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3 years ago

#6,7. Fill in the blank. Then show or explain how your answer works.

Mathematics

1 answer:

nika2105 [10]3 years ago

5 0

69 because yeahhhhhhhhh

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1/1×3 + 1/3×5 + ... + 1/47×49 HELP PLZ

Natalka [10]

Answer:

24/49

Step-by-step explanation:

Let's add the terms and see if there's a pattern

$\dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}=\dfrac{5+1}{1\times 3\times 5}=\dfrac{2}{5}\quad\text{sum of 2 terms}\\\\\dfrac{2}{5}+\dfrac{1}{5\times 7}=\dfrac{14+1}{5\times7}=\dfrac{3}{7}\quad\text{sum of 3 terms}$

Suppose we say the sum of n terms is (n/(2n+1)), the next term in the series will be 1/((2n+1)(2n+3)) and adding that to the presumed sum gives ...

$\dfrac{n}{2n+1}+\dfrac{1}{(2n+1)(2n+3)}=\dfrac{n(2n+3)+1}{(2n+1)(2n+3)}=\dfrac{2n^2+3n+1}{(2n+1)(2n+3)}\\\\=\dfrac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\dfrac{n+1}{2n+3}\text{ matches }\dfrac{(n+1)}{2(n+1)+1}$

Then it appears the sum of n terms is (n/(2n+1)). So, the sum of 24 terms is ...

$S_{24}=\dfrac{24}{2\times24+1}=\boxed{\dfrac{24}{49}}$

3 0

3 years ago

What is the gcf of 2,4a

-BARSIC- [3]

4.

2,4

4

Hope this helps!

3 0

3 years ago

If my car averages 27 miles to the gallon, how many miles can I drive on3/4 tank of gas

AURORKA [14]

Answer:

20.25 miles

Step-by-step explanation:

If your car travels 27 miles on a full tank of gas, then your car will travel $27\cdot\frac{3}{4}$ miles on $\frac{3}{4}$ tank of gas.

$27 \cdot 0.75 = 20.25$

I hope this helped!

7 0

3 years ago

The photo printed has length of 6 imams width of 4. A smaller picture is printed the ratio of the new picture to the size of the

Serggg [28]

We know the width of the first picture, is 4
we know the ratio from smaller to larger is 1.5:2

thus $\bf \cfrac{\textit{width of small}}{\textit{width of large}}\qquad 1.5:2\implies \cfrac{1.5}{2}=\cfrac{w}{4}$

solve for "w".

we know the length of the first picture, 6

$\bf \cfrac{\textit{length of small}}{\textit{length of large}}\qquad 1.5:2\implies \cfrac{1.5}{2}=\cfrac{L}{6}
$

solve for "L".

3 0

3 years ago

PLEASE HELPPPPP<br> M=2<br> N=16<br> P=1/3

andre [41]

Answer:

Step-by-step explanation:

Based on the information you have given me, p = 1/3.

All we need to do is substitute that value into the expression:

12p = 12(1/3) = 4

4 0

3 years ago

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