Which polynomial is equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x)?
<h3><u><em>
Answer:</em></u></h3>
The polynomial equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x) is ![x^3 + 2x^2 + x + 3](https://tex.z-dn.net/?f=x%5E3%20%2B%202x%5E2%20%2B%20x%20%2B%203)
<h3><u><em>Solution:</em></u></h3>
Given that two polynomials are:
and ![(x^3 - x^2 + 3x)](https://tex.z-dn.net/?f=%28x%5E3%20-%20x%5E2%20%2B%203x%29)
We have to find the result when
is subtracted from ![(x^3 - x^2 + 3x)](https://tex.z-dn.net/?f=%28x%5E3%20-%20x%5E2%20%2B%203x%29)
In basic arithmetic operations,
when "a" is subtracted from "b" , the result is b - a
Similarly,
When
is subtracted from
, the result is:
![\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)](https://tex.z-dn.net/?f=%5Crightarrow%20%28x%5E3%20-%20x%5E2%20%2B%203x%29%20-%20%28-3x%5E2%20%2B%202x%20-%203%29)
Let us solve the above expression
<em><u>There are two simple rules to remember: </u></em>
- When you multiply a negative number by a positive number then the product is always negative.
- When you multiply two negative numbers or two positive numbers then the product is always positive.
So the above expression becomes:
![\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3](https://tex.z-dn.net/?f=%5Crightarrow%20%28x%5E3%20-%20x%5E2%20%2B%203x%29%20%2B%203x%5E2%20-2x%20%2B%203)
Removing the brackets we get,
![\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3](https://tex.z-dn.net/?f=%5Crightarrow%20x%5E3%20-%20x%5E2%20%2B%203x%20%2B%203x%5E2%20-2x%20%2B%203)
Combining the like terms,
![\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3](https://tex.z-dn.net/?f=%5Crightarrow%20x%5E3%20-x%5E2%20%2B%203x%5E2%20%2B%203x%20-%202x%20%2B%203)
![\rightarrow x^3 + 2x^2 + x + 3](https://tex.z-dn.net/?f=%5Crightarrow%20x%5E3%20%2B%202x%5E2%20%2B%20x%20%2B%203)
Thus the resulting polynomial is found
The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees
<em><u>Solution:</u></em>
Given that exterior angle of triangle is 140 degrees
The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
Given that adjacent angles are congruent
Let one of the non adjacent interior angles be "x"
x + x = 140
2x = 140
x = 70
So the two interior angles are 70 degrees and 70 degrees
Let us find the third interior angle
The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees
70 + 70 + third angle = 180
third angle = 180 - 70 - 70
third angle = 180 - 140
third angle = 40 degrees
Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees
Answer:
oh 21
Step-by-step explanation:
1 times 12 is 12 and 3/4 times 12 is 36/4 =9. 9 plus 12 is 21
Answer:
Since C is the mid point,
therefore, (6x - 4)/2 = 4x-3
=> 6x - 4 = 2X(4x-3) = 8x - 6
=> 6x - 8x = -6 + 4
=> -2x = -2
=> x = (-2)/(-2) = 1
Hence, CD = AC = 4x - 3 = 4X1 - 3 = 1
Step-by-step explanation: