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madreJ [45]
2 years ago
5

On a map of the city, 8th Street is a line segment from point (1,4) to point (6,9). J Street is a line segment that starts at (4

,–14) and stops at (–5,4). If the city council extends 8th Street in a straight line, where will it intersect J Street?
Mathematics
1 answer:
Dominik [7]2 years ago
8 0
The intersection of 8th street and J street can be determined by setting up an equation for each line segment given the points mentioned above. Note that the equation of a line can be obtained from two points such that:

y - y1 = m(x-x1), where m = (y2-y1)/(x2-x1)

For instance, the equation for 8th street is given by: y - 4 = [(9-4)/(6-1)]*(x-1). On the other hand, the equation for J street is given by: y + 14 = [(4+14)/(-5-4)]*(x-4). Simplifying the 2 equations we get: Eqn. (1) y = x + 3 and Eqn. (2) y = -2x - 6

Solving the 2 equations simultaneously, we obtain x = -3, y = 0. Thus, if the city council extends 8th street in a straight line, it will intersect J street at (-3,0).

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Since molly's solution tally's with the given solution, hence <em>Molly's solution is correct.</em>

Given the working on a partial product of 93 and 51 carried out by Molly as shown:

\begin{array}{llrr} &&93 \\ &&\underline{{}\times51} \\ &\blueD{\text{Step 1}}&\blueD{3}& \blueD{1\times3\text{ ones}}\\ &\greenD{\text{Step 2}}&\greenD{90}& \greenD{1\times 9\text{ tens}}\\ &\maroonD{\text{Step 3}}&\maroonD{150}& \maroonD{50\times 3\text{ ones}}\\ &\goldE{\text{Step 4}}&\underline{{}+\goldE{ 4{,}500}}& \goldE{50\times 9\text{ tens}}\\ &\purpleD{\text{Step 5}}&\purpleD{4{,}743}& \end{array}​

This partial product can also be solved as shown below:

93 \times 51 = (90+3)\times (50+1)

Applying the distributive law:

93 \times 51 = 90(50) + 90(1) + 3(50) + 3(1)\\93 \times 51 =4500 + 90 + 150 + 3\\93 \times 51 =4500+240+3\\93 \times 51 =4740+3\\93 \times 51 =4743

Since molly's solution tally's with the given solution, hence <em>Molly solution is correct.</em>

Learn more about partial product at: brainly.com/question/24716925

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