For exponential functions
y=ab^x,
where
a is the scale vertical stretch factor,
b is the base, and
x the exponent (also independent variable)
It is a know fact that if the scale factor (1/2 or 2 in the answer choices) is positive, the graph is increasing if the base (3 or 1/3) is greater than 1.
This means that the base cannot be equal to 1/3. This eliminates choices 3 and 4.
Next, for a base greater than 1 (3>1), and the scale factor positive, it is a dilation (image gets bigger) if the scale factor is greater than 1. This eliminates the first choice where a=2.
This leaves us with the second choice where a=1/2, b=3, which is a shrink of the given exponential base function.
the teacher has 2 1/4 pounds of clay so none of the students have enough
Answer:
<em>(3/2, 1, 3/2)</em>
Step-by-step explanation:
Given the simultaneous equation
-x+y+z=1... 1
x-y+z=2 ... 2
x+y-z=1 .... 3
Add equation 1 and 2;
-x+x + y - y + z + z = 1+2
0 + 0 + 2z = 3
2z = 3
z = 3/2
Add equation 2 and 3
x+x = 2 + 1
2x = 3
x = 3/2
Substitute x = 3/2 and z = 3/2 into 3
From 3;
x+y-z = 1
3/2 + y - 3/2 = 1
y + 0 = 1
y = 1
<em>Hence the solution (x, y, z) is (3/2, 1, 3/2)</em>
Answer:
$3,650 in total
Step-by-step explanation:
If you calculate
Answer:
It will take 3.2 hours for 8 inches of snow to fall.
Step-by-step explanation:
You can solve this be going "backwards".
You have 2.5 inches of snow falling per hour for x hours until you get 8 inches of snow, which can be represented like this:
2.5x=8 From here you being to solve by isolating x on one side of the equation. You would divide both sides by 2.5 to do this
2.5x=8
/2.5 /2.5
8 divided by 2.5 is 3.2 and you then get
x=3.2
It takes 3.2 hours for 8 inches of snow to fall
