2.5(4p-16) simplified
1 answer:
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Answer:
The matrix equation is
Step-by-step explanation:
* Lets change the story problem to equations
- The distance between the starting point and checkpoint 1 is x
- The distance between checkpoint 1 to checkpoint 2 is y
- The distance between checkpoint and the finish line is z
- The total distance for the race is 120 miles
∴ x + y + z = 120 ⇒ (1)
-The distance from the starting point to checkpoint 1 is 35 miles
more than half the distance from checkpoint 1 to checkpoint 2
∵ The distance from the starting point to checkpoint 1 is x
∵ The distance from checkpoint 1 to checkpoint 2 is y
- x is more than half y by 35
∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides
∴ x - (1/2) y = 35 ⇒ (2)
- The distance from checkpoint 2 to the finish line is 20 miles less
than twice the distance from checkpoint 1 to checkpoint 2
∵ The distance from checkpoint 2 to the finish line is z
∵ the distance from checkpoint 1 to checkpoint 2 is y
- z is less than twice y by 20
∴ z = 2y - 20 ⇒ add 20 to both sides
∴ z + 20 = 2y ⇒ subtract z from both sides
∴ 2y - z = 20 ⇒ (3)
* Now lets write the three equations
# x + y + z = 120 ⇒ (1)
# x - (1/2) y = 35 ⇒ (2)
# 2y - z = 20 ⇒ (3)
- Now lets write the matrix equation that models this situation
∴
9514 1404 393
Explanation:
We can find the slope by solving for y.
3x +2y +7 = 5x +3y +10
-2x -3 = y . . . . . . . . . . . . . add -5x-10-2y to both sides of the equation
In this form, the slope (m) is the coefficient of x, -2. Hence m = -2.
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<em>Alternate solution</em>
A graph of the equation shows it has an x-intercept of -1.5 and a y-intercept of -3. The slope (m) is then "rise" divided by "run", or ...
m = rise/run = -3/1.5
m = -2
