Answer:
Step-by-step explanation:
length * width * height = 1050 cubic ft
(10x + 5)* (2x -1) * (x +3) = 1050
(10x + 5 )(2x-1) = 10x*(2x - 1) + 5*(2x -1)
= 10x*2x - 10x*1 + 5*2x - 1*5
= 20x² - 10x + 10x - 5 = 20x² - 5
(10x + 5)(2x -1)(x+3) = (20x² -5) *(x + 3)
=20x²*(x +3) - 5*(x +3)
= 20x³ + 60x² - 5x - 15
20x³ + 60x² - 5x - 15 = 1050
20x³ + 60x² - 5x - 15 - 1050 = 0
20x³ + 60x² - 5x - 1065 = 0
By trial and error method , (x -3 ) is a factor
Synthetic method:
3 ( 20 60 -5 -1065
( 60 360 1065
20 120 355 0
20x² + 120x + 355 = 0
Divide the equation by 5
4x² + 24x + 71 = 0 . Solving this equation gives imaginary number. So, ignore these values.
So, value of x = 3
height = 3+ 3 = 6 ft
Length = 10*3 + 5 = 30 + 5 = 35ft
Width = 2x - 1 = 2*3 - 1 = 6 - 1 = 5 ft
Check: length * width * height = 35 * 5 * 6 = 1050 cubic ft
The sum of interior angles of a triangle is always* 180°, so the following triangles are possible:
- 90°, 40°, 50°
- 82°, 38°, 60°
- 59°, 31°, 90°
_____
The following are not possible triangles.
- 65°, 25°, 75° — add to 165° ≠ 180°
- 57°, 70°, 33° — add to 160° ≠ 180°
_____
* in plane Euclidean geometry. There are other topologies such that the sum of angles of a triangle differs from 180°.
Answer:
D
Step-by-step explanation:
108+31= 139
180-139= 41
In order to factor a value out of an expression we must divide each term by this value, so ((1/3)*y - 3/2)/-(1/3) = (-1/3)*(-y + 9/2)
Answer:
D
Step-by-step explanation:
square root of 26 is about 5 and the square root of 106 is about 10
