If x varies directly as y and x=4 when y=6,find the value of x when y=12

Mathematics

1 answer:

Over [174]3 years ago

8 0

Answer:

10?

Step-by-step explanation:

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What is the equations for f(x)?

Wittaler [7]

$f(x) = -8\cdot 4^x$

You reflect a function with respect to the $x$ axis by changing its sign.

In fact, if you consider the two alternatives

$x \mapsto f(x)$ and $x \mapsto -f(x)$

you can see that you're choosing opposite outputs for the same inputs.

In other words, one graph will be made of points like $(x,f(x))$ , the other of points like $(x,-f(x))$

And the transformation

$(x,y) \to (x,-y)$

is exactly a reflection with respect to the $x$ axis.

6 0

4 years ago

Identify all of the following solutions of square root of x plus 14 end root plus 2 equals x.

BabaBlast [244]

$\bf \sqrt{x+14}+2=x\implies \sqrt{x+14}=x-2\impliedby \textit{squaring both sides}
\\\\\\
(\sqrt{x+14})^2=(x-2)^2\implies x+14=x^2-4x+4
\\\\\\
0=x^2-5x-10\impliedby \textit{now, using the quadratic formula}
\\\\\\
x=\cfrac{5\pm\sqrt{(-5)^2-4(1)(-10)}}{2(1)}\implies x=\cfrac{5\pm\sqrt{25+40}}{2}
\\\\\\
x=\cfrac{5\pm \sqrt{65}}{2}\implies x=
\begin{cases}
\cfrac{5+ \sqrt{65}}{2}\\\\
\cfrac{5- \sqrt{65}}{2}
\end{cases}$