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.
Looking at the two black dots
5 bulbs cost $9
Divide total cost by number of bulbs bought:
9 / 5 = $1.80 per bulb.
10 bulbs cost $18
Divide total cost by number of bulbs bought:
18 / 10 = $1.80 per bulb
The cost for one bulb is $1.80
X = first number
x - 8 = 2nd number
5x = 3rd number
x + x - 8 + 5x = 69
7x - 8 = 69 <=== this is the equation u would use
7x - 8 = 69
7x = 69 + 8
7x = 77
x = 11
1st number = 11
2nd number : x - 8 = 11 - 8 = 3
3rd number : 5x = 5(11) = 55
Answer:
December
Step-by-step explanation:
There are 12 months in a year and if the x value is equal to 12, and December is the 12th month of the year then x=December in the calender year.
