Answer:
2x-3y=9 and 4x-6y=30
Step-by-step explanation:
hello :
note y=(2/3)x+5 no y=23x+5
2/3 is the slope....... all lines parallel to this line has same slope.
1) 2x-3y=9 means : 3y = 2x-9 divide by 3 : y=(2/3)x-3..same slope.
2) 4x-6y=30 means : 6y= 4x-30 divide by 6 : y=(4/6)x -30/6
but 4/6 = 2/3 so : y=(2/3)x-5..same slope.
Answer:
gguj
Step-by-step explanation:
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a tree casts a 25-foot shadow on sunny day. If the angle of elevation from the tip of the shadow to the top of the tree is 32 degree, what is the height of the tree to the nearest tenth of a foot?
Tan(32)=H/25
0.624869=H/25
H=.624869 X 25
H=15.6 feet-Height of the tree.
In throwing a dice, there are 6 possible outcomes, namely 1, 2, 3, 4, 5 and 6.
P=(no. of favourable outcomes)/(no. of possible outcomes)
When we multiply the probability of an event with no. of trials, the we get the expected frequency of that event.
1) P(getting 1)=1/6
expected frequency of getting 1
=P(getting)1)×no. of trials
=1/6×600=100
But it is given that one is scored 200 times, so it makes a large difference from expected frequency, which is 100.
Therefore, the dice is not fair.
2) P(getting a tail)=0.3
estimate for the number of times the coin will land on a tail
=expected frequency of getting a tail
=P(getting a tail)×no. of trials
=0.3×150=45
3)P(getting a six)=2/3
expected frequency of getting a six
=P(getting a six)×no. of trials
=2/3×300=200
4)P(getting a three)=0.5
expected frequency of getting a three
=P(getting a three)×350
=0.5×350=175
Answer:
300 mph
Step-by-step explanation:
Let's say x is the speed of the plane in still weather.
The time it takes flying against the wind is:
990 mi / (x − 30 mph)
The time it takes flying with the wind is:
990 mi / (x + 30 mph)
The total time is 6⅔ hours, so:
6⅔ hr = 990 mi / (x − 30 mph) + 990 mi / (x + 30 mph)
6⅔ = 990 / (x − 30) + 990 / (x + 30)
20/3 = 990 / (x − 30) + 990 / (x + 30)
Solving this equation for x, multiply both sides by 3 (x − 30) (x + 30):
20 (x − 30) (x + 30) = 2970 (x + 30) + 2970 (x − 30)
20 (x² − 900) = 2970x + 8910 + 2970x − 8910
20x² − 18000 = 5940x
20x² − 5940x − 18000 = 0
x² − 297x − 900 = 0
Factor:
(x − 300) (x + 3) = 0
x = 300 or -3
Since x must be positive, x = 300 mph.
