Question

The Torres family drove 1,375 miles during their 6 1/4 day vacation. Find the average number of miles they traveled each day.

Answer 1

Answer:

$\color{red} {{{\Large {\bf{To\:\:Simplify\::\frac{\sin ^4(x)-\cos ^4(x)}{\sin ^2(x)-\cos ^2(x)}}}}}}$

$\color{green}{{{\large {\bf{Your\:\:Answer\::\frac{\sin ^4(x)-\cos ^4(x)}{\sin ^2(x)-\cos ^2(x)}=1}}}}}$

$\color{yellow} {\Huge {\sf{Solution:}}}$

$\color{blue} {\large {\bf{Factor\:\sin ^4(x)-\cos ^4(x)}}}$

$\tt \color{blue} {\mathrm{Rewrite\:}\sin ^4(x)-\cos ^4(x)\mathrm{\:as\:}(\sin ^2(x))^2-(\cos ^2(x))^2=(\sin ^2(x))^2-(\cos ^2(x))^2}$

$\color{fuchsia} {\normalsize {\mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=(a^b)^c}}$

$\color{fuchsia} {\normalsize \sin ^4(x)=(\sin ^2(x))^2}$

$\color{fuchsia} {\normalsize =(\sin ^2(x))^2-\cos ^4(x)}$=

$\color{fuchsia} {\normalsize \mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=(a^b)^c}$

$\color{fuchsia} {\normalsize \cos ^4(x)=(\cos ^2(x))^2}$

$\color{fuchsia} {\normalsize =(\sin ^2(x))^2-(\cos ^2(x))^2}$=

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}$x^2-y^2=(x+y)(x-y)

$(\sin ^2(x))^2-(\cos ^2(x))^2=(\sin ^2(x)+\cos ^2(x))(\sin ^2(x)-\cos ^2(x))$

=$(\sin ^2(x)+\cos ^2(x))(\sin ^2(x)-\cos ^2(x))$=

$\color{blue} {\large {\bf{Factor\:\sin ^2(x)-\cos ^2(x)}}}$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}$x^2-y^2=(x+y)(x-y)

$\sin ^2(x)-\cos ^2(x)=(\sin (x)+\cos (x))(\sin (x)-\cos (x))$

(x)=(sin(x)+cos(x))(sin(x)−cos(x))

=(\sin (x)+\cos (x))(\sin (x)-\cos (x))=(sin(x)+cos(x))(sin(x)−cos(x))

$\large=(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))\ \textless \ br /\ \textgreater \ (x))(sin(x)+cos(x))(sin(x)−cos(x))\ \textless \ br /\ \textgreater \ \large =\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{\sin ^2(x)-\cos ^2(x)}$=

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}$x^2-y^2=(x+y)(x-y)

$\sin ^2(x)-\cos ^2(x)=(\sin (x)+\cos (x))(\sin (x)$

$(x)=(sin(x)+cos(x))(sin(x)−cos(x))\ \textless \ br /\ \textgreater \ =\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{(\sin (x)+\cos (x))(\sin (x)-\cos (x))}$=

$\mathrm{Cancel\:}\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{(\sin (x)+\cos (x))(\sin (x)-\cos (x))}:\quad \sin ^2(x)+\cos ^2(x)Cancel \ \textless \ br /\ \textgreater \ (sin(x)+cos(x))(sin(x)−cos(x))$

$\mathrm{Cancel\:the\:common\:factor:}\:\sin (x)+\cos(x)Cancelthecommonfactor:sin(x)+cos(x)$

=$\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)-\cos (x))}{\sin (x)-\cos (x)}$=

$\mathrm{Cancel\:the\:common\:factor:}\:\sin (x)-\cos$

$\mathrm{Use\:the\:following\:identity}:\quad \cos ^2(x)+\sin$

$\huge \boxed{\color{red} {\ \huge =1}}$

Answer 2

Answer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollarsAnswer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollarsAnswer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollarsAnswer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollarsAnswer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollarsAnswer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollarsAnswer:

the cost of each notebook is 4.89 dollars.

Step-by-step explanation:

first is you subtract the 60.54 dollars to 45.87 dollars which is the costs of calculator

so the difference now is 14.67 dollars

after, you divide the difference which is the 14.67 dollars by 3 which is the 3 packs of notebooks

the answer is each packs of notebook have a costs of 4.89 dollars