Answer: The answers are
Step-by-step explanation: Given in the question that Lana completed a 10-mile race in 90 minutes by running and walking both. She usually runs at a pace of 8.5 minutes per mile and walks at a pace of 12 minutes per mile. We need to find the number of minutes for which she ran and walk throughout the race.
Let, Lana runs for 'x' miles and walks for 'y' miles. Then, we have
Multiplying the first equation by 8.5 and subtracting from the second equation, we have
Therefore,
Thus, time for which Lana ran is
And, the time for which Lana walks is
Thus, the answers are
Answer:
f(x)=start fraction 4 over x squared End fraction minus start fraction 2 over x end fraction +1
Answer:
X=7
Step-by-step explanation:
4x-(2x-9)=23 simplified would be
4x-2x+9=23
2x+9=23
2x=14
X=7
Answer:
1/10
Step-by-step explanation:
To convert a ratio to a fraction, you divide the number on the left by the number on the right. This gets you (3/5)/6. When dividing fractions by whole numbers, you need to convert the whole number to a fraction. I converted 6 to 6/1, so that gave me (3/5)/(6/1). You then multiply the top number by the bottom number to get the numerator of the answer, and the middle 2 numbers multiplied is the denominator. The answer is (3x1)/(5x6), or 3/30, which can be simplified to 1/10.
Answer:
The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
Step-by-step explanation:
It is given that the coefficient of the matrix of a linear equation has a pivot position in every row.
It is provided by the Existence and Uniqueness theorem that linear system is said to be consistent when only the column in the rightmost of the matrix which is augmented is not a pivot column.
When the linear system is considered consistent, then every solution set consists of either unique solution where there will be no any variables which are free or infinitely many solutions, when there is at least one free variable. This explains why the system is consistent.
For any m x n augmented matrix of any system, if its co-efficient matrix has a pivot position in every row, then there will never be a row of the form [0 .... 0 b].