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How many houses will be in each side of the street? Show calculations 1.6 Represent the street light information on a graph. Use the cetacean plane below.

Mathematics

ScanSolve AI Answer

Answer

21

Step-by-step solution

4 steps
  1. Determine the number of houses on each side of the street (Question 1.5).

    The Y-axis of the provided graph represents the house numbers. The maximum value indicated on the Y-axis is 21. This suggests that the street has houses numbered up to 21.

  2. State the number of houses and show calculations (Question 1.5).

    Based on the maximum house number shown on the graph's Y-axis, it is inferred that there are 21 houses on each side of the street.
    To verify this with the sequence formula Tn=4n+1T_n = 4n + 1:
    If the last house number is 21, then:

    21=4n+121 = 4n + 1 20=4n20 = 4n n=5n = 5

    This means the 5-th street light would be on the 21-st house, consistent with the graph's maximum Y-value.
    The number of houses on each side of the street is 21\boxed{21}.

  3. List the points to be plotted (Question 1.6).

    The street light information consists of the position of the street light (nn) and the corresponding house number (TnT_n). Using the formula Tn=4n+1T_n = 4n + 1 from the previous problem:

    • For the 1st street light (n=1n=1): T1=4(1)+1=5T_1 = 4(1) + 1 = 5. Point: (1,5)(1, 5)
    • For the 2nd street light (n=2n=2): T2=4(2)+1=9T_2 = 4(2) + 1 = 9. Point: (2,9)(2, 9)
    • For the 3rd street light (n=3n=3): T3=4(3)+1=13T_3 = 4(3) + 1 = 13. Point: (3,13)(3, 13)
    • For the 4th street light (n=4n=4): T4=4(4)+1=17T_4 = 4(4) + 1 = 17. Point: (4,17)(4, 17)
    • For the 5th street light (n=5n=5): T5=4(5)+1=21T_5 = 4(5) + 1 = 21. Point: (5,21)(5, 21)
  4. Represent the information on the graph (Question 1.6).

    Plot the points $(1, 5)$, $(2, 9)$, $(3, 13)$, $(4, 17)$, and $(5, 21)$ on the provided Cartesian plane. The X-axis represents the position of the street light, and the Y-axis represents the house number. After plotting these points, draw a straight line connecting them, as this sequence represents an arithmetic progression.

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