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Chris is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chris strings the lights along the length of the ceiling, a distance of 55 feet. Next, Chris strings the lights along the width of the ceiling, a distance of 48 feet. Then Chris strings the lights straight back to the original corner. At this point, Chris has used ___ feet of lights.  

Chris has made a right triangle, so the diagonal is sqrt(55² + 48²)  

                                                             diagonal = sqrt(3025 + 2304)  =  73   

So Chris has used 55 + 48 + 73 feet of lights  =  176 feet  

_.

Thank you :)

Chris has strung a right triangle of lights   with legs 48  and 55

   the diagonal is fond with Pythag theorem

          d  =  sqrt (48^2 + 55^2)  = 73 ft

48 + 55 + 73 = 176 ft total

Sorry, wrong answer

I see the 9th one now....1 3 3 4

Use complementary counting and find the number of boxes that don't  have a bobblehead inside.

\(1 - (\frac{1}{6})^3 = \boxed{\frac{215}{216}}\)

Hello CubeyPenguin!

34/60+9/60*2 = 52/60 = 13/15 right?

I think there may have been a mistake. 

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English translation: What is 17 parts 30 plus 3 parts 20 times 2 ?????

\(\frac{17}{30} + \frac{3}{20} \cdot 2\)

\(\frac{34}{60} + \frac{9}{60} \cdot 2 = \frac{52}{60} = \boxed{\frac{13}{15}}\)

**edit: fixed

Ohhh thank you. 

I didn't know. :))

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\(A = \frac{bh}{2} = \frac{12b}{2} = 28 \quad \rightarrow \quad b = \frac{14}{3}\)

\(P = b + 2\sqrt{b^2 + h^2} = \frac{14}{3} + 2\sqrt{(\frac{14}{3})^2 + 12^2}\)

We only care about the denominator: y^2 - 8y + 2.

The denominator can't be equal to 0, so we are looking for the roots of y^2 - 8y + 2 = 0.

From Vieta's formulas, the sum is -b/a = 8.

When denominator = 0    undefined 

roots =  4 +- sqrt 14          sum = 8    

As a general note, for a square array with \(n\) dots on each side, the number of squares is:

\(1^2 + 2^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6}\)

Hello Guest!

For future refrence, screenshotting will make it slightly easier for the answerers to read. :))

The answer is D. Look at the roots of the parabola, -2 and -5, this means that when -2 and -5 is plugged into x, then y will be 0. 

Checking, D is the only answer that fits.

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The zeros of the quadratic are at x = -5 and x = -2, so the equationis \(y = (x+5)(x+2).\) Expand this to get the answer.

Sadly, I think the best way is to just count. 

1 by 1 = 16 squares

2 by 2 = 9 squares 

3 by 3 = 4 squares

4 by 4 = 1 square

Note that all the numbers above are squares, this will be a useful pattern when you need to find all the numbers quickly. 

1+4+9+16 = 30. 

I hope this helped. :))

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I think that in this case, it might be easier just to convert to base 10 and multiply. 

11001 in binary is 25. 

10011 in binary is 19. 

19*25 = 475. 

475 = 111011011 in binary

I hope this helped. :)))

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Looking at ElectricPavlov's graph, my answer is not right. 

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12*14*10/1/2/3 = 280. 

So I think that you can hold 280 boxes in the truck. 

280*.25 = 70. 

So our answer hopefully is 70. :))

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Equate the two polynomials and solve for the x points of intersection

3-x = 1+x+x^2

x^2 +2x -2 = 0

Well it said 'graphing' in the Q ....so here is the graph of the two polynomials

  I think you can take it from here !

Sorry, but hte answer was 9.

1 + x + x^2 + x^3 = 3 - x + x^3

1 + x + x^2 = 3 - x

x^2 + 2x - 2 = 0

So, we can use the quadratic equation to find the 2 ys, or we can simpify it a bit first. 

(-b+sqrt(b^2-4ac))/2a- (-b-sqrt(b^2-4ac))/2a = sqrt(b^2-4ac)/a

Now, the difference is sqrt(b^2 - 4ac). 

sqrt(2^2 - 4(-2))/1

sqrt(8)

2sqrt(2)

I hope this helped. :))

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space diagonal = \(\sqrt{3^2+ 4^2 + 5^2} \)

edit: sniped

sqrt (3² + 4² +5⁵ ) = ..............

Here are some ways.....can you think of any more?

1 1 1 36

1 1 2 18

1 1 3 12

1 1 4 9

1 1 6 6

1 2 2 9

1 2 3  6

2 2 3 3