What do you mean this sentence?
the time a pump takes to drain the pool varies inversely with the power in watts of the pump,
The meaning would be : if we have a power in watts greater the time to drag the pool will be less because the relation between power and time is inverse.
40 watts--------------5 hours)
100 watts------------ x
because the relation between power and time is inverse, we multiply directly.
40 watts(5 hours)=100 watts x
x=(200 watts hours) / 100 watts=2 hours.
Answer: the time would be 2 hours. (the new pump is faster)
Complete question :
A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?
1) 2 1/2 feet
2) 3 feet
4) 5 feet
5) 8 1/2 feet
Answer:
2.5
Step-by-step explanation:
Solving for X in the perimeter equation :
2[(12+2x)+15+2x)]=74
Open the bracket
2[(12 + 2x + 15 + 2x)] = 74
2(27 + 4x) = 74
54 + 8x = 74
8x = 74 - 54
8x = 20
x = 20/8
x = 2.5
Hence, width fo border = 2.5
The intercepts and the graph on your worksheet are not correct. Please see below for details:
has solutions at x=-1 and x=3 (use the quadratic formula to solve). That means these are the x-intercepts, namely points:
(-1,0) and (3,0).
The y-intercept comes from setting x=0 and calculating the y value:
so the y-intercept is (0,-3).
Now to the graph: Based on the form of the function we can see this is a quadratic function and its graph will be a parabola. You can reformat the expression in the following form
and that will indicate that the apex of the parabola (open up) will be at the point (1,-4).
Knowing the apex, the x intercepts, and the y intercept, we can graph it now.
Graph is in the image attached.
1/3 or 5/6
Lets make the fractions into decimals. To make a fraction into decimal you have to divide the numerator by the denominator. The numerator is the top part of a fraction and the denominator is the bottom part of the fraction.
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Calculations
1/3
1 ÷ 3 = 0.3333....
5/6
5 ÷ 6 = 0.83333...
0.83333... is greater then 0.3333.....
Therefore 5/6 is greater then 1/3
1/3 is smaller then 5/6
