Answer:
Option C) 4 cubic inches is the volume of the rectangular prism.
Step-by-step explanation:
It is given that, 108 cubes with an edge length of 1/3 inch are needed to fill a rectangular prism.
Therefore, the volume of the rectangular prism is equal to the volume of the 108 cubes needed to fill that rectangular prism.
So, we need to find out the volume of those 108 cubes in order to find the volume of the rectangular prism.
The formula for finding the volume of a cube is given by,
Volume of a cube = a³
where a represents the edge length
We know that, the edge length is 1/3 inch.
⇒ a = 1/3
Volume of a cube = (1/3)³
⇒ 1/3 × 1/3 × 1/3
⇒ 1/27 cubic inches
To find the volume of 108 cubes :
⇒ 108 × volume of one cube
⇒ 108 × 1/27
⇒ 4 cubic inches.
∴ The volume of 108 cubes is the volume of rectangular prism which is 4 cubic inches (option C)
Answer:
135/1000
27/200
Step-by-step explanation:
Step-by-step explanation:
I guess method 1 means to deal with whole factors.
x + 5 = (x - 2)(x + 5)
for (x + 5) <> 0 we can divide both sides by this factor :
1 = x - 2
x = 3
for the second solution we deal with
x + 5 = 0
x = -5
so, for x = -5 and x = 3 both functions deliver the same output, and these are the intersection points.
method 2 : we multiply the expression out and solve it then
x + 5 = (x - 2)(x + 5)
x + 5 = x² + 5x - 2x - 10 = x² + 3x - 10
0 = x² + 2x - 15
the general solution to such a square equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -15
x = (-2 ± sqrt(2² - 4×1×-15))/(2×1) =
= (-2 ± sqrt(4 + 60))/2 = (-2 ± sqrt(64))/2 = (-2 ± 8)/2 =
= -1 ± 4
x1 = -1 + 4 = 3
x2 = -1 - 4 = -5
and you get the 2 solutions again. as expected, they are the same as with method 1, of course.
Answer:
Option E
Step-by-step explanation:
We know that
√25 = 5
√36 = 5
√30 lies between √25 and √36.(5 and 6l
Hence, Option E is correct
Answer:
113 degrees
Step-by-step explanation:
Two angles are called supplementary when they add up to 180 degrees
