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Compute a + 5b.

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\(ab^2=\dfrac{27}{5}\\ a^2b=1080\\ b=\dfrac{1080}{a^2}\\ a\cdot (\dfrac{1080}{a^2})^2=\dfrac{27}{5}\)

\(\dfrac{1080^2}{a^3}=\dfrac{27}{5}\\ a=\sqrt[3]{\dfrac{5\cdot 1080^2}{27}}\)

\(a=60\)

\(b=\dfrac{1080}{60^2}\)

\(b=\dfrac{3}{10}\)

\(a+5b=61.5\)

  !

I just looked and this question now has 2 answers.

Thanks  answerers.   

Next time could you please leave a note here saying that you have answered.  

Thanks for posting as I have requested. 

The only thing helperid is right about is that more words, especially polite words, would be more likely to give you the answer that you want.

Also, it is a little easier for answerers if you add the address with a hyperlink, but that is not a big deal.

Answerers,

Please answer on the original thread and leave a note here saying that you have done so.

Thank dude, I also need some help on 2 and 3 but i now fully understand 1!

1. When Yin attempts to add all the positive integers from 1 through 99, he accidentally skips a number and gets the sum 4909. Which number did Yin skip?     

The formula for the sum of numbers 1 + 2 + 3 • • • + n   is (n)(n+1) / 2     

(99)(100) / 2 = 4950      If Yin got 4909 he omitted (4950 – 4909) = 41  

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Wait thats wrong

$1 + 4 + 7 + \dots + 94 + 97 = \frac{n (2a + (n - 1) d)}{2} = \frac{32 (2 \cdot 1 + 31 \cdot 3)}{2} = 1520$

1/2 * 1/8 = 1/16

Wanda has 4 vases of flowers.

Let 'x' number of vases contain 10 orchids,

then (4-x) number of vases contain 3 begonias.

Then, total number of flowers = 10(x) + 3(4-x)

Given that there are 19 flowers in vases total

So,           10(x) + 3(4-x) = 19

                10x + 12 - 3x = 19

                     7 x = 7

                       x = 1

So, Wanda have 1 vase of 10 orchids and 4-1 = 3 

number of vases containing 3 begonias.

in the calculator use the  +- key          

4 is greate than -4    so  the  second portion becomes   ab(4) = 3120

 -4   is for the first part   a/b (-4) = -60/13

4 ab = 3120

ab = 780  

b = 780/a        

                 -4 a/b = -60/13

                 -4a / (780/a) = -60/13

                    a^2 / 195   = 60/13

                     a = sqrt [ 60(195)/13]    = 30      then b = 780/30=26    you can finish .......

Good technique, but there's a little hiccup:  90 / 6 = 15 not 20.  You get the same answer, though.    

_.

39000 * .042= ...........        

     (    EMPLOYER will pay an additional 39 000 * .062   )

Find the smallest positive integer b for which x^2 + bx + 2010 factors into a product of two binomials, each having integer coefficients.     

The product of (x + 30)(x + 67) will give you a "b" equal to 97.  If you can find one smaller than that, my hat is off to you.  

_.

See similar

https://web2.0calc.com/questions/help-with-line_23

Multiply numerator and denominator by   sqrt (245)   to get

   6 sqrt 245 / 245    

fifty seven

Sorry, misread the problem.  

The sum is limited by the small range of g       b = 1

Find slope between the two lines to be   12/11

point slope form ( use either point)

y-7 = 12/11 ( x-8)     multiply by 11 to get rid of fraction

11y -77 = 12x - 96   re-arrange

-12x+11y = - 19    since A needs to be positive, multiply through by -1

12x -11y = 19

the squares 16 and 25 add to 41        so:     4 and 5

four.

The smallest n that works is 200, because the only ordered pairs (a,b) such that a^2 + b^2 = 200 are (2,14), (10,10), and (14,2).

Hint:   r = hypotenuse           18/2 = leg 

V = 1/3(9pi * √135)