Hello! And thank you for your question!

First use the rule: A/b x c/d = ac/bd

3 x 2 over 5 x 3

Simplify 3 x 2:

6 over 5 x 3

Simplify 5 x 3:

6/15

Simplify further:

2/5

Final Answer:

2/5

3 0

2 years ago

The function f(x)=2^x and g(x)=f(x+k). If k=-5,what can be concluded about the graph of g(x)?

melamori03 [73]

$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
\\\\
f(x)= A(\mathbb{R})^{ Bx+ C}+ D
\\\\
f(x)= A sin\left( B x+ C \right)+ D
\\\\
--------------------$

$\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if } B\textit{ is negative}\\
~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\
~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}$

$\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by } D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{ B}$

with that template in mind

$\bf f(x)=2^x\qquad 
\begin{cases}
g(x)=f(x+k)&k=5\\
\qquad\quad f(x+5)\\
\qquad \quad 2^{x+5}
\end{cases}$

notice, in g(x)

B = 1, no change from parent

C= +2

8 0

3 years ago

Read 2 more answers

Can help me complete this problem please :,c

GalinKa [24]

Answer:

= 30.144 km²

Step-by-step explanation:

Area of a sector is given by the formula;

θ/360 × πr², where θ is the angle subtended by the arc to the center of the circle, and r is the radius.

Area = 54/360 × 3.14 × 8 × 8

= 30.144 km²