Okay, here we have this:
Considering the provided expression, we are going to analize which exponential expression is equivalent, so we obtain the following:
As the property of the exponent of a multiplication says that it is equal to the product of each number raised to that power. We have this:
Finally we obtain that the correct answer is the option D.
The domain is the set of allowed x inputs, or x coordinates of a function. In this case, any point on the curve has an x coordinate that is 4 or smaller.
Therefore, the domain is the set of numbers x such that
To write this in interval notation, we would write This interval starts at negative infinity and stops at 4. We exclude infinity with the curved parenthesis and include 4 with the square bracket.
-----------------------------------------------------------------------
The range is the set of possible y outputs. Every point on this curve has a y coordinate that is either 0 or it is larger than 0.
The range is the set of y values such that
In interval notation, it would be written as This time we start at 0 (including this endpoint) and "stop" at infinity
note: we always use curved parenthesis at positive or negative infinity because we cannot reach either infinity
All the answers to the given parts are mentioned below -
<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
We can write the proportional relationship as -
y = kx
Now, from the given information, we can write -
2 scoops need 0.5 gallon of water
6 scoops need 1.5 gallon of water
So -
k = 2/0.5
k = 2/(1/2)
k = 2 x 2 = 4
Equations that represents the relationship can be written as -
y = 4x + c
Now, 2 scoops need 0.5 gallon of water.
2 = 4 x 1/2 + c
2 = 2 + c
c = 0
So, the equation will be y = 4x.
Graph of y = 4x is attached at the end.
For 10 scoops of water -
10 = 4x
x = 2.5 gallons of water is needed.
Therefore, all the answers to the given parts are mentioned above.
To solve more questions on proportional relationship, visit the link below-
#SPJ1
