Answer: 3y - x - 42 = 0
Step-by-step explanation:
The equation y + 1 = -3(x - 5)
Now expand the expression by opening the brackets
y + 1 = -3x + 15
Recall,
Equation of line , y = mx + c , where m = slope
rearranging the equation above in order to determine the ( m)
y = -3x -1 + 15
y = -3x + 14
Recall again condition for perpendicularity
m₁m₂ = -1
From the equation given, m₁ = -3, therefore , to get m₂
-3 x m₂ = -1
-3m₂ = -1
Therefore m₂ = -1/-3
m₂ = 1/3
Now , to find the equation of the second line parallel to the first one,
Just replaced the -3 in the equation above by m₂ = 1/3 in
y = -3x + 14
y = x/3 + 14
Now , multiply both the RHS and LHS of the equation by 3, to make it a linear.
3y = x + 3 x 14
3y = x + 42
3y - x - 42 =0
Answer:
It'll take 10.6638 years to double his money.
Step-by-step explanation:
Since the invested capital is compounded continuosly we need to use the apropriate formula shown below:
M = C*e^(r*t)
Where M is the final value, C is the initial value, r is the rate of interest and t is the total time elapsed. In this case we want to double our investment, since the amount invested was 2800, then we need to have a final value of 2*2800 = 5600. Applying these values to the formula:
5600 = 2800*e^(0.065*t)
2800*e^(0.065*t) = 5600
e^(0.065*t) = 5600/2800
e^(0.065*t) = 2
ln(e^(0.065*t)) = ln(2)
0.065*t = ln(2)
t = ln(2)/0.065 = 10.6638 years
It'll take 10.6638 years to double his money.
In order for them to work the same amount of time, you would have to make Lucas work for five hours (so he could have the same minimum time as Jonathan). So multiply Lucas's 30 minutes by five, and that equals a total of 2 hours and 30 minutes. So when Jonathan works for five hours he plays for three hours, but when Lucas works for 5 hours he only plays for 2 hours and 30 minutes. So Jonathan spends more time playing video games.
Answer:
D = 59t
P = 42t
5 hours after noon, darmian is 17 miles closer to the stadium than paisley
Step-by-step explanation:
At noon, Damian is 383 miles away from the stadium and paisley is 315 miles away from the stadium.
Now, we are told that damians speed is 59 mph while paisley's speed is 42 mph.
At t hours after noon, their distance covered will be;
Damian; D = 59t
Paisley; P = 42t
This is because distance = speed × time
Now, 5 hours after noon, their respective distance covered will be;
D(5) = 59 × 5 = 295 miles
P(5) = 42 × 5 = 210 miles
This means that;
distance of Damian from the stadium is; 383 - 295 = 88 miles
Distance of paisley from the stadium is;
315 - 210 = 105 miles
Difference in their distances to the stadium = 105 - 88 = 17 miles
Thus, 5 hours after noon, darmian is 17 miles closer to the stadium than paisley
recall that when it comes to absolute value expressions, once we remove the bars, it turns always to positive, so | -5 |, the bars go poof, and tada!! 5.
