Answer:
Step-by-step explanation:
The equation for solving for density is:
Density = mass / volume
Then plug in the values:
Density = 6 g / 12 mL
Divide and don't forget the units!
Density = 0.5 g/mL
The point of intersection of the two lines is at (1,-1)
<h3>System of equation</h3>
The given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
Learn more on system of equation here: brainly.com/question/25976025
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Answer:
Her initial position was:
-29ft
Where we use the minus sign because this is below the ocean's surface.
Now we also know that she keeps descending at a rate of -29ft per minute, then if she keeps descending for t minutes, her position will be:
P(x) = -29ft - 29ft/min*t
Now, we also know that she does not want to descend more than 81ft below the ocean's surface, then we have the inequality:
P(x) ≥ -81ft
-29ft - 29ft/min*t ≥ -81ft
Now let's isolate t in one side:
- 29ft/min*t ≥ -81ft + 29ft = -52 ft
- 29ft/min*t ≥-52 ft
t ≤ -52ft/(- 29ft/min) = 1.79 min
Then the maximum amount of time that she can keep descending is 1.79 minutes.
Answer:
Point R is at (−20, 10), a distance of 30 units from point Q
Step-by-step explanation:
Q has coordinates (-20,-20).
P has coordinates (10,-20)
Since point R is vertically above point Q, it will have the same x-coordinate as Q.
Let R have coordinates (-20,y).
It was given that;
.
The coordinates of R are (-20,10).
The dstance from Q is 30 units.
Answer:
an = 2·2^(n-1)
Step-by-step explanation:
There are simple tests to determine whether a sequence is arithmetic or geometric. The test for an arithmetic sequence is to check to see if the differences between terms are the same. Here the differences are 2, 4, 8, so are not the same.
The test for a geometric sequence is to check to see if the ratios of terms are the same. Here, the ratios are ...
4/2 = 2
8/4 = 2
16/8 = 2
These ratios are all the same (they are "common"), so the sequence is geometric.
The general term of a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
Filling in the values for this sequence, we find the general term to be ...
an = 2·2^(n-1)
