Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
second equation:
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Answer:
x = 6
Step-by-step explanation:
3(x - 4) = 12 - 2(x - 3)
3x - 12 = 12 - 2x + 6
3x - 12 = 18 - 2x
+2x + 2x
5x -12 = 18
+ 12 +12
5x = 30
x = 6
If this answer is correct, please make me Brainliest!
Answer:
School District pays $42 less to substitute teacher than Mr. Dietz.
Step-by-step explanation:
Given:
Salary of Mr. Dietz per year = $22570
Number of days in a year = 185 days.
Amount paid for Substitute teacher per day = $80
We need to find the Amount less paid to substitute teacher then Mr Dietz when Mr. Dietz takes a day off.
Solution:
First we will find the Amount paid for per day of Mr. Dietz.
Amount paid for per day of Mr. Dietz can be calculated by dividing Salary of Mr. Dietz per year with Number of days in a year.
framing in equation form we get;
Amount paid for per day of Mr. Dietz = 
Now we will find Amount less paid to substitute teacher then Mr Dietz.
Amount less paid to substitute teacher then Mr Dietz can be calculated by subtracting the Amount paid for Substitute teacher per day from Amount paid for per day of Mr. Dietz.
framing in equation form we get;
Amount paid for Substitute teacher per day = $122 - $80 = $42
Hence School District pays $42 less to substitute teacher than Mr. Dietz.
80 * 3.5 = 280
she travels around 280km in 3.5 hours.
Answer:
the probability of getting the exact coins that make $0.15 is 33.3% (1/3)
Step-by-step explanation:
