This is the same as showing the following system of equations doesn't have a solution:
or in matrix form,
The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.
And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:
(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)
So there are indeed no such scalars <em>c₁</em>, <em>c₂</em>, and <em>c₃</em>.
Solve for x over the real numbers:2 x^2 - 3 x - 2 = x + 4
Subtract x + 4 from both sides:2 x^2 - 4 x - 6 = 0
The left hand side factors into a product with three terms:2 (x - 3) (x + 1) = 0
Divide both sides by 2:(x - 3) (x + 1) = 0
Split into two equations:x - 3 = 0 or x + 1 = 0
Add 3 to both sides:x = 3 or x + 1 = 0
Subtract 1 from both sides:Answer: x = 3 or x = -1
Answer:
The next three terms are 54, 162, 486
Step-by-step explanation:
Exponential sequences you multiply to find the next term
6 x 3 = 18 (to find the next term you can multiply the previous term by 3)
18 x 3 = 54
54 x 3 = 162
162 x 3 = 486
Find the difference:
1400 - 1250 = 150
Divide the difference by the starting value:
150 / 1250 = 0.12
Multiply by 100:
0.12 x 100 = 12% increase.
Answer:
700
Step-by-step explanation:
The 9 = 9
The 0 = 0
The 7 = 700
The 5 = 5000
