Which hill described in the table is the steepest? Explain.
Street Horizontal
Distance (ft) Vertical Rise
of Street (ft)
Dixie Hill 80 40
Bell Hill 80 20
Liberty Hill 80 60
A) Bell Hill; it rises 1 foot for every 4 feet of horizontal travel.
B) Dixie Hill; it rises 2 feet for every 1 foot of horizontal travel.
C) Liberty Hill; it rises 4 feet for every 3 feet of horizontal travel.
D) Liberty Hill; it rises three-fourths foot for every 1 foot of horizontal travel.
I chose D
) Liberty Hill; it rises three-fourths foot for every 1 foot of horizontal travel. This is because Liberty Hill has the highest ratio of vertical rise to horizontal distance, meaning that it is the steepest of the three hills listed in the table.
DOes that mean I am right?
Yes, you are correct. The steepest hill in the table is Liberty Hill, which rises three-fourths of a foot for every 1 foot of horizontal travel.
Max charges $3.50 per hour when he mows lawns, plus $6.00 for transportation expenses. Which function rule represents the amount y Max charges to mow lawns for x hours? (1 point)
y = 9.50x
y = 6.00x + 3.50
y = 3.50x + 6.00
y = 2.5x
I chose y = 3.50x + 6.00
You are correct. The function rule that represents the amount y Max charges to mow lawns for x hours is y = 3.50x + 6.00. This is because Max charges $3.50 per hour to mow lawns, which is represented by the term 3.50x. In addition, he charges $6.00 for transportation expenses, which is represented by the constant term of 6.00.
The sale price of ground beef at a local grocery store is $1.49 for the first pound and $1.09 for each additional pound. Which function rule shows how the cost of ground beef, y, depends on the number of pounds, x? (1 point)
y = 1.49x + 1.09
y = 1.09(x – 1) + 1.49
y = (1.09 + 1.49)x
y = 1.09x + 1.49
I chose y = 1.09(x – 1) + 1.49
You are very close, but the correct function rule that shows how the cost of ground beef, y, depends on the number of pounds, x is y = 1.49 + 1.09(x-1).
The initial cost of the 1st pound is $1.49 and each additional pound costs $1.09. Since we don't want to count the cost of the 1st pound twice, we only need to add the $1.09 cost to the remaining pounds, which is (x-1).
So, the function rule becomes y = 1.49 + 1.09(x-1) which simplifies to y = 1.09x + 0.4.
so the answer then is y = 1.09x + 1.49?
No, the correct answer is y = 1.49 + 1.09(x-1) which simplifies to y = 1.09x + 0.4.
This is because the initial cost of 1 pound of ground beef is $1.49 and each additional pound costs $1.09. Since we do not want to include the cost of the first pound again, we only want to add the $1.09 cost to the remaining pounds, which is (x-1).
Therefore, the function rule that shows how the cost of ground beef, y, depends on the number of pounds, x is y = 1.49 + 1.09(x-1), which simplifies to y = 1.09x + 0.4.
To determine which hill is the steepest, we need to compare the ratios of vertical rise to horizontal distance for each hill.
For option A, Bell Hill rises 1 foot for every 4 feet of horizontal travel.
For option B, Dixie Hill rises 2 feet for every 1 foot of horizontal travel.
For option C, Liberty Hill rises 4 feet for every 3 feet of horizontal travel.
For option D, Liberty Hill rises three-fourths foot for every 1 foot of horizontal travel.
To compare these ratios, we can simplify them by finding the common denominator.
Option A: 1 foot of vertical rise for every 4 feet of horizontal travel is equivalent to 1/4.
Option B: 2 feet of vertical rise for every 1 foot of horizontal travel is equivalent to 2/1 or simply 2.
Option C: 4 feet of vertical rise for every 3 feet of horizontal travel can be simplified to 4/3.
Option D: Three-fourths of a foot of vertical rise for every 1 foot of horizontal travel is equivalent to 3/4.
Now we can compare these simplified ratios. The steepest hill will have the highest ratio.
Comparing the simplified ratios:
Option A: 1/4
Option B: 2
Option C: 4/3
Option D: 3/4
Out of these options, option C (Liberty Hill; it rises 4 feet for every 3 feet of horizontal travel) has the highest ratio, making it the steepest hill described in the table.