Answer:
Daniel
Step-by-step explanation:
Daniel ran 5000/40=500=4=125 meters in 1 minutes
Andy ran 4550/37=122.9729... some less than 123 meters in second
Daniel was faster than Andy
2x3x5=30
3 is from the amount of sides in the triangle
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:
(simplified form)
Step-by-step explanation:
I is the total length of all the 5 rods.
Each of the 5 parts lengths are
, respectively.
<em>We add all of them and equate it to I:</em>

<em>Simplifying this, we take like terms and add:</em>
<em>
</em>
Answer: the number of multiple choice questions in the test is 12.
the number of short response questions in the test is 8.
Step-by-step explanation:
Let x represent the number of multiple choice questions in the test.
Let y represent the number of short response questions in the test.
The total number of questions in the test is 20. It means that
x + y = 20
The multiple choice questions are worth 3 points each and the short response question are worth 8 points each. The total number of points is 100. It means that
3x + 8y = 100 - - - - - - - - - - 1
Substituting x = 20 - y into equation 1, it becomes
3(20 - y) + 8y = 100
60 - 3y + 8y = 100
- 3y + 8y = 100 - 60
5y = 40
y = 40/5 = 8
x = 20 - y = 20 - 8
x = 12