!!! 25 POINTS HELP PLS

Mathematics

1 answer:

weqwewe [10]3 years ago

3 0

Answer:

Option (3)

Step-by-step explanation:

Given functions are,

f(x) = $\frac{1}{4^x}$

g(x) = log(2x)

By using a graphing utility we can draw the graphs of the given system of equations.

Common points of the graph will be the solutions of the equations,

From the graph attached,

Solution of the functions is → (0.937, 0.273)

→ (0.9, 0.3)

Option (3) will be the answer.

You might be interested in

How do I solve for an absolute value equation?

Vitek1552 [10]

Answer:

The absolute value is always positive no matter if there's a negative.

Step-by-step explanation:

6 0

3 years ago

The volume of a cylinder is 97 ft cubed. if the dimensions are doubled, what will be the new volume?

Airida [17]

See, pls, this explanation:
1) formula for volume of cylinder is: V=πR²h, where R - radius of the bottom (circle), h - height of the cylinder.
2) if new_R=2R and new_h=2h then new_V=π(new_R)²(new_h)=8πR²h=8*97=776 ft³

Answer: 776 ft³.

7 0

4 years ago

write the equation of the line that passes through the vertex of the parabola y=-2x^2+12x-11 and the point (-2,47)

pshichka [43]

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{-11} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{12}{2(-2)}~~,~~-11-\cfrac{12^2}{4(-2)} \right)\implies \left( 3~~,~~-11+\cfrac{144}{8} \right) \\\\\\ (3~~,~~-11+18)\implies (3~~,~~7) \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{vertex}{(\stackrel{x_1}{3}~,~\stackrel{y_1}{7})}\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{47}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{47}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{3}}}\implies \cfrac{40}{-5}\implies -8$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-8}(x-\stackrel{x_1}{3}) \\\\\\ y-7=-8x+24\implies y=-8x+31$