calculusxy
  • calculusxy
MEDAL!!! What values of m satisfies the equation m^2 - 5m = 36 ? A. -1 and 5 B. 2 and -3 C. 4 and -1 D. 6 and -6 E. 9 and -4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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calculusxy
  • calculusxy
\[m^2 - 5m = 36\]
anonymous
  • anonymous
Sub and chug
anonymous
  • anonymous
subtract 5m from both sides

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More answers

hartnn
  • hartnn
start by subtracting 36 from both sides, then it'll come in the form of \(ax^2+bx+c = 0\)
anonymous
  • anonymous
its E.
calculusxy
  • calculusxy
I still don't understand @hartnn
anonymous
  • anonymous
e) 9,-4
hartnn
  • hartnn
|dw:1439831848970:dw|
calculusxy
  • calculusxy
Okay
hartnn
  • hartnn
now there are several methods to solve it. lets use the easiest one, splitting the middle term can you think of 2 numbers whose sum is -5 but product is -36?
hartnn
  • hartnn
hint : one of the number is positive
calculusxy
  • calculusxy
Well I can find 9 and -4 but if I add them, it is 5 not -5.
hartnn
  • hartnn
right so change the signs of both the numbers and try :)
calculusxy
  • calculusxy
So that would be -9 and 4 right?
hartnn
  • hartnn
correct! :) so we split our middle term -5m as -9m + 4m
anonymous
  • anonymous
its 9 and -4
hartnn
  • hartnn
\(m^2 -9m+4m -36 = 0 \) lets consider 1st 2 terms only m^2 -9m what do you see common from both these terms?
calculusxy
  • calculusxy
The variables are the same.
hartnn
  • hartnn
Hi Ana, we really appreciate you helping the asker by giving them the answer, but this site is primarily for the purpose of learning which can be done only by interactions, like we are doing right now :)
hartnn
  • hartnn
so, "m" is common right? can you factor out m from m^2-9m ?
calculusxy
  • calculusxy
I am not sure :\
hartnn
  • hartnn
\(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\)
hartnn
  • hartnn
\(m^2 -9m = m\times m - 9\times m = m \times (m-9)\) see if this makes sense :)
calculusxy
  • calculusxy
Yes :)
hartnn
  • hartnn
cool, so lets test how much have you understood :P what is common from +4m -36 ?? factor that out!
calculusxy
  • calculusxy
4 and if you factor that out, then we can have \[4 \times m - (4 \times 9) = 4(m - 9)\]
hartnn
  • hartnn
excellent! so now we have \(m (m-9) +4 (m-9) = 0\) what is common from 1st 2 terms!?? factor that out!
calculusxy
  • calculusxy
I don't understand what you mean
hartnn
  • hartnn
\(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\) \(\large m(m-9) + 4(m-9) =0\\ \text {(m-9) is common from both therms!} \\ \Large (m-9)(m+4) =0 \)
calculusxy
  • calculusxy
Oh yes !
hartnn
  • hartnn
so now we use the fact that if ab =0 a= 0 or b=0
hartnn
  • hartnn
(m-9)(m+4) = 0 then ?
calculusxy
  • calculusxy
Would that mean that m = 0?
hartnn
  • hartnn
(m-9)(m+4) = 0 means either one of (m-9) or (m+4) has to be 0, so that product becomes 0 means m-9 =0 OR m+4 = 0 makes sense?
calculusxy
  • calculusxy
Yes.
hartnn
  • hartnn
m-9 = 0 what does m equal ?? m+4 = 0 what does m equal ??
calculusxy
  • calculusxy
m-9=0 m = 9 m+4 = 0 m = -4
hartnn
  • hartnn
\(\huge \checkmark\)
calculusxy
  • calculusxy
Oh!!! Thank you so much!!! I get how it is 9 and -4 thank you!
calculusxy
  • calculusxy
I have another question.
hartnn
  • hartnn
welcome ^_^ happy learning :)
hartnn
  • hartnn
sure, ask
calculusxy
  • calculusxy
|dw:1439833174185:dw|
calculusxy
  • calculusxy
In the figure about, point A is the center of the circle and a vertex of the right triangle, which has an area of 12 square units and where angle BAC is the right. Point D (not shown) is the point of intersection of the perimeter of circle A and segment An. The ratio of Ab to AC is 2 to 3 and the ratio of AD and AB is 1 to 2. What is the area of the shaded region, in square units?
calculusxy
  • calculusxy
@hartnn

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