The answers are 
and 8 · 8 · 8
Explanation:
The volume of a cube or space a cube occupies is calculated by multiplying the length, height, and width. Additionally, because in a cube all sides are equal in length, the formula for volume is V= 
. According to this, if the side length is 8 inches the volume can be represented as 
or V= 8 · 8 · 8 because the symbol · represents multiplication. Also, this can be solved as V = 512 cubic inches. This makes the following options correct: and 8 · 8 · 8.
Answer:
an = 4n +5
Step-by-step explanation:
First we need to find a common difference
d = a2-a1 = 13-9 = 4
The formula for an
an =a1+d(n-1)
an = 9 + 4(n-1)
Distributing
an = 9+4n-4
Combine like terms
an = 4n +5
Answer:
4) VW= 23
5) VW= 12
6) VW= 75
Step-by-step explanation:
4)
VU= 31
WU= 8
subtract 8 from 31
VW= 23
5)
UW= 18
UV= 6
subtract 6 from 18
VW= 12
6)
UV= 30
WU=45
add 30 and 45
VW= 75
Question 14, Part (i)
Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,
A+B+C+D = 360
A+90+C+90 = 360
A+C+180 = 360
A+C = 360-180
A+C = 180
Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.
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Question 14, Part (ii)
Let
x = measure of angle 1
y = measure of angle 2
z = measure of angle 3
Back in part (i) above, we showed that y + z = 180
Note that angles 1 and 2 are adjacent to form a straight line, so we can say
x+y = 180
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We have the two equations x+y = 180 and y+z = 180 to form this system of equations
Which is really the same as this system
The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.
