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SO, perpendicular lines mean the slope is the opposite reciprocal of the given one.

5/4, opposite reciprocal is -4/5.

Let's see here...

We can test these values on a graph by graphing the equation.

So, from the point and the slope given, I've found the y-intercept to be -3.

I believe the y-intercept is opposite, but not a reciprocal. 

Hmmm..... I've been graphing for a bit but I don't think that strategy is going to work. Cphill, can you take it from here?

C(-4,-2) and D(-2,-5)

The slope between these  =   [ -5 - -2] / [ -2 - -4]   =  [ -5 + 2] / [ -2 + 4]   =  -3/2

So...we're trying to solve this

[-1 - -3] / [7 - x] = -3/2     

[ 2] / [ 7 -x] = -3/2      cross-multiply

2 * 2  = -3 [ 7 - x]     simplify

4 = -21  + 3x       add 21 to both sides

25  = 3x      divide both sides by 3

25 / 3   = x  = 8 + 1/3

You can call me Emma, Emily, or Lily.

You too Caligirl!

I am perplexed!

WOW! LOL

Sorry guys that is Not the answer I was hoping for :(

Sqrt 25 = +5

It is NOT -5

This is by convention.

Think about this

10 - sqrt4 = 10 - 2 =8

It does NOT equal 10 - -2 or  12!

HOWEVER

IF X^2 = 9

THEN

X = + SQRT3. OR  X= - SQRT3

Let's first see what we can eliminate 

(0, 0) isn't equidistant because it's 4 units from A and 2 units from B

(-3,0)  is only 1 unit from B......it's 5 units from A

(-4, - 5) 

√ [ (-4 - 0)^2 + (-5 +4)^2 =  √ [16 + 1]  = √ 17 from A

√ [(-4 +2)^2 + (-5 - 0)^2]  = √ [ 4 + 25] = √29 from B

Then ( 3, 0) must be correct...proof :

√ [ (3 -0)^2 + (-4 -0)^2 ] = [ 9 + 16]  = √25 =  5 units from A

√[ (-2 - 3)^2 + (0 - 0)^2 ]  = √ (-5)^2  = √25  = 5 units from B

Express $3.\overline{4}_{13}$ as a base 10 fraction in reduced form

But I don't remember doing anything like this before  :/

A vaguely obvious answer is 3/4 but I dont know. So I decided to go for a mathematics site seeing trip.

I did it as a division in base 13

4 doesn't go into 3 so that is 0.

Carry the carry the 3

4 into 39 is 9 carry 3

Etc

So that is 0.9 repeater base 13

To change to base 10 I did it as the infinite sum of a GP.

a=9/13  r=1/13

S infinity = (9/13)/ (1- 1/13)

=9/13.   ÷    12/13

=3/4

Mmm maybe it would have been easier to say 3/4 in the first place.

4/6 in lowest terms is 2/3.

9 1/15 - 8 4/7 = 52/105

4 + 5 × (13 + 7) × 18 + (2 × 4 × 0) × (5 + 8)

4 + 5 * (20) * 18 + (0) * (13)  =

4 + [ 100 * 18 ]  + 0  =

1804

2/5*5/8 = 1/4, or .25

25 is your answer.

-6x^2 - 5x -21

The discriminant   =   [ (-5)^2 - 4(-6)(-21) ]  =  [25  - 504]   =  [- 479]

The answer can be either:

\(\sqrt{25}=5\)

Or

\(\sqrt{25}=-5\)

If you get the square of both numbers, they both equal 25:

\(-5^2=5^2\Rightarrow 25=25\)

Multiplying two negatives equals a positive result.

Hope it helped!

Thank you, melody! So, the square root of 25 can be ±5 because 5*5=25 and (-5)*(-5)=25.

HOWEVER, (-5)*5 is NOT 25, it is -25.

Rarinstraw,  I think that you should expand on your answer.

The poster is probably wondering why -5 isn't an answer too :/

sqrt(25) = 5

Let N be the number...so.....

4N  - 9   = N       add 9 to both sides, subtract N from both sides

3N  = 9      divide both sides by 3

N = 3

Note the pattern for n ≥ 0....where n is an integer

3^[1+ 4n]    ends in 3

3^[2 + 4n]   ends in 9

3^[3 + 4n]   ends in 7

3^[4 + 4n]   ends in 1

So  

3^20  = 3^[4 + 4*4]   ends in 1  

it's 3. 3 times 4 is 12, 12-9 is 3