Answer:
the coefficient of x is 2
Step-by-step explanation:
(3x - y + z) + (2x - y - z) - (3x - y - z) = 3x - y + z + 2x - y - z - (3x - y - z)
Apply the distributive law: - (a - b) = -a + b
Therefore, - (3x - y - z) = -3x + y + z
So (3x - y + z) + (2x - y - z) - (3x - y - z) = 3x - y + z + 2x - y - z - 3x + y + z
Collect like terms: = 3x + 2x - 3x - y - y + y + z - z + z
Combine like terms: = 2x - y + z
Therefore, the coefficient of x is 2
Therefore, the coefficient of x is 2
Easy, first turn the factions into deciamls, then so 1.16-7.8=6.64. So, 6.64
<span>-4(X+2)-1/2(2X-6)
-4*x + -4*2 - (1/2)*2x -(1/2)*(-6)
-4x - 8 - x + 3
-4x - x - 8 + 3
-4x - x + 3 - 8
-5x - 5
</span>
Answer:
2 to 10 or 1 to 5
Step-by-step explanation:
Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
