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ozzi
3 years ago
10

F(x) = x3 + 5x2 - x - 5 What are the factors of f(x)?

Mathematics
1 answer:
Inessa [10]3 years ago
4 0
Hello

x^3+5x²-x-5=x²(x+5)-1(x+5)
=(x+5)(x²-1)=(x+5)(x-1)(x+1)

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What is the equation of the line that is perpendicular to y= -3x + 1 and passes through (2,3)?
Aleonysh [2.5K]

Answer:

\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}

Step-by-step explanation:

\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).

\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}

3 0
3 years ago
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A farmer has a water tank for cows in the shape of a cylinder with a radius of 7 ft and a height of 3 ft. The tank comes equippe
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Answer:

volume of the tank be when the sensor turns on = 92.316 ft³

Step-by-step explanation:

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= 461.58 ft³

The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity.

volume of the tank be when the sensor turns on = 20% of Volume of a cylinder

= 0.20 * 461.58 ft³

= 92.316 ft³

volume of the tank be when the sensor turns on = 92.316 ft³

5 0
3 years ago
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