Casey's drill team squad was responsible for painting props for a performance at a band contest. The squad painted 18 props in 9
1 answer:
Answer: They would paint 36 props in 3 hours.
Step-by-step explanation:
Given: The squad painted 18 props in 90 minutes.
Time taken to paint each prop =
= 5 minutes
Now, 1 hour = 60 minutes
3 hours = 3 x 60 minute = 180 minutes
Total props painted in 3 hours = (180 )÷5
= 36
Hence, with same rate , they would paint 36 props in 3 hours.
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We have that
Let y be the first root, then y - 6 will be the second one. Since both roots make the quadratic equation equal to 0, we have that:
Solve for y:
Plug in y = 5/2 into original quadratic equation and solve for c:
So, the answer is c = -35/4
Let y be the first root, then y - 6 will be the second one. Since both roots make the quadratic equation equal to 0, we have that:
Solve for y:
Plug in y = 5/2 into original quadratic equation and solve for c:
So, the answer is c = -35/4
Answer:
a)
Reduced Row Echelon:
Solution to the system:
b)
Reduced Row Echelon:
Solution to the system:
x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.
Step-by-step explanation:
To find the reduced row echelon form of the matrices, let's use the Gaussian-Jordan elimination process, which consists of taking the matrix and performing a series of row operations. For notation, R_i will be the transformed column, and r_i the unchanged one.
a)
Step by step operations:
1. Reorder the rows, interchange Row 1 with Row 2, then apply the next operations on the new rows:
Resulting matrix:
2. Set the first row to 1
Resulting matrix:
3. Write the system of equations:
Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:
b)
1.
Resulting matrix:
2. Write the system of equations:
Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:
x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.