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# Urgent Questions, help!

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1) Compute 2) One day, I decide to run to the park. On the way there, I run at a rate of  miles per hour for  hours. On the way back, I take the same path and jog at a slower rate of  miles per hour so that it takes me  hours to get home. Given that , what is ? Express your answer as a common fraction.

3) 4)

Find a non-zero value for such that  ax^2+8x+4=0 has only one solution.

Thanks!🙏🏼

Jul 10, 2018

### 5+0 Answers

#1
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Is your 2nd question missing some numbers?

Jul 10, 2018
#2
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3)

Simplify the following:
2 + i - 4 - i + 2 + 4 i

Group like terms in 2 + i - 4 - i + 2 + 4 i.
2 + i - 4 - i + 2 + 4 i = (2 - 4 + 2) + (i - i + 4 i):
(2 - 4 + 2) + (i - i + 4 i)

Evaluate 2 - 4 + 2.
2 - 4 + 2 = 0:
i - i + 4 i

Add like terms in i - i + 4 i.
i - i + 4 i = 4 i:
4 i

1) Just evaluate by any calculator:

(2011^2 - 2006^2) / (2010^2 - 2007^2)

=5 / 3

Jul 10, 2018
edited by Guest  Jul 10, 2018
#5
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Hey, I think you made a little mistake at the begining...

I think the equation should be (2+i)-(-4)+(-i)+(2+4i)...

Guest Jul 11, 2018
#3
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Here's  (1)   without a calculator....note that the numerator and  denomonator  are  both just the difference of squares...so we have :

(2011 + 2006) ( 2011  - 2006)

_______________________    =

(2010 + 2007) ( 2010 - 2007)

(4017) (5)

_________  =

(4017) (3)

5

__

3   Jul 10, 2018
#4
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Here's  4

ax^2   + 8x  +  4   = 0

If this has only one solution.....then it will be true  that the  discriminant given by  (8)^2  - 4 (a) (4)  will = 0

So we have

(8)^2  - 4 (a) (4)   =  0   simplify

64  - 16a    = 0      add   16a  to both sides

64   = 16a        divide both sides by 16

4  =  a   Jul 10, 2018