Look at the slope. if the slopes are the same, the two lines are parallel. if the slopes are negative reciprocals, the lines are perpendicular. otherwise, neither, the two lines will intersect.
6y=x+9
y=(1/6)x+(9/6)
the slope is 1/6, while the second line has a slope of 7, so the two lines have different slopes, so choice D is correct.
Answer:
x = 23 degrees
Step-by-step explanation:
Supplementary angles add up to 180 degrees. Thus, 3x - 17 degrees plus al 5x + 21 deg must equal 180 degrees.
Combining like terms, we get 8x - 4 = 180, or 8x = 184.
Dividing both sides by 8 yields x = 184/8 = 23 = x (measured in degrees)
Answer:
- 4 nickels
- 60 mph
Step-by-step explanation:
1. If all were dimes, the value would be $8.00. The value is actually $0.20 less than that. Replacing a dime by a nickel decreases the value by $0.05, so there must be $0.20/$0.05 = 4 nickels.
2. The total of the two speeds is the rate of closure: (420 mi)/(4 h) = 105 mi/h. The speed of the second car is found by subtracting the speed of the first car from this total:
105 mph - 45 mph = 60 mph
Answer:
- the largest number that cannot be made is 23
- see below for an explanation
Step-by-step explanation:
<em>Why numbers greater than 23 can be made</em>
From any number that Larry can make that includes an appropriate number of stamps, Larry can ...
- add 1 by adding 1×9 and taking away 2×4
- add 2 by adding 2×9 and taking away 4×4
- add 3 by adding 3×9 and taking away 6×4
- add 4 by adding 1×4
- add 5 by adding 4 and 1 (add 9, take away 4)
- add 6 by adding 4 and 2 (add 2×9, take away 3×4)
- add 7 by adding 4 and 3 (add 3×9, take away 5×4)
- add 8 by adding 2×4
- add 9 by adding 1×9
Clearly, for Larry to be able to continue adding any number, he must start with a number that contains at least 6×4 cents = 24 cents.
Larry can make 24 cents from 6 4-cent stamps. Using the above table, he can add any amount to that.
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<em>Why 23 cannot be made</em>
For 23 cents, the number of stamps must include 0, 1, or 2 9-cent stamps, so there are 3 cases to try for making 23:
- 23 cannot be made from 0 9-cent stamps because 23 is not divisible by 4
- 23 cannot be made using 1 9-cent stamp, because 14 is not divisible by 4
- 23 cannot be made using 2 9-cent stamps, because 5 is not divisible by 4.
Therefore, 23 cannot be made.
