Find the midpoint of (9,2) and (-7,-9)
1 answer:
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Answer:
<em>Answers below</em>
Step-by-step explanation:
<u>Equation</u>
Let's call:
p = number of pennies Janesa has in her pocket
n = number of nickels Janesa has in her pocket
She has 24 coins in total, thus:
Since each penny is worth $0.01 and each nickel is worth $0.05, and Janesa has $1 in total:
Multiplying by 100:
A. Completing the equation:
B.
From [1]:
Substituting into [2]:
Simplifying:
Rearranging:
B. There are 5 pennies in Janesa's pocket
C. Since each penny is worth $0.01, the total value of pennies is 5*$0.01=$0.05
The total value of the pennies is $0.05
D. The total value of the nickels is 19*$0.05 = $0.95
E. Jackson should say she has 19 nickels and 5 pennies
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.)