Where 1/4 represents Bob and 1/6 represents Ted...
1/4x + 1/6x = 1
Multiply the two so there is no fraction by the GCF of 12.
3x + 2x = 12
Add 3x and 2x.
5x = 12
Divide by 5.
x = 12
Plug this value in.
With that, the answer is 2 hours and 24 minutes with x = 12 meaning 144 minutes.
The smallest amount of points at which they could intersect is 2.
<h3>
Answer:</h3>
(-4, 15), (1.5, 4)
<h3>
Step-by-step explanation:</h3>
This is easily solved using a graphing calculator. (See attached.)
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Algebraically, the solution is found by equating the expressions for y:
... -2x +7 = y = 2x² +3x -5
... 2x² +5x -12 = 0 . . . . rearranged to standard form
... (2x -3)(x +4) = 0 . . . . factor
The x-values of the points of intersection are those that make these factors be zero:
... 2x-3 = 0 ⇒ x = 3/2
... x+4 = 0 ⇒ x = -4
The linear equation is the easiest to use to find the corresponding y-values.
... for x = 3/2, y = -2(3/2) +7 = 4
... for x = -4, y = -2(-4) +7 = 15
The points of intersection are (-4, 15) and (3/2, 4).