First, let x or any variable represent the number of paintings Kate initially has. After selling 12 of it, her paintings now becomes only x - 12. Then, she purchased 7 more making the number of her paintings become x - 12 + 7 = x - 5. This number tantamount to 21.
x - 5 = 21 ; x = 26
Thus, Kate initially had 26 paintings.
In solving equations, each must have vales of x and y. X is any number and Y is the output of any number. If you substitute x for a number, you can solve the equation for y.
Answer:

Step-by-step explanation:
The logistic equation is the following one:

In which P(t) is the size of the population after t years, K is the carrying capacity of the population, r is the decimal growth rate of the population and P(0) is the initial population of the lake.
In this problem, we have that:
Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. This means that
.
The number of fish tripled in the first year. This means that
.
Using the equation for P(1), that is, P(t) when
, we find the value of r.









Applying ln to both sides.


This means that the expression for the size of the population after t years is:

Answer:
because m || n and x || y => ∠6 = ∠11 = 112°
Step-by-step explanation:
Answer:
=
3
7
.
7
2
Step-by-step explanation:
Add
2
4
.
4
5
24.45
24.45
to both sides of the equation
1
3
.
2
7
=
−
2
4
.
4
5
1
3
.
2
7
+
2
4
.
4
5
=
−
2
4
.
4
5
+
2
4
.
4
5