Answer:
The constant of proportionality is:
Step-by-step explanation:
We know that when y varies directly with x, we get
y ∝ x
y = kx
k = y/x
where 'k' is called the constant of proportionality
From the graph, it is clear that the point (2/5, 1/2) passes through the line which represents the direct relationship.
so we have the point (2/5, 1/2), and
x = 2/5
y = 1/2
so substituting x = 2/5 and y = 1/2 in the equation
k = y/x
k = [1/2] / [2/5]
k = [1 × 5 ] / [2 × 2 ]
k = 5/4
Therefore, the constant of proportionality is:
If his best time is x, and the best time is smaller, then (1+1/3)*x=his second best time. If x+4=his second best time (since his second best time is 4 seconds slower), then (1+1/3)*x=x+4. Multiplying it out, we get (3/3+1/3)*x=x+4
=4x/3=x+4. Subtracting x from both sides, we get 4x/3-3x/3=x/3=4. Multiplying both sides by 3, we get x=12=his best time
9514 1404 393
Answer:
y > 1/2x + 2
Step-by-step explanation:
The points shown on the line are separated by a "rise" of 1 unit vertically, and a "run" of 2 units horizontally. Its slope is rise/run = 1/2.
The line crosses the y-axis at y=2, so the y-intercept is 2.
The boundary line is then ...
y = mx + b . . . . . . . where the slope is m and the y-intercept is b
y = 1/2x + 2 . . . . . . the equation of the boundary line
__
The line is dashed, and the shaded area is above the line, where y-values are greater than the y-value on the line. Then the y-values on the line are NOT included in the solution set. The inequality is ...
y > 1/2x + 2
19 - (1 - 4x) - 9x + 30 = -5x+48
(Don't forget the negativity symbol before the answer, if it isn't visible. It's not fully visible on my screen.)
