Answer: (1.) 1/3
(2.)2/3
(3.) 2:1
(4.) 1/2
Step-by-step explanation:
(1.) 12 mult. problems and 12+24=36 total so 12/36 =1/3
(2.) 24 div. problems and 36 totals so 24/36 =2/3
(3.) 24 div and 12 mult =24/12 or 2/1
(4.) 12 mult and 24div =12/24=1/2
Answer: she would catch up with Tom in 1 hour.
Step-by-step explanation:
Let t represent the time it will take for Mary to catch up with Tom.
Tom leaves his boat from a dock and travels at a rate of 25 miles per hour.
Distance = speed × time
Distance travelled by Tom in t hours is
25 × t = 25t
Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. Converting 10 minutes to hours, it becomes 10/60 hour
Time spent by Mary is (t - 10/60) hours. If she travels at a rate of 30 miles per hour, it means that the distance that she would travel in
(t - 10/60) hours is
30(t - 10/60)
= 30t - 5
By the time she catches up with Tom, they would have covered the same distance. It means that
25t = 30t - 5
30t - 25t = 5
5t = 5
t = 5/5 = 1 hour
To factor the given function, find a term that is divisible by both terms. For this problem, the factor would be 2, since 2x^2 and -18 are both divisible by 2.
2(x^2 - 9)
You could further factor out x^2 - 9 because it is factorable by (x - 3) and (x + 3). Thus, it would be
2(x -3)(x+3)
The constant of proportionality based on the situation is 0.4
Step-by-step explanation:
Tanner cycled 8 miles in 20 minutes
We need to find the constant of proportionality based on the situation
1. The distance is proportion to the time, because the distance and
the time increased together
2. If the distance d and the time is t, then d ∝ t
3. The equation of the direct proportion is d = k t, where k is the
constant of proportionality
∵ d = k t
∵ d = 8 miles
∵ t = 20 minutes
- Substitute these values in the equation above
∴ 8 = k (20)
- Divide both sides by 20
∴ k = 0.4
The constant of proportionality based on the situation is 0.4
Learn more:
You can learn more about proportionality in brainly.com/question/10708697
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