Let
x--------> <span>the speed of the boat in mph
we know that
</span>going upstream the speed is x-7
<span>going downstream the speed is x+7
</span>
let the distance be d
<span>time to go upstream = d/(x-7) </span>
<span>time to go downstream = d/(x+7)
</span>
time going upstream is 3 times going downstream
so
<span>3d/(x+7) = d/(x-7) </span>
<span>divide by d </span>
<span>3/(x+7) = 1/(x-7) </span>
<span>3x-21 = x+7 </span>
<span>2x = 28 </span>
<span>x = 14
</span>
the answer is
<span>the speed of the boat in still water is 14 mph</span>
Answer:

It has one solution
Step-by-step explanation:
![14x + 12] = 0\\\\14x+12=0\\\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}\\14x+12-12=0-12\\\\Simplify\\14x=-12\\\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14x}{14}=\frac{-12}{14}\\\\Simplify\\x=-\frac{6}{7}](https://tex.z-dn.net/?f=14x%20%2B%2012%5D%20%3D%200%5C%5C%5C%5C14x%2B12%3D0%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D12%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C14x%2B12-12%3D0-12%5C%5C%5C%5CSimplify%5C%5C14x%3D-12%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D14%5C%5C%5Cfrac%7B14x%7D%7B14%7D%3D%5Cfrac%7B-12%7D%7B14%7D%5C%5C%5C%5CSimplify%5C%5Cx%3D-%5Cfrac%7B6%7D%7B7%7D)
for an expression or relation to be a function, it must not have any x-coordinate values repeated, let's check this one

Answer:
-5
Step-by-step explanation:
Moving all terms of the quadratic to one side, we have
.
A quadratic has one real solution when the discriminant is equal to 0. In a quadratic
, the discriminant is
.
(The discriminant is more commonly known as
, but I changed the variable since we already have a
in the quadratic given.)
In the quadratic above, we have
,
, and
. Plugging this into the formula for the discriminant, we have
.
Using the distributive property to expand and simplifying, the expression becomes

Setting the discriminant equal to 0 gives
.
We can then solve the equation as usual: first, divide by 2 on both sides:
.
Squaring both sides gives
,
and subtracting 5 from both sides, we have
