The length of which line segment is equal to the exact value of the sine if theta?
1 answer:
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Answer:
The last graph
Step-by-step explanation:
We transform functions in the following ways:
- multiplying the function by a number to stretch or shrink it
- multiplying by a negative to flip the orientation of the function
- adding/subtracting a value to the input x to shift it horizontally
- adding/subtracting a value to the output (or outside the function operation) to shift it vertically or horizontally.
Looking at the equation we can see
- Vertically shrunk by 0.5
- Negative leading coefficient to flip the graph's orientation
- Horizontal shift of the vertex of 3 units to the left from (0,-2) to (-3,-2)
- Vertical shift of the vertex of 2 units downward (-3,0) to (-3,-2)
The last graph has vertex (-3,-2) and satisfies the the equation.
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