Answer:
Step-by-step explanation:
The coordinates of QS are:
The ratio is represented as:
Required
Find the coordinates of R
The coordinates of R is calculated by:
Substitute values for m, n, x's and y's
<em>None of the options is correct</em>
Answer:
200 times
Step-by-step explanation:
45 + 0.4x = 75 + 0.25x
45 + 0.4x - 45 = 75 + 0.25x -45
0.4x = 30 + 0.25x
0.4x - 0.25 x = 30 + 0.25x - 0.25x
0.15x = 30
Multiply by 100 on each side to make it easier.
15x = 3000
x = 200
Answer: it will take her 56.67 seconds or 0.945 minutes to race 2 laps
Step-by-step explanation:
It takes Ella 1 minute and 25 seconds to complete the cheep beach course.
We can express this time in seconds or minutes. Expressing it in seconds,
1 minute = 60 seconds
Therefore,
1 minute and 25 seconds = 60 +25 = 85 seconds
If the course is 3 laps long, that means she completed 3 laps in 85 seconds. The time it will take her to race 2 laps would be
(2 × 85)/3
= 56.67 seconds
Converting to minutes, it will be
56.7/60 = 0.945 minutes
Answer:
1. sinα = +2√5/5 2. cosα = +√5/5 3. cotα = +1/2 4. secα = +√5 5. cosecα = +√5/2.
Step-by-step explanation:
1. Since tan(α) = 2 and 1 + cot²α = cosec²α
1 + 1/tan²α = 1/sin²α
1 + 1/2² = 1/sin²α
1 + 1/4 = 1/sin²α
5/4 = 1/sin²α
sinα = ±√(4/5)
sinα = ±2/√5
sinα = ±2√5/5
Since 0<α<π/2, sinα = +2√5/5
2. sin²α + cos²α = 1
(2/√5)² + cos²α = 1
4/5 + cos²α = 1
cos²α = 1 - 4/5
cos²α = 1/5
cosα = ±1/√5
cosα = ±√5/5
Since 0<α<π/2, cosα = +√5/5
3. cotα = 1/tanα = 1/2
Since 0<α<π/2, cotα = +1/2
4. secα = 1/cosα = 1/±1/√5 = ±√5
Since 0<α<π/2, secα = +√5
5. cosecα = 1/sinα = 1/±2/√5 = ±√5/2
Since 0<α<π/2, cosecα = +√5/2
Answer:
Yes, John did write his systems of equations correctly.
Step-by-step explanation:
FedEx charges him a flat rate of $5, so the 5 stands alone in the problem, and $0.50 per pound, so the 0.5 stands with the x because it represents each pound.
UPS doesn't charge him a flat rate so there is no stand-alone number. Since they charge $2 per pound, 2 is with the x, again representing each pound.