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Natasha_Volkova [10]
2 years ago
6

1.Consider the system of equations. x-5y=2

Mathematics
1 answer:
JulijaS [17]2 years ago
8 0
1.Consider the system of equations. x-5y=2
3x-10y=11

(a) Jamar rewrote the first equation as –2x + 10y = –4. What justification did he have for doing this?

(b)Jamar combined the equation in Part (a) with the second equation in the system to get x = 7. Explain Jamar’s reasoning.

(c) What is the solution of the system? (d) How do you know, without graphing, that the graph of 4x – 15y = 13 passes through the point whose coordinates are the solution of the system?

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Given collinear points E, F and G such that point F is the midpoint of segment EG. Find the new length of EG given that EF =5x+9
Veseljchak [2.6K]

Answer:

The length of EG is 58 units

Step-by-step explanation:

The midpoint of a segment divides it into two equal part

Let us use this rule to solve our question

∵ E, F, and G are collinear points

∵ Point F is the midpoint of segment EG

→ That means F divides EG into 2 equal segments EF and FG

∴ EF = FG

∵ EF = 5x + 9

∵ FG = 3x + 17

→ Equate them

∴ 5x + 9 = 3x + 17

→ Subtract 3x from both sides

∵ 5x - 3x + 9 = 3x - 3x + 17

∴ 2x + 9 = 17

→ Subtract 9 from both sides

∴ 2x + 9 - 9 = 17 - 9

∴ 2x = 8

→ Divide both sides by 2 to find x

∵ \frac{2x}{2}=\frac{8}{2}

∴ x = 4

→ Substitute x by 4 in EF and FG to find their lengths

∵ EF = 5(4) + 9 = 20 + 9 = 29

∵ FG = 3(4) + 17 = 12 = 17 = 29

∵ EG = EF + FG

∴ EG = 29 + 29 = 58

∴ The length of EG is 58 units

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