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\(2x^2 + 5x + 3 = 0\) factors to \((2x+3)(x+1) = 0\).

This means that \(x = \frac{-3}{2}\) and \(x = -1\). 

- Daisy

Correct me if i'm wrong CPhill and if you'd like to explain it a bit better then I did, that would be great 

Honestly we can already cancel out 3 of these answer choices because they just don't make since (A,B,D) C is the only one that makes total sense. 

63 miles per hour

63*4= 252

63*6=378

63*8= 504

63*19=630 

Hope this makes sense!

Using dimensional analysis

1.  2500 m   x   1 km  / 1000m     [cancel  m ] =  [2500 * 1  /1000]km   =  2.5 km

2. 7.1 hr  x  60min / 1 hr   [cancel hr ] =  [7.1 * 60 / 1 ] min  = 426 min

3 . 460 microliters x  1 L  / 1000000 microliters   [ cancel microliters ] =

[ 460 * 1 / 1000000]  mkicroliters  = .00046  L

4.  4.83 kg  x   1000g / 1 kg   [ cancel kg] =  4.83 x 1000/1 =  4830  g

Ohh yes i do!! thanks so much for that

Thanks for that excellent answer, Daisy...!!!

We can also find the slope using the two points Daisy chose in another manner [we actually could use any two points on the line  ....they will give the same result  ]

slope  = [ subtract the y coordinates in some order ] / [ subtract the x coordinates in the same order ]

[ 5 - 3 ] / [ 1 - 0 ]  =   2  / 1    =  2

OK....look at the slope

[ Subtract the y coordinates in some order ] / [ Subtract the x coordinates in the same order ] =

[2 - 2 ] / [ 5 - 1 ] =    0  / 4     =   0

See???

By this graph, we can pick two points to find the slope. Two clear points are \((0, 3)\) and \((1, 5)\). Slope = \(\frac{rise}{run}\). The rise is \(2\) and the run is \(1.\) Therefore, the slope is \(\frac{2}{1} = 2\), or \(D\).

- Daisy

Mathtoo...The common ratio  can be found by dividing a successive term by the preceding one

So   [-5/3 ]  / [ -3/5 ] =  -5/3 * -5/3   =  25  / 9

Check for yourself that  [-125 / 27]  / [ -5/3 ]  gives the same result...!!!

So it's 0? It makes sense yes, could you explain more 

Problem 1: We have K H D B D C M(Kilo, Hecto, Deca, Basic, Deci, Centi, and Mili)

To get from meters to kilometers, we have to move the decimal point \(3\) points to the left. This will give us \(2.5\) km. 

Problem 2: There are \(60\) minutes in an hour, and there are \(7.1\) hours, so we need to multiply \(60 \times 7.1 = 426\) min. 

Problem 3: To convert microliters to liters we have to move the decimal point \(6\) times to the left. This gives us \(0.00046\) L.

Problem 4: To convert kilograms to grams, we do the exact opposite of what we did in the first problem. We move the decimal point \(3\) times to the right. This will give us \(4830\) g.

- Daisy

Note....NSS....when  the y coordinates are the same....the slope has to  be 0.....because both points lie  - in this case  - on the line   y  = 2...this is a horizontal line....and a horizontal line always has a slope  = 0

Does that make sense???....if not....we  can prove it mathematically, if you want

Let  the  x coordinates  of the vertices be   x1, x2 and x3

And we know that  x1  + x2  + x3  = 10

And the   x coordinates of the midpoints of the sides  are

( x1 + x2 ) / 2     =  x1 /2 +  x /2    

(x2 + x3)/2  =     x2 / 2  +  x3 /2

(x1 + x3) / 2  =    x1 /2  + x3/2

Summing these, we get

(x 1/ 2) *2   +  ( x2 / 2) * 2   +  (x3 /2) *2  =

x1   +  x2  +  x3     =      10

Since this is a straight line....The slope will give us the rate of change

We have the points   (0, 400)  and  (12 ,0)

slope  =   [ 400 - 0 ] / [ 0 - 12 ] =  -400 /12    =  -100/3....just as Mathtoo found !!!

Ughhh, answered the wrong question. Find the midpoints of sides: x1+x2/2, x1+x3/2+x2+x3/2, we already know that x1+x2+x3=10, so 10*2=20, but 20/2=10.

Correct! That's how you do it!

3x² - 24x + 55

                                                      Factor  3  out of the first two terms.

   =   3(x² - 8x) + 55

                                                      Add  16  and subtract  16  inside the parenthesees.

   =   3(x² - 8x + 16 - 16) + 55

                                                      Factor  x² - 8x + 16  as a perfect square trinomial.

   =   3( (x - 4)² - 16) + 55

                                                      Distribute the  3  to the terms in parenthesees.

   =   3(x - 4)² - 48 + 55

                                                      Combine  -48  and  55  to get  7 .

   =   3(x - 4)² + 7

   =   a(x + d)² + e

So...

a + d + e   =   3 + -4 + 7   =   6

ok thanks so much!

Thank you, hectictar! Nice solution!

I think the answer is (B), because: After 12 years, the resale price finally hit 0, so 400/12=33.333 and goes on forever. 

So, the value drops $100 every 3 years, to make it, so it can work.

g(x)  =  √x

                       Plug in  16  for  x .

g(16)  =  √16

g(16)  =  4

And...

t(x)  =  3 - g(x)

                                          Since  g(x)  =  √x  , we can substitute  √x  in for  g(x) .

t(x)  =  3 - √x

                                          Plug in  g(16)  for  x .

t(g(16))  =  3 - √[ g(16) ]

                                          Since  g(16)  =  4 , we can substitute  4  in for  g(16) .               

t(g(16))  =  3 - √[ 4 ]

t(g(16))  =  3 - 2

t(g(16))  =  1

Also...

t(g(16))  =  3 - g( g(16) )  =  3 - g( 4 )  =  3 - 2  =  1

Thanks! I understand better!

Thanks! I fixed my answer, haha!

- Daisy

I got it so nevermind. 

300>150>100

300 and 300>150>300

Correct  !!!