Consider point P(x,y) such that P, X and Y are collinear,
As vectors
XP = XO + OZ where O(0,0)
XP = OZ - OX
XP= (x,y) - (-3,3)
XP = (x+3, y-3)
Similarly,
PY = (6-x, -3-y)
But XP= 2^PY
[x+3, y-3] = [2(6-x), 2(-3-y)]
Given both vectors are equal, as they go in the same direction, Solve for x and y accordingly:
x+3 = 12 - 2x
x = 3
y-3 = -6-2y
y = -1
Therefore, P(3,-1)
Answer:
1:50 PM
Step-by-step explanation:
Left school at 10:38 AM,
took them 51 minutes,
38+51=89,
89-60=29,
so when they drove to the museum, it was 11:29 AM.
From here, they stayed at the museum for 1 hour and 26 minutes,
so they stayed at the museum until 12:55 AM since 29+26=55.
Now, it took them 55 minutes to drive back to the school,
so 12:55 plus another 55 minutes,
it's going to be 1:50 PM when Dale's class got back to school.
Answer:
Step-by-step explanation:
Angles EBC and EDC are the same. and straight lines equal 180
so now to solve for x
Y = - 10x has a negative slope, m = -10, and a y-intercept of (0, 0).
The graph includes the following points:
{(-2, 20), (-1, 10), (0, 0), (1, -10), (2, -20)}.
Attached is a screenshot of the graph, where it includes the y-intercept crossing along the point of origin, (0, 0).
Please mark my answers as the Brainliest, if you find this helpful :)
Answer: it will take 14 years
Step-by-step explanation:
A savings account is started with an initial deposit of $600. This means that the principal P is
P = 600
It was compounded annually. This means that it was compounded once in a year. Therefore,
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
The duration of time that for which the money stayed in the account is t years. So
Time = t
The formula for compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years. Therefore,
a) the equation to represent the amount of money in the account as a function of time in years would be
A = 600 (1+0.021/1)^1×t
A = 600 (1.021)^t
b) the amount of time it takes for the account balance to reach $800 would be
800 = 600 (1.021)^t
Dividing both sides of the equation by 600, it becomes
1.33 = (1.021)^t
t = 14
