Answer: 7(11x + 3) . ______________________________________________________ Explanation: ______________________________________________________ We are asked to: "Factor the expression: 77x + 21 ." ______________________________________________________ Upon examination of <u>both</u>: "<u><em>77x</em></u>" and "<u><em>21</em></u>" ; we can see that "<u><em>7</em></u>" is the greatest common factor (GCF) of BOTH. We can examine this visually, but let us write this out: _______________________________________________________ 21: 1, 3, <em><u>7</u></em>, 21
77x ; or simply: 77: 1, <u><em>7</em></u>, 11, 77 _____________________________ So, to proceed: _____________________________ Write down a: "7" ; _______________________________ 7 *( ????) ________________________________ Note the distributive property of multiplication: ______________________________________ a(b+c) = ab + ac ; AND:
a(b - c) = ab - ac; ____________________________________________________ So , we write down a "7" ; ____________________________________________________ 7*( ??? ____________________________________________________ The first value is: "+77x" ; so, " 7 * ? = 77x ?" ;
We can examine this visually and realize that the value is "11x";
or we can divide, as follows: (77x/ 7 = 11x ). ___________________________________________ So we have already written down: 7* (??? ) ________________________________________ We can down rewrite as: " 7 * (11x ......) ________________________________________ (since " 7 * 11x = 77x ") ; _____________________________________ The next (and in our case, final !) value in our expression is: __________________________________________________ " +21 " ; __________________________________________________ We have written down: 7* (11x ......) __________________________________________________ So now, we need to determine: "7 * ? = 21" ? __________________________________________________ We can inspect visually and determine the value is: "3" ; __________________________________________________ Or we can solve by division, as follows: __________________________________________________ "7 * ? = 21 ?" ; 21 / 7 = ? ; 21 / 7 = 3 . The value is: "3" . __________________________________________________ So , we have: " 7 * (11x .....) " ; now we can rewrite as: ____________________________________________________________ " 7*(11x + 3)" ; or, simply: " 7(11x +3)" ; The multiplication is implied). _________________________________________________________ The answer is: 7(11x +3) . _______________________________________ Does our answer make sense? Let us check!
The answer; " 7(11x +3) " is the factored expression of: "(77x + 21)" ; __________________________________________________ So: " 7(11x +3) " should EQUAL "77x +21 " . Is this true?? ___________________________________________________________
Remember the distributive property of multiplication: ________________________________________________________ a(b+c) = ab +ac ; ________________________________________________________ So; " 7(11x +3) " = (7*11x) + (7*3) ; which equals: _______________________________________________ 77x + 21 . Yes! ________________________________________________________
115 degrees because there are 180 degrees in a triangle so let the missing angle in the trinagle be x. Then we have x+75+40=180. Solving for x and subtracting that from 180 (supplementary angles) we get 115 degrees.
