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
Answer:
It's the Option A.
Step-by-step explanation:
h(x) = g(x - 3)
The -3 moves the whole graph of g(x) 3 units horizontally to the right.
The perimeter of an object is found by adding all of the sides. The sides of his frame would be 2 ft, 2 ft, 1.5 ft (18 inches / 12 inches per foot = 1.5 feet), 1.5 feet. Adding these together we get a total length of 7 feet. However, he may want to use a slightly longer board to account for any errors!
Option B is the correct answer because you start with 15 gallons (y-intercept), and the car consumes or decreases at 0.03 gal/per mile (your slope or m).
Answer:
y=a(x-p)(x-q)
y=a(x+2+√2)(x+2-√2)
passing through point (-1,1)
substitute
1=a(-1+2+√2)(-1+2-√2)
1=a(1+√2)(1-√2)
1=a(1-2)
1=a(-1)
a=1/(-1)
a=-1
y=-(x+[2+√2])(x+[2-√2])
y=-(x2+4x+2)
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