hectictar

13 - 36x²  =  -12                  Subtract 13 from both sides of the equation.

-36x²  =  -25                        Divide both sides of the equation by  -36  .

x²  =  25 / 36                        Take the ± square root of both sides.

x  =  ± √[ 25 / 36 ]

x  =  ± 5/6

-2x  <  16 - 3           Simplify the right side.

-2x  <  13                 Divide both sides of the inequality by  -2  , and, since it is negative, flip the sign.

x  >  -13/2

x  >  -6.5

x can be any  number on this blue line:

So...we can see that the smallest integer value of    x    is    -6      

We can get this quadratic equation into standard form.

y  =  x(x - 4)          Distribute the x to both terms in parenthesees.

y  =  x² - 4x

Is that all the question asks for?

true     

You can type it into the bar using this key:  /

For example, to do:    \(\frac5{16}\)

Type:                         5/16

If the numerator or denominator contains another operation,

you may need to put parenthesees around it.

For example, to do:  \(\frac{5+72}{3591*210}\)

Type:                       (5+72)/(3591*210)

I got a strange answer for part A) , but I will post it anyway....

∠BAD  =  ∠BAC - ∠DAC

tan(∠BAC)  =  BC / AC            Since  AC = BC  , replace  " AC " with " BC ".

tan(∠BAC)  =  BC / BC

tan(∠BAC)  =  1

∠BAC  =  arctan(1)

∠BAC  =  45º

cos(∠DAC)  =  AC / AD

BC    =  0.5AD                         Multiply both sides of the equation by 2 .

2BC  =  AD                              Since  AC = BC  , replace  " BC " with " AC ".

2AC  =  AD

cos(∠DAC)  =  AC / AD            Replace  " AD "  with  " 2AC " .

cos(∠DAC)  =  AC / (2AC)        Reduce fraction by  AC

cos(∠DAC)  =  1/2

∠DAC  =  arccos(1/2)

∠DAC  =  60º

∠BAD  =  ∠BAC - ∠DAC

∠BAD  =  45º - 60º

∠BAD  =  -15º

......

Maybe it is supposed to be     BD = 0.5AC     or     DC = 0.5AC         ?

Here's one more explanation... 

Let's look at half of  X² 's  picture:

A  +  B  +  C      =  180º        B = 90º because it is the corner of a square.

A  +  90º  +  C   =  180º        AB = BC,   so ▵ABC is isosceles.. this makes  m∠A   =   m∠C

A  +  90º  +  A   =  180º        Subtract  90º  from both sides of this equation.

A  +  A  =  90º                       Combine like terms.

2A = 90º                               Divide both sides of the equation by 2.

A = 45º

If   16^n = 1/64  , find the value of n .

\(16^n=\frac1{64} \\~\\ (2^4)^n=\frac1{(2^6)} \\~\\ (2^4)^n=2^{-6} \\~\\ 2^{4\cdot n} = 2^{-6} \\~\\ 4\cdot n=-6 \\~\\ n=\frac{-6}4 \\~\\ n=-1.5\)

I'm also relieved for the end of the school year!