Mr. Grant needs 30 pieces of felt he can buy them in packs of 10 or as single pieces what are the different ways Mr Grant can bu
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<h3>Answer: (a - 1)(2a² + a + 2)</h3>
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Explanation:
Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2
Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.
If we tried say a = -1, then,
2a³-a²+a-2 = 2(-1)³-(-1)²+(-1)-2 = -6
The result is not zero, so a = -1 is not an actual root.
But if we tried say a = 1, then,
2a³-a²+a-2 = 2(1)³-1²+1-2 = 0
We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.
Since a = 1 is a root, this makes (a-1) to be a factor.
From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.
Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.
Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.
1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.
According to this theorem,
Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then
Take positive value x. You get
2. According to the previous theorem,
Then
Answer:
This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then
This means that you cannot find solutions of this equation. Then CD≠2 cm.