whymenotsmart

Because the rain would make the picnic cloth wet, make the people wet, and produce a sad mood?! This is not a math question, right, this is a math fourm please don't post these questions!

We  can find  the height  of  this triangle  as  follows

Using  Heron's Formula  we have  the area as

sqrt  (9 (9-8) (9-6) (9 - 4))  = sqrt  ( 9 * 3 * 5)  =  3sqrt(15)

So.....to find the height we  have

Area  = (1/2)(BC) height

3sqrt (15)  =  (1/2)(4) height

3sqrt (15)  = 2 * height

(3/2)sqrt (15)  = 1.5 sqrt (15)  =  height  = y coordinate of A

And we  can find  the  x coordinate  of A  by the Pythagorean Theorem

sqrt  [ AC^2  -  height of ABC^2 ]   = sqrt  (8^2   -(1.5 sqrt (15))^2  )  = sqrt (30.25)  =  5.5

So....the coordinates  of A  = (5.5, 1.5sqrt (15))

We  can use a formula to find  the coordinates  of  the center  of the incircle

Let B = (4,0)  and C  = (4,0)

x coordinate  of incenter  =

[ Ax* a  + Bx* b  + Cx * c ]  / perimeter

Where Ax = the x coordinate  of A  Bx  = x coordinate of B    Cx  = x coordinate of C

And a, b , c  are  the sides lengths opposite A, B and C

So  we have

[ 5.5 (4)  + (4)(8)  + (0)(6)] / 18  =  3

Similarly the  y coordinate  of the center of  the incircle  =  

[Ay * a  + By * b + Cy * c ]  / 18 

[ 1.5sqrt (15)(4)  + (0)(8) + (0)(6)  / 18   =  sqrt (15)/3   =    radius  of incircle

Then the  height of triangle ANM = height of triangle ABC  - 2* incircle radius = sqrt (15)  ( 3/2 - 2/3)  =

(5/6) sqrt (15 )

And since triangles  AMN and ABC  are similar

Then

MN  / height of AMN  =  BC / height of ABC

MN  / [ (5/6)sqrt (15) ] =   4 /  [  (3/2 ) sqrt (15) ]

MN =  4 (5/6)  / (3/2)   =  4 ( 5/6) (2/3)  =  40 /18  =  20/9  

Hope this helps, whymenotsmart/(theisocelestriangle)^m^

 Given parallelogram ABCD, whose perimeter is 124 units, E is the foot of the perpendicular from A to BC and F is the foot of the perpendicular from A to CD. Also, AE= 7 units and AF= 24 units. The area of the parallelogram ABCD is the sum of area of triangle ABC and triangle ACD

We have,

124=2(a+b)⇒a+b=62units Area of parallelogram=base∗height=7a=24b⇒7(62−b)=24b⇒b=43431=14units⇒a=62−14=48unitsTherefore area of ABCD=7a=7(48)=336sq.units

Hope this helps, whymenotsmart^m^.

 P cannot fall into area ABFE, because then, any triangle DPC is greater than any triangle APB.  P also cannot fall into area EID because all triangles BPC would be greater than all triangles APB.

If P falls into any of the regions IFC, ICG of IGD, all triangles APB will have greater areas than either triangles BPC or CPD. And these areas are 3/8 of the square ABCD = 37.5%.....so that's the probabilty that triangle APB will have a greater area than either BPC or CPD.

Hope this helps, whymenotsmart^m^.

yeah, I just accidently told you the answer:(

oops, I accidently gave the whole answer, sry

There are 10C3 = 120 possibilities for the 3 white balls that are drawn (since we don't care about the order), and 10 possibilities for the SuperBall.

Hope this helps, whymenotsmart^m^. Guest, you can take it from here.

for some reason, it's not letting me edit the question:(

Answer:

k = 13The smallest zero or root is x = -10

===============================

Work Shown:

note: you can write "x^2" to mean "x squared"

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) = x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+10 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line.

Hope this helps, whymenotsmart^m^.