Answer:
(-3,-12)
Step-by-step explanation:
Multiply the first equation by three to match the second equations y-term
The y-terms cancel out
Add the x-terms with each other and the terms after the equal sign as well
Divide -57 by 19
Input your x-term (-3) into one of the two first equations and multiply
Either:
Simplify your terms
Divide
Answer:
EG = 19
Step-by-step explanation:
* Lets explain how to solve the problem
- If a line bisects another line that means the point of intersection
divides the second line into two equal parts
∵ EF bisects CD at G
∴ CG = GD
∵ CG = 5x - 1
∵ GD = 7x - 13
∴ 7x - 13 = 5x - 1
* Lets solve the equation
∵ 7x - 13 = 5x - 1
- Subtract 5x from both sides and add 13 to both sides
∴ 7x - 5x = 13 - 1
∴ 2x = 12
- Divide both sides by 2
∴ x = 6
- Point G divides EF into two parts EG and GF
∴ EF = EG + GF
∵ EF = 6x - 4
- Substitute the value of x to find EF
∵ x = 6
∴ EF = 6(6) - 4 = 36 - 4 = 32
∴ EF = 32
∵ GF = 13
- Substitute the values of EF and GF in the equation of EF
∴ 32 = EG + 13
- Subtract 13 from both sides
∴ 19 = EG
* EG = 19
36% = 36/100 divide both numerator and denominator by 4 gives you 9/25
Answer:
(1, 4.5 )
Step-by-step explanation:
The required point is at the midpoint of AB
Use the midpoint formula
Given A(4, 3) and B(- 2, 6 ), then
midpoint = [ 0.5(4 - 2), 0.5(3 + 6) ] = (1, 4.5 )
Answer:
B: II, IV, I, III
Step-by-step explanation:
We believe the proof <em>statement — reason</em> pairs need to be ordered as shown below
Point F is a midpoint of Line segment AB Point E is a midpoint of Line segment AC — given
Draw Line segment BE Draw Line segment FC — by Construction
Point G is the point of intersection between Line segment BE and Line segment FC — Intersecting Lines Postulate
Draw Line segment AG — by Construction
Point D is the point of intersection between Line segment AG and Line segment BC — Intersecting Lines Postulate
Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH — by Construction
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II Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC — Midsegment Theorem
IV Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC — Substitution
I BGCH is a parallelogram — Properties of a Parallelogram (opposite sides are parallel)
III Line segment BD ≅ Line segment DC — Properties of a Parallelogram (diagonals bisect each other)
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Line segment AD is a median Definition of a Median