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mash [69]
2 years ago
15

I need help simple explanation if possible

Mathematics
1 answer:
Yuki888 [10]2 years ago
8 0
Answer: X=1

Step-by-step explanation:
The hypotenuse is √2 which means that x²+x²=(√2)² using Pythagoras
Simplify and solve
2x²=2
x²=1
X=√1
X=1
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Step-by-step explanation:

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2. Determine the sum of the first 400 ODD numbers.<br><br>​
il63 [147K]

Odd numbers take the form 2n-1, where n\ge1 is an integer. When n=400, the last odd number would be 799. So we're adding

S=1+3+5+\cdots+795+797+799

By reversing the order of terms, we have

S=799+797+795+\cdots+5+3+1

and we can pair up terms in both sums at the same position to write

2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

2S=400\cdot800\implies S=160,000

###

We could also make use of the formulas,

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2

We have

S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000

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At a construction site, a builder plans to cut down an 8-foot-by-9-foot piece of plywood. She plans to discard any pieces that s
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GIVEN:
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the width be "w"
We know,
Perimeter (P) of a rectangle = 2 (L + w) 
Substituting the values of P, L and w , we get,
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                                  96 / 2 = 30 + w
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So, the width of the rectangular banner is 18 ft.
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