Which equation is equivalent to 2 4x = 8x-3

Mathematics

2 answers:

Reil [10]3 years ago

8 0

Answer:

D! 2^4x=2^3x-9

Step-by-step explanation:

edge

Stolb23 [73]3 years ago

6 0

Answer:

x = -9

Step-by-step explanation:

the equation is 2^4x = 8^x - 3.

therefore 2^4x = 2^3(x-3)

since both have powers of 2

therefore

4x = 3(x-3)

4x = 3x - 9

4x -3x = -9

x = -9

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An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0). Which equation represent

Alchen [17]

Check the picture below. So the ellipse looks more or less like so.

since the major axis is over the x-axis, is a horizontal ellipse, notice the "a" component length and the value for "c".

$\bf \textit{ellipse, horizontal major axis}
\\\\
\cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1
\qquad 
\begin{cases}
center\ ( h, k)\\
vertices\ ( h\pm a, k)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2- b ^2}
\end{cases}\\\\
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$\bf \begin{cases}
h=0\\
k=0\\
a=10\\
c=8
\end{cases}\implies 8=\sqrt{a^2-b^2}\implies 8^2=a^2-b^2\implies b^2=10^2-8^2
\\\\\\
b=\sqrt{100-64}\implies b=6
\\\\\\
\cfrac{(x-0)^2}{10^2}+\cfrac{(y-0)^2}{6^2}=1\implies \cfrac{x^2}{100}+\cfrac{y^2}{36}=1$