Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:
Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t
Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0
Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles
So after 70 min's of driving, Dale will be 36.5 miles from his destination.
-36x+30
-24x+20
-18x+15
-12x+10
Answer:
and 
in interval notation.
Step-by-step explanation:
We have been given a compound inequality 
. We are supposed to find the solution of our given inequality.
First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.
Dividing by negative number, flip the inequality sign:
Dividing by negative number, flip the inequality sign:
Upon merging both intervals, we will get:
Therefore, the solution for our given inequality would be and in interval notation.
Answer:
<h2>3.05x(output for x)</h2><h2>39.65</h2>
Step-by-step explanation:
<h3>to understand this</h3><h3>you need to know about:</h3>
<h3>let's solve:</h3>
according to the question
the function is
f(x)=3.05x(first answer)
let's justify
f(1)=3.05×1
=3.05
LIKEWISE
f(3)=3.05×3
=9.15
therefore
it is the function
answer for the second question
f(13)=3.05×13
=39.65
Answer:
f(1/3) = 1
Step-by-step explanation:
Plug 1/3 in for n
f(1/3) = 3(1/3)
Now simplify
f(1/3) = 1 { 3(1/3) = (3/1)(1/3) = 3/3 = 1 }
