Answer:
A. 1,485 cubic cm. B. 27
Step-by-step explanation:
The new prism is dilated by a factor of 3, that means it's made bigger, 3 times bigger on each side.
The dimensions of the new prism are then 12 cm by 7.5 cm by 16.5 cm.
Its volume is then of 12 x 7.5 x 16.5 = 1,485 cubic cm
To answer the second question...
Let's calculate the volume of the original prism:
The original prism's volume was 4 x 2.5 x 5.5 = 55 cubic cm
The new volume is then 1485 / 55 = 27 times bigger than the original.
Which is normal, since we increased each side (dimension) by a factor of 3, so 3x3x3 = 27.
Firstly, write out as a number, using a few repeats of the decimal. If we multiply this number by 10 it will give a different number with the same digit recurring. When two digits recur multiply by 100 so that the recurring digits after the decimal point keep the same place value.
Answer:
a) 2
b) s₁ and s₂
c) First linear equation: 5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
Second linear equation: 5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
Step-by-step explanation:
The problem statement, establishes two constraints, each one of them will need a slack variable to become a linear equation, so the answer for question
a) 2.
b) The constraints are: s₁ and s₂
c) First constraint
5*x₁ + 8*x₂ + 10*x₃ ≤ 173
We add slack variable s₁ and the inequality becomes
5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
The second constraint is:
5*x₁ + 4*x₂ + 17*x₃ ≤ 254
We add slack variable s₂ and the inequality becomes
5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
To combine like terms and single out one term to take it easier to solve, the 6x was moved to the other side to combine like terms.
Subtracting 6x from 10x which is 4x
