Answer:
7.5 minutes
Step-by-step explanation:
Given
See attachment for complete question
Let
From the question, we have the following points
--- When he first sees it
--- 3 minutes later
First, we calculate the rate (m)
The discharge rate is 2/3 gallons per minute
To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons
To calculate time (t), we have:
Solve for t
It works well to put both equations in the same form. Here, we use "general form". Any common factors are removed from the numbers. The leading coefficient is positive.
The equations are inconsistent if the x and y coefficients have the same ratio but the constants are different. They are consistent otherwise.
1. 8x +y +4 = 0
.. 8x +y +4 = 0
"consistent" . . . . . and also "dependent"
2. 7x +2y +6 = 0
.. 7x +2y +1 = 0
"inconsistent"
3. x +y +3 = 0
.. x +y +3 = 0
"consistent" . . . . . and also "dependent"
4. x -2y -7 = 0
.. x +3y -7 = 0
"consistent" . . . . . (x, y) = (7, 0)
5. 2x -y +5 = 0
.. 2x -y -2 = 0
"inconsistent"
Answer: The proof is mentioned below.
Step-by-step explanation:
Here, Given : m∠AOC = 160° m∠AOD= (3x-10)° and m∠ DOC= (x+14)°
Prove: x= 39°
Statement Reason
1. m∠AOC = 160°, m∠AOD= (3x-10)° 1. Given
and m∠ DOC= (x+14)°
2. m∠AOD+m∠DOC=m∠AOC 2. Because OD divides ∠AOC
into ∠AOD and ∠DOC
3. (3x-10)° +(x+14)°= 160° 3. By substitution
4. 4x+4 = 160° 4. By equating like terms
5. 4x= 156° 5. By subtraction property
of equality
6. x= 39° 6. By division property of equality
