Answer:
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Step-by-step explanation:

The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42
<u>Using trial and error method we will find the first root of the polynomial.</u>
1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42
1 - 10 - 53 - 42 ≠ 0
Therefore 1 is not a root
-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42
- 1 - 10 + 53 - 42
53 - 53 = 0
Therefore - 1 is a root of the polynomial.
Therefore ( x + 1) is a factor.
<u>Now by long division or by using synthetic division we can find other factors.</u>
<u>Synthetic Division :</u>
-1 | 1 -10 -53 - 42
| 0 - 1 11 42
|______________________
1 - 11 - 42 0
Therefore ,
------ ( 1 )
<u>Next further factorize x² - 11x - 42</u>
x² - 11x - 42
= x² - 14x + 3x - 42
=x(x - 14) + 3 (x - 14)
=(x + 3 )(x - 14)
Therefore ,

Answer:

Step-by-step explanation:
<u>Right Triangle</u>
The figure shows a right triangle with angles 2 and 3 unknown.
The sum of the internal angles of all triangles is 180°, since one of them is 90°, then the sum of the rest of the angles is 90°. It means that:

The measures of both angles are expressed as functions of x. Substituting their values:
x+8 + 2x + 7 = 90
Simplifying:
3x + 15 = 90
Operating:
3x = 90 - 15 = 75
Solving:
x = 75 / 3 = 25
x = 25°
Now, the measure of angle 2=x+8 = 33°

The volume of the triangular prism is 5√3 cubic units if the height of the triangular prism is √3 units. Option (B) is correct.
<h3>
What is volume?</h3>
It is defined as a three-dimensional space enclosed by an object or thing.
We have a triangular prism shown in the picture with dimensions.
As we know, the volume of the triangular prism is given by:
V = bhl/2
h = √[2²- (2/2)²]
h = √(4-1)
h = √3 units
V = (2×√3×5)/2
V = 5√3 cubic units
Thus, the volume of the triangular prism is 5√3 cubic units if the height of the triangular prism is √3 units. Option (B) is correct.
Learn more about the volume here:
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Answer:
=12 units
Step-by-step explanation:
When a square is cut along one diagonal, it forms a right angled triangle whose legs are the sides of the square and the hypotenuse is the diagonal of the square.
Therefore, the Pythagoras theorem is used to find the hypotenuse.
a² + b² = c²
(6√2)²+(6√2)²=c²
72+72=c²
c²=144
c=√144
=12
The diagonals of the square measure 12 units each.