35

    ∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides

    ∴ x – (1/2) y = 35 ⇒ (2)

    – The distance from checkpoint 2 to the finish line is 20 miles less

     than twice the distance from checkpoint 1 to checkpoint 2

    ∵ The distance from checkpoint 2 to the finish line is z

    ∵ the distance from checkpoint 1 to checkpoint 2 is y

    – z is less than twice y by 20

    ∴ z = 2y – 20 ⇒ add 20 to both sides

    ∴ z + 20 = 2y ⇒ subtract z from both sides

    ∴ 2y – z = 20 ⇒ (3)

    * Now lets write the three equations

    # x + y + z = 120 ⇒ (1)

    # x – (1/2) y = 35 ⇒ (2)

    # 2y – z = 20 ⇒ (3)

    – Now lets write the matrix equation that models this situation

    \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )