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calculusxy
 one year ago
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
calculusxy
 one year ago
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0subtract 5m from both sides

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1start by subtracting 36 from both sides, then it'll come in the form of \(ax^2+bx+c = 0\)

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1I still don't understand @hartnn

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1now 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
 one year ago
Best ResponseYou've already chosen the best response.1hint : one of the number is positive

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1Well I can find 9 and 4 but if I add them, it is 5 not 5.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1right so change the signs of both the numbers and try :)

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1So that would be 9 and 4 right?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1correct! :) so we split our middle term 5m as 9m + 4m

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(m^2 9m+4m 36 = 0 \) lets consider 1st 2 terms only m^2 9m what do you see common from both these terms?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1The variables are the same.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1Hi 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
 one year ago
Best ResponseYou've already chosen the best response.1so, "m" is common right? can you factor out m from m^29m ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(m^2 9m = m\times m  9\times m = m \times (m9)\) see if this makes sense :)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1cool, so lets test how much have you understood :P what is common from +4m 36 ?? factor that out!

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.14 and if you factor that out, then we can have \[4 \times m  (4 \times 9) = 4(m  9)\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1excellent! so now we have \(m (m9) +4 (m9) = 0\) what is common from 1st 2 terms!?? factor that out!

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1I don't understand what you mean

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\) \(\large m(m9) + 4(m9) =0\\ \text {(m9) is common from both therms!} \\ \Large (m9)(m+4) =0 \)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1so now we use the fact that if ab =0 a= 0 or b=0

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1Would that mean that m = 0?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1(m9)(m+4) = 0 means either one of (m9) or (m+4) has to be 0, so that product becomes 0 means m9 =0 OR m+4 = 0 makes sense?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1m9 = 0 what does m equal ?? m+4 = 0 what does m equal ??

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1m9=0 m = 9 m+4 = 0 m = 4

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1Oh!!! Thank you so much!!! I get how it is 9 and 4 thank you!

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1I have another question.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1welcome ^_^ happy learning :)

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439833174185:dw

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1In 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?
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