Answer:

Step-by-step explanation:
The standard form of a quadratic is 
We will use the x and y values from each of our 3 points to find a, b, and c. Filling in the x and y values from each point:
First point (-5, 0):
and
0 = 25a - 5b + c
Second point (9, 0):
and
0 = 81a + 9b + c
Third point (8, -39):
and
-39 = 64a + 8b + c
Use the elimination method of solving systems on the first 2 equations to eliminate the c. Multiply the first equation by -1 to get:
-25a + 5b - c = 0
81a + 9b + c = 0
When the c's cancel out you're left with
56a + 14b = 0
Now use the second and third equations and elimination to get rid of the c's. Multiply the second equation by -1 to get:
-81a - 9b - c = 0
64a + 8b + c = -39
When the c's cancel out you're left with
-17a - 1b = -39
Between those 2 bolded equations, eliminate the b's. Do this by multiplying the second of the 2 by 14 to get:
56a + 14b = 0
-238a - 14b = -546
When the b's cancel out you're left with
-182a = -546 and
a = 3
Use this value of a to back substitute to find b:
56a + 14b = 0 so 56(3) + 14b = 0 gives you
168 + 14b = 0 and 14b = -168 so
b = -12
Now back sub in a and b to find c:
0 = 25a - 5b + c gives you
0 = 75+ 60 + c so
0 = 135 + c and
c = -135
Put that all together into the standard form equation to get

This type of situation applies first order type of equation. In this case, the equation is ln( A0/A1) = kt. A is the number of bacteria cultured. A0 is equal to 150. when A1 is 300, t is 20 minutes. that is ln (150/300) = k *20 the other condition is represented by ln (A0/1200) = 60k. k is equal to -0.0347. hence the first order equation is equal to ln (150/A1) = -0.0347 t
It is because you only have one output for every input
-3(5 + 8x) - 20 ≤ -11 |use distributive property: a(b + c) = ab + ac
-15 - 24x - 20 ≤ -11
-35 - 24x ≤ -11 |add 35 to both sides
-24x ≤ 24 |change signs
24x ≥ -24 |divide both sides by 24
x ≥ -1
Answer:
The y-variable will be eliminated when adding the system of equations.
There is only one solution to the system of equations.
Step-by-step explanation:
-x + 6y = 16 (1)
8x - 6y = -2 (2)
Add the equations to eliminate y
-x + 8x = 16 +(-2)
7x = 16 -2
7x = 14
x = 14/7
x = 2
Substitute x = 2 into (1)
-x + 6y = 16 (1)
-2 + 6y = 16
6y = 16 + 2
6y = 18
y = 18/6
y = 3
(x, y) = (2, 3)