Let's solve your equation step-by-step.
<span><span><span><span>x2</span>+4</span>+32</span>=<span><span>12<span>x2</span></span>+48
</span></span>Step 1: Simplify both sides of the equation.
<span><span><span>x2</span>+36</span>=<span><span>12<span>x2</span></span>+48
</span></span>Step 2: Subtract 12x^2+48 from both sides.
<span><span><span><span>x2</span>+36</span>−<span>(<span><span>12<span>x2</span></span>+48</span>)</span></span>=<span><span><span>12<span>x2</span></span>+48</span>−<span>(<span><span>12<span>x2</span></span>+48</span>)
</span></span></span><span><span><span>−<span>11<span>x2</span></span></span>−12</span>=0
</span>Step 3: Use quadratic formula with a=-11, b=0, c=-12.
<span>x=<span><span><span>−b</span>±<span>√<span><span>b2</span>−<span><span>4a</span>c</span></span></span></span><span>2a
</span></span></span><span>x=<span><span><span>−<span>(0)</span></span>±<span>√<span><span><span>(0)</span>2</span>−<span><span>4<span>(<span>−11</span>)</span></span><span>(<span>−12</span>)</span></span></span></span></span><span>2<span>(<span>−11</span>)
</span></span></span></span><span>x=<span><span>0±<span>√<span>−528</span></span></span><span>−<span>22
Hopefully this helps!
</span></span></span></span>
Each hiker will receive 6 ounces each.
I think the relationship between the weight of a stack of standard 8.5x11 copier paper vs number of sheets of paper is proportional because :
Let us assume here, in this situation that each page has the same weight so if i want to find the weight of the complete stack, i will multiply the number of sheets of paper by the weight of a single sheet of paper.
N=NOe^-kt
N=mass at time t
NO = initial mass
k= 0.1476
t= time, in days
We are asked to find the half-life, which means you want to find how long it will take for half of the substance to decay/disappear (depending on situation).
If we are looking for half-life, we can simply set N to half of NO (which we are given a value of 40grams for)
Therefore:
N = 20
NO = 40
plugging these values and the value given for k back into the equation you get:
20 = 40e^-0.1476(t)
We are looking for t, so we have to manipulate the formula to get t by itself on one side of the equation.
We can start by dividing 40 from both sides, and you get:
0.5 = e^-0.1476(t)
We have the exponential function "e".
To get rid of e, we can use natural log (ln)
if e^y=x then ln (x) = y
look back at our equation we can set
0.5 = x
-0.1476(t) = y
Rewriting it in natural log form:
ln (0.5) = -0.1476(t)
Plug in ln (0.5) on a calculator to find its value and we get:
-0.693147 = -0.1476(t)
*Note: normally, getting a negative value would suggest that we did something wrong, because you cannot have a negative value as your t (you cannot have negative days), but because there is a negative on both sides of the equation, they will cancel out in this case.
The last step is to simply divide both sides by -0.1476
therefore:
T = 4.696119
But it asks you for the answer to the nearest tenth (one place after decimal pt) so
T (half life) = 4.7 days
Hope that helps :)
I believe its b hope this helped
