Answer:
This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.
One potential confusion students may have follows from the subtle difference between what the car is doing and the idea of slope as the ratio between the change in vertical distance on the graph and the change in horizontal distance on the graph. Because the car is traveling one mile on a down-hill slope, the situation could be represented as a right triangle with a hypotenuse of 5,280 ft and a leg of 250 ft; using the Pythagorean Theorem they would find that the other leg is approximately 5,274 ft. Following through on this interpretation, a student might conclude that the car travels a horizontal distance of approximately 5,274 ft for every 250 ft in vertical distance and arrive at a slope of approximately -0.047. While this is, in some sense, the slope of the hill, it is not the slope of the function as described. This interpretation yields numbers that are very close to the situation described in the task, yet conceptually different since the distance traveled by the car would now be expressed in terms of horizontal distance traveled as opposed to distance along the slope of the hill to compute the elevation. If students do indeed pursue this line of reasoning, the task provides an opportunity to compare and contrast the graph of the function and what it represents with a drawing of the hill and the vertical and horizontal distances traversed with each mile down the slope.
Step-by-step explanation:
Answer:
Option C.
Step-by-step explanation:
The given logarithmic equation is
It can be written as
![[\because log_ax=y\Leftrightarrow x=a^y]](https://tex.z-dn.net/?f=%5B%5Cbecause%20log_ax%3Dy%5CLeftrightarrow%20x%3Da%5Ey%5D)
Now, to check whether is a true solution or not. Substitute in the LHS of given equation.
![[\because log_aa^x=x]](https://tex.z-dn.net/?f=%5B%5Cbecause%20log_aa%5Ex%3Dx%5D)
Hence, is a true solution because 
.
Therefore, the correct option is C.
<u>8th Grade: </u>90 x 0.80 = 72
<u>7th Grade:</u> 80 x 0.75 = 60
Conclusion: 8th Graders like pop music more because 72 out of the 90 in 8th grade Dave surveyed enjoy it, compared to the 60 out of 80 in 7th grade that enjoyed it.
Answer:
Twenty two over nine.
Step-by-step explanation:
The bar over the 4 means that 4 is recurring .44444......... It goes on with out bounds and is equal to 4/9.
So 2.4 = 2 4/9
= 22/9.
