Answer:
3 1/3 feets
Step-by-step explanation:
Given that:
Height of aquarium = 1 3/4 feets
Area of aquarium = 5 5/6 ft²
The length of aquarium = x
Aquarium is shaped in the form of a rectangle :
Area of a rectangle = Length * width
5 5/6 = x * 1 3/4
35/6 = 7x/4
Cross multiply :
7x * 6 = 35 * 4
42x = 140
x = 140 / 42
x = 3 14/42
x = 3 1/3 feets
Hence, Length of the back of aquarium is 3 1/3 feets
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:
x >_ 1
Step-by-step explanation:
Solving an inequality is a lot like solving an equation. Just pretend the inequality symbol is an equal sign!
(also i wont be using the _ or equal to symbol because I'm too lazy, so you'll get >_ or <_ for those, sorry)
8 + 4x >_ 12
-8 -8
4x >_ 4
/4 /4
x >_ 1
The three slices are each approximately 1/9 pound in weight, and, since 2/9 is less than 1/4, he can eat 2 whole slices and be okay. If he wants to eat partial slices, then he could eat 2 1/4 slices, as each slice weighs 4/36 pounds, so 2 slices would equal 8/36 pounds, leaving 1/36 pound left over in his diet, which is a quarter of the third slice.
2.25
