C, G, and D are collinear. E, G, and F are also collinear. The two lines
1 answer:
Answer:
EG is 19 units
Step-by-step explanation:
Let us solve the question
∵ Lines CD and EF intersected at point G
∴ CD = CG + GD
∴ EF = EG + GF
∵ Line EF bisects line CD
→ That means G is the midpoint of CD
∴ CG = GD
∵ CG = 5x -1
∵ GD = 7x - 13
→ Equate them to find x
∴ 7x - 13 = 5x -1
→ Add 13 to both sides
∴ 7x -13 + 13 = 5x - 1 + 13
∴ 7x = 5x + 12
→ Subtract 5x from both sides
∴ 7x - 5x = 5x - 5x + 12
∴ 2x = 12
→ Divide both sides by 2
∴
∴ x = 6
∵ EF = 6x - 4
→ Substitute x by 6 to find its length
∴ EF = 6(6) - 4 = 36 - 4
∴ EF = 32
∵ EF = EG + GF
∵ GF = 13
∴ 32 = EG + 13
→ Subtract 13 from both sides
∵ 32 - 13 = EG + 13 - 13
∴ 19 = EG
∴ EG = 19 units
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Answer:
A dress originally costs $120
Step-by-step explanation:
To find the original cost of the dress, we will follow the steps below;
let x represent the original cost of the dress
75% of x = $90
× x = $90
= $90
MULTIPLY both-side of the equation by 100
× 100 = $90×100
At the right-hand side of the equation, 100 will cancel out 100, leaving us with just 75x
75x = $9000
DIVIDE both-side of the equation by 75
75x/75 = $9000/75
At the left-hand side of the equation 75 will cancel-out 75 leaving us with just x
x= $9000/75
x = $120
A dress originally costs $120
