The answer is x = 2a^3 - 3a
Original Figure:
Length = 15
Width = 5
Height = 10
Volume = Length*Width*Height
Volume = 15*5*10
Volume = 750
New Figure
Length = 3
Width = 1
Height = 2
Each dimension has been divided by 5 (eg: 15/5 = 3)
Volume = Length*Width*Height
Volume = 3*1*2
Volume = 6
The old volume was 750 and it changes to 6
Notice how 750/6 = 125
Which can be rearranged to 750/125 = 6
Answer: if you divide the old volume by 125, then you get the new volume
Note: the new volume is 125 times smaller than the old volume
Put another way, the old volume is 125 times larger compared to the new volume
The fact that 125 = 5^3 is not a coincidence. If you divide each dimension by some number k, then you divide the volume by k^3
Answer:
C. (3,2)
Step-by-step explanation:
to begin the substitution method, we can begin by substituting the answer choice value into the given system or equations to determine if the values make the equation true.
the first choice is (2,1)
3(2) + 2(1) = 13
6 + 2 is not equal to 13. Therefore this answer choice is incorrect.
second choice (1,2)
3(1) + 2(2) = 13
3 + 4 is not equal to 13. This answer is also incorrect.
third choice (3,2)
3(3) + 2(2)
9 + 4 = 13 is true!
we can also substitute these x and y values for the equation underneath:
y = x - 1
2 = 3 - 1
2 = 2 is true! Therefore, C. (3,2) is correct!
Answer:
The solution of the equation are x = - 1 , y = 0 and z = 3
Step-by-step explanation:
Given three linear equation as :
6 x - y + z = - 3 ......A
4 x - 3 z = - 13 ......B
2 y + 5 z = 15 ......C
Solving eq A and C
I.e 2× (6 x - y + z ) = -3 ×2
or, 12 x - 2 y + 2 z = - 6
So, ( 12 x - 2 y + 2 z ) + ( 2 y + 5 z) = - 6 + 15
Or, 12 x + 7 z = 9 ......D
Solving eq B and D
I.e 3 × ( 4 x - 3 z ) = - 13 × 3
or, 12 x - 9 z = - 39
So, ( 12 x + 7 z ) - ( 12 x - 9 z ) = 9 + 39
or, 16 z = 48
∴ z =
i.e z = 3
put the value of z in eq D
So, 12 x + 7×3 = 9
Or, 12 x = 9 - 21
or, 12 x = - 12
∴ x = -
I.e x = - 1
Now, Put The value of z in eq C
or, 2 y + 5 z = 15
or, 2 y + 5 × 3 = 15
Or, 2 y = 15 - 15
or, 2 y = 0
∴ y = 0
Hence The solution of the equation are x = - 1 , y = 0 and z = 3 Answer