Check the picture below
hmmm so, notice the arrows, if we simply multiply top and bottom of one fraction by the other's denominator, we end up with two fractions, with the same denominator
now, what can be between 49/56 and 24/56
well, 25/56, or 26/56 or 48/56 or 39/56 and so on
once the denominators are the same, is just a matter of which numerator is larger or smaller, to see who is who
R is between S and T, so this implies that R is on line ST and we can say
SR+RT = ST
plug in the given expressions to get
(-2x+24)+(4x+10) = 4x+12
Now solve for x
(-2x+24)+(4x+10) = 4x+12
-2x+24+4x+10 = 4x+12
2x+34 = 4x+12
2x+34-2x = 4x+12-2x
34 = 2x+12
34-12 = 2x+12-12
22 = 2x
2x = 22
2x/2 = 22/2
x = 11
If x = 11, then RS is,
RS = -2*x+24
RS = -2*11+24
RS = -22+24
RS = 2
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Answers:
x = 11 and RS = 2
There is you just need to find it
Answer:
E. (You always start with the given statement)
C.
A.
D.
B.
Step-by-step explanation:
The first line is given and therefore goes with E. Given.
The second line comes from the definition of median.
It bisects the opposite side from the vertex is being drawn from: So we have FA=FB, BE=EC, and CG=GA.
Second box goes with C.
Third line says FA/FB=1, BE/EC=1, and CG/GA=1.
How did they get this. It looks like they divided previous equation on both sides by right hand side's expression.
For example:
FA=FB
Divide both sides by FB you get:
FA/FB=FB/FB
FA/FB=1
So third line goes with A.
The fourth line is substitution property. 1=1(1)(1)=1(FA/FB)(BE/EC)(CG/GA). They replaced the 1's with what we had in the previous line.
Fifth line is Ceva's Theorem since it states that the FA:FB=BE:EC=CG:GA=1 implies the medians are concurrent.
