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Vedmedyk [2.9K]
3 years ago
12

= Initial Knowledge Check Rewrite the expression by factoring out (y+9). 3y^2 (y + 9) + 7(y+9)​

Mathematics
1 answer:
alex41 [277]3 years ago
6 0

Answer:

3y {}^{2} (y + 9) + 7(y + 9) \\  = (y + 9)(3y { }^{2}  + 7)

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3 years ago
If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?
lorasvet [3.4K]
You can make a start by putting together an expression for the sum of the even integers between 1 and k inclusive.

Let S be the sum of the even integers between 1 and k inclusive.

Then:
<span><span>S=2+4+6+⋯+(k−2)+k</span></span>

As k is even, you can say r = 2k and so:

<span><span>S=2(1+2+3+⋯+(r−1)+r)</span></span>

<span>Now the sum of the first </span><span>r</span><span> numbers is well-known, it's the </span><span>r</span>th triangle number and we have:

<span><span>1+2+3+⋯+(r−1)+r=<span><span>r(r+1)/</span>2</span></span></span>
<span>Now we can keep it simple and say </span><span><span>2k=4r </span></span><span>and so:</span>

<span><span>S=2(1+2+3+⋯+(r−1)+r)=4r=2<span><span>r(r+1)</span>2</span>=r(r+1)</span></span>

<span>So you can build a quadratic in </span><span>r</span><span> and so get </span><span>k.</span>
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Answer:

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Step-by-step explanation:

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What is the greatest common factor of 24 and 40
Stels [109]

Answer:

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Step-by-step explanation:

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