What percent of 100 is 14
2 answers:
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The volume of a cuboid is given by length × width × height
We have:
Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x
Substituting these into the formula, we have:
7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6
Drawing the graph is one way of finding the solution (refer to the graph below):
We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8
Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft
Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches
Answer: x = 9.6 inches
We have:
Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x
Substituting these into the formula, we have:
7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6
Drawing the graph is one way of finding the solution (refer to the graph below):
We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8
Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft
Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches
Answer: x = 9.6 inches
Answer: Any real number x as long as and
In other words, anything but 0 or -2/3 is valid.
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Explanation:
Set the denominator equal to zero and solve for x
2(3x^2 + 2x) = 0
3x^2 + 2x = 0
x(3x + 2) = 0
x = 0 or 3x+2 = 0 .... zero product property
x = 0 or 3x = -2
x = 0 or x = -2/3
If either x = 0 or x = -2/3, then the denominator 2(3x^2 + 2x) will be zero. But recall that we cannot have zero in the denominator. Dividing by zero is not allowed. The expression is undefined when we divide by zero.
Therefore, we must exclude x = 0 and x = -2/3 from the domain. Any other real number is valid as an x input.