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.
Answer:
20 units
Step-by-step explanation:
s = 8
Perimeter = s + s + 
= 8 + 8 + 4
= 20 units
Answer is:
a) 32
b) 59
Both are arithmetic sequences
Answer:
third number = 4,
equation of y, y = 5x - 11
equation of n, n = 4x
equation of x, n + x + y =19
Step-by-step explanation:
so lets write evertything as a n equation. n + x + y =19. N is the first number, x is the second number, and y is the third number. We will write the equation for y as follows 5x - 11. N will be four times the second number, so 4x. If substitute the values for out equation for x we will find what x equals to. So (4x) + x + (5x - 11) = 19
10x = 30
x = 3.
Then you substiute the answer for x in the equation for y. This will get you 5(3) - 11
15 - 11
4 = third number
Answer:
B- 78
Step-by-step explanation:
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