Answer:
3y + 5x = 0
Step-by-step explanation:
The slope of the line = (y2-y1) / (x2-x1) = (5-0)/(-6-(-3))
= 5 / -3 = -5/3
Using the point-slope form , the line that passes through the origin and parallel to this line is
y - 0 = -5/3(x - 0)
y = -5/3 x
Multiply through by 3:-
3y = -5x
5x + 3y = 0
X = 3
y = 5
(3,5)
I used substitution because It seemed the easiest.
From the second equation I isolated it for Y to get y=20-5x
I plugged this in to the other equation for the Y value to perform substitution.
-7x + 8 (20-5x) = 19
then it's simple algebra
-7× + 160 - 40x = 19
-47x + 160 = 19
subtract 160 from both side and divide both side by -47 to isolate x.
-47x = -141
x=3
then to find Y, simple plug this into one of the equation above. or simply use this one that we already isolated for Y:
y=20-5x
y=20-5 (3)
y=5
hope that helps
Answer:
If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
Given
← factor numerator and denominator
=
← cancel (x - 3) on numerator / denominator
= 
For each question, there is a 1/2 chance at getting the question correct by guessing.
Let's take a scenario to better understand.
Suppose the true-false paper has 5 questions. For a perfect score by guessing, you'd need to get all 5 correct (ie (1/2)⁵)
The reason why you multiply is because you need each 1/2 simultaneously for a perfect score, which is an important concept when doing binomial probability later on.
Thus, let's use this knowledge to answer the question.
We need the minimum amount of questions such that the probability is less than 1/10.
We can write an inequality for this:

Now, we need to log both sides to find n.

n > 3.3219...
n ≈ 4
Thus, 4 questions is the minimum number of questions needed.