Perform the operation indicated, then place the answer in the proper location on the grid. The perimeter of a triangle is 7a - 1
1b. If two of its sides are 2a + b and a - 9b, what is the third side?
1 answer:
Answer: 4 a - 3 b
Step-by-step explanation:
Since, the perimeter of the triangle = sum of all the three side of the triangle.
Here, two sides of the triangle are 2a + b and a - 9b,
And, the perimeter of the triangle = 7 a - 11
Let third side = x
Therefore, 2 a + b + a - 9 b + x = 7 a - 11 b
⇒ 3 a - 8 b + x = 7 a - 11 b
⇒ x = 7 a - 11 b - 3 a + 8 b
⇒ x = 4 a - 3 b ( by operating like terms)
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Answer:
The interpolating polynomial is .
Step-by-step explanation:
We want to find a quadratic polynomial such that
,
and
. In order to do this let us write
.
Now, evaluating the polynomial in the points -1, 1 and 2 we get
This relations give us a linear system of equations:
where the ,
and
are the unknowns.
The augmented matrix of the system is
In this matrix it is easy to eliminate the 1's of the first column and get
From this matrix we can find the values of each unknown. Notice that the second row gives us that yields
.
Then, the third row means that gives
. So,
.
Finally, the first row is and substituting is
that yields
.
Therefore, the interpolating polynomial is
.