At a local preschool, there is a ratio of 3 boys to every 4 girls. If there are 245 total preschoolers enrolled, how many boys a
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The answer is: [C]: " f(c) = 
c + 32 " .
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Explanation:
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Given the original function:
" c(y) = (5/9) (x <span>− 32) " ; in which "x = f" ; and "y = c(f) " ;
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</span>→ <span>Write the original function as: " y = </span>(5/9) (x − 32) " ;
Now, change the "y" to an "x" ; and the "x" to a "y"; and rewrite; as follows:
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x = (5/9) (y − 32) ;
Now, rewrite THIS equation; by solving for "y" ; in terms of "x" ;
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→ That is, solve this equation for "y" ; with "c" as an "isolated variable" on the
"left-hand side" of the equation:
We have:
→ x = " (
) * (y − 32) " ;
Let us simplify the "right-hand side" of the equation:
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Note the "distributive property" of multiplication:
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a(b + c) = ab + ac ; <u><em>AND</em></u>:
a(b – c) = ab – ac .
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As such:
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" () * (y − 32) " ;
= [ () * y ] − [ () * (32) ] ;
= [ () y ] − [ () * (
" ;
= [ () y ] − [ (
] ;
= [ () y ] − [ (
] ;
= [ (
) ] − [ ( ] ;
= [
] ;
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And rewrite as:
→ " x = " ;
We want to rewrite this; solving for "y"; with "y" isolated as a "single variable" on the "left-hand side" of the equation ;
We have:
→ " x = " ;
↔ " = x ;
Multiply both sides of the equation by "9" ;
9 * = x * 9 ;
to get:
→ 5y − 160 = 9x ;
Now, add "160" to each side of the equation; as follows:
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→ 5y − 160 + 160 = 9x + 160 ;
to get:
→ 5y = 9x + 160 ;
Now, divided Each side of the equation by "5" ;
to isolate "y" on one side of the equation; & to solve for "y" ;
→ 5y / 5 = (9y + 160) / 5 ;
to get:
→ y = (9/5)x + (160/5) ;
→ y = (9/5)x + 32 ;
→ Now, remember we had substituted: "y" for "c(f)" ;
Now that we have the "equation for the inverse" ;
→ which is: " (9/5)x + 32" ;
Remember that for the original ("non-inverse" equation); "y" was used in place of "c(f)" . We have the "inverse equation"; so we can denote this "inverse function" ; that is, the "inverse" of "c(f)" as: "f(c)" .
Note that "x = c" ;
_____________________________________________________
So, the inverse function is: " f(c) = (9/5) c + 32 " .
_____________________________________________________
The answer is: " f(c) = c + 32 " ;
_____________________________________________________
→ which is:
→ Answer choice: [C]: " f(c) = c + 32 " .
_____________________________________________________
________________________________________________________
Explanation:
________________________________________________________
Given the original function:
" c(y) = (5/9) (x <span>− 32) " ; in which "x = f" ; and "y = c(f) " ;
________________________________________________________
</span>→ <span>Write the original function as: " y = </span>(5/9) (x − 32) " ;
Now, change the "y" to an "x" ; and the "x" to a "y"; and rewrite; as follows:
________________________________________________________
x = (5/9) (y − 32) ;
Now, rewrite THIS equation; by solving for "y" ; in terms of "x" ;
_____________________________________________________
→ That is, solve this equation for "y" ; with "c" as an "isolated variable" on the
"left-hand side" of the equation:
We have:
→ x = " (
Let us simplify the "right-hand side" of the equation:
_____________________________________________________
Note the "distributive property" of multiplication:
__________________________________________
a(b + c) = ab + ac ; <u><em>AND</em></u>:
a(b – c) = ab – ac .
__________________________________________
As such:
__________________________________________
" (
= [ (
= [ (
= [ (
= [ (
= [ (
= [
_______________________________________________
And rewrite as:
→ " x =
We want to rewrite this; solving for "y"; with "y" isolated as a "single variable" on the "left-hand side" of the equation ;
We have:
→ " x =
↔ "
Multiply both sides of the equation by "9" ;
9 *
to get:
→ 5y − 160 = 9x ;
Now, add "160" to each side of the equation; as follows:
_______________________________________________________
→ 5y − 160 + 160 = 9x + 160 ;
to get:
→ 5y = 9x + 160 ;
Now, divided Each side of the equation by "5" ;
to isolate "y" on one side of the equation; & to solve for "y" ;
→ 5y / 5 = (9y + 160) / 5 ;
to get:
→ y = (9/5)x + (160/5) ;
→ y = (9/5)x + 32 ;
→ Now, remember we had substituted: "y" for "c(f)" ;
Now that we have the "equation for the inverse" ;
→ which is: " (9/5)x + 32" ;
Remember that for the original ("non-inverse" equation); "y" was used in place of "c(f)" . We have the "inverse equation"; so we can denote this "inverse function" ; that is, the "inverse" of "c(f)" as: "f(c)" .
Note that "x = c" ;
_____________________________________________________
So, the inverse function is: " f(c) = (9/5) c + 32 " .
_____________________________________________________
The answer is: " f(c) =
_____________________________________________________
→ which is:
→ Answer choice: [C]: " f(c) =
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Given:
Violinists : Cellists = 7:3.
Number of violinists in the school orchestra = 21
To find:
The combined number of cellists and violinists.
Solution:
Let the number of violinists and cellists in the school orchestra are 7x and 3x respectively.
Then, combined number of cellists and violinists is
...(i)
Number of violinists in the school orchestra = 21
Divide both sides by 7.
Now, the combined number of cellists and violinists is
[Using (i)]
Therefore, the combined number of cellists and violinists is 30.