Deshaun made 143 for 11 hours of work. At the same rate, how much would he make for 9 hours of work?
2 answers:
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(See the imagine for reference)
Let’s solve where they have a triangle, so the height is 9 cm, the base is 3 cm:
1/2 • 9 • 3 = 13.5
Since there’s 2 triangles we do:
13.5(2) = 27
Now the rectangle in the middle, where the height is 9cm and the base is 12cm:
12 • 9 = 108
Add up the areas:
108 + 27 = 135
Let’s solve where they have a triangle, so the height is 9 cm, the base is 3 cm:
1/2 • 9 • 3 = 13.5
Since there’s 2 triangles we do:
13.5(2) = 27
Now the rectangle in the middle, where the height is 9cm and the base is 12cm:
12 • 9 = 108
Add up the areas:
108 + 27 = 135
9514 1404 393
Answer:
A. 3×3
B. [0, 1, 5]
C. (rows, columns) = (# equations, # variables) for matrix A; vector x remains unchanged; vector b has a row for each equation.
Step-by-step explanation:
A. The matrix A has a row for each equation and a column for each variable. The entries in each column of a given row are the coefficients of the corresponding variable in the equation the row represents. If the variable is missing, its coefficient is zero.
This system of equations has 3 equations in 3 variables, so matrix A has dimensions ...
A dimensions = (rows, columns) = (# equations, # variables) = (3, 3)
Matrix A is 3×3.
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B. The second row of A represents the second equation:
The coefficients of the variables are 0, 1, 5. These are the entries in row 2 of matrix A.
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C. As stated in part A, the size of matrix A will match the number of equations and variables in the system. If the number of variables remains the same, the number of rows of A (and b) will reflect the number of equations. (The number of columns of A (and rows of x) will reflect the number of variables.)