Answers:
1) The value of <em>AB</em> is: " 59 units."
2) The value of <em>BC</em> is: "21 units."
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3) The value of <em>AB</em> + <em>BC</em> ;
= 59 units + 21 units ;
= [the value of <em>AC </em>] ;
= {" 80 units ".}.
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<u>Step-by-step explanation: </u>
Given the following—and based on the assumption that we are dealing with: "geometric lines"—and/or: "geometric line segments"—we are asked to:
"Find the value of: " AB and BC" .
{<u>Given</u>: " <em>AB</em> = (8x + 3) ; <em>BC </em>= (2x + 7) ; <em>AC </em>= 80 ".}.
----------------------------------------------------------------------------------------------=-
<u>Note</u>: The following "<u>line graphs</u>" are "<u>Not Drawn to Scale</u>."
| (8x + 3) | (2x + 7) |
|<--------------->|<------------------->|
<----·|----------------->|<------------------->| {<u>Note</u>: "Not drawn to scale."}.
A B C
<-----|----------------->|<------------------->|
A C
<-----|<--------------------------------------->|
<-----|----------------------------------------->|
A {"<em>AC</em> = 80 ".} C
<---|------------------------------------------>|
A {"<em>AC</em><em> </em>= 80 ".}. C
| (8x + 3) ; + (2x + 7) = 80 ;
<-----|----------------->|<--------------------->I
A B C
So: We have to find the value of:
1) <em>AB </em>; which is: (8x + 3) ; <u>And:</u>
2) <em>BC </em>; which is: (2x + 7) .
To get these values; we need to find the value for "x".
So: (8x + 3) + (2x + 7) = 80 ;
➝ 8x + 3 + 2x + 7 = 80 ;
➝ Now, Let us combine the "like terms" on the "<u><em>left-hand side</em></u>" of the equation:
+8x + 2x + 3 + 7 ;
➝ to get: + 8x + 2x = + 10x ; <u><em>and:</em></u>
+3 + 7 = 10 ;
To get: "10x + 10" ;
Now, we can rewrite the equation:
{" 70 ÷ 10 = 7 ."}. " 10x + 10 = 80 ;
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To solve for "x" ; there are many ways:
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Method 1) We have: " 10x + 10 = 80 " ;
➝ Now, subtract "10" from each side of the question;
10x + 10 − 10 = 80 − 10 ;
to get: 10x = 70 ;
➝ Now, divide each side of the equation by: "10" ; to isolate "x" on one side of the equation; & to solve for "x" ;
10x /10 = 70 /10 ; to get: " x = 7 "
Method 2)
At the moment above in which we have:
" 10x = 70 " ; we know that "10x ÷ 10 = 1x" ; and then "70 ÷ 10 = 7 ".
{<u>Note that any value; divided by "</u><u>10"</u> ; is equal to:
{"that value" moved Back by: "One" decimal space.}.
So: " 1x = 7 " ; ↔ " x = 7 ".
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Method 3) :
When we have: " 10x /10 = 70 /10 " ; we have " 1x " on the "<u>left-hand side</u>" of the equation; <u><em>and:</em></u> "{ 70 /10 }" = {" 70 ÷ 10 = 7 ."}.
Note that: {" 70 ÷ 10 = 7 "} ; can be determined in many ways;
For instance: {" 70 ÷ 10 = <u> ? </u>"} ;
➝ The zeros for Both the numerator <u><em>and</em></u> denominator "cancel out"—
and we have: " " ;
➝ Cancel out each of the two (2) "zeros" ; and we have: " "
➝ This is assuming that we figure out that: " ."
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<u>Now; let's find the correct values for this Brainly Question</u>:
1) <em>AB </em>= 8x + 3 ;
Substitute our calculated value for "x" ; and solve:
➝ <em>AB </em><em> </em>= 8x + 3 ; ↔ 8(7) + 3 = 56 + 3 = 59 .
➝ <em>BC </em>= 2x + 7 ; ↔ 2(7) + 7 = 14 + 7 = 21 .<em>
</em><u>Note</u>:
➝ <em>AC</em> = 80 = <em>AB</em> + BC ≟ 59 + 21 ≟ 80 ? Yes!
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Answers:
1) The value of <em>AB</em> is: " 59 units."
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2) The value of <em>BC</em> is: "21 units."
___
3) The value of <em>AB</em> + <em>BC</em> ;
= 59 units + 21 units = {<u>The value of </u><u><em>AC</em></u><em> </em><u>}</u> = "80 units".}.
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Hope this answer—along with explanations—is helpful to you.
Best wishes in your academic pursuits!
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