Melanie charges $4.50 per hour when she washes cars, plus $5.00 for supplies. Which function rule represents the amount y Melanie charges to wash cars for x hours? (1 point)
a) y = 0.50x
b) y = 4.50x + 5.00
c) y = 5.00x + 4.50
d) y = 9.50x
The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. Which function rule shows how the cost of apples, y, depends on the number of pounds, x?
a) y = 1.10(x – 1) + 1.35
b) y = 1.10x + 1.35
c) y = 1.35x + 1.10
d) y = (1.10 + 1.35)x
If there's a constant term, that just plugs right in. Melanie always has $5.00 for supplies.
If there's a cost which is "per" unit, that is the slope of the line. Each new unit adds some fixed amount. Melanie gets $4.50 for each new hour worked.
So, y = 4.50x + 5.00
Do the other in like wise, but note that the first unit's cost is different from the others'.
The first answer is b.
What do you think the second answer is?
Which quadratic rule represents the data in the table?
x -1, 0, 1, 2, 3
y 6, 5, 6, 9, 14
The quadratic rule that represents the data in the table is y = x^2 + 5.
Here's how to check:
- When x is -1, y = (-1)^2 + 5 = 6.
- When x is 0, y = (0)^2 + 5 = 5.
- When x is 1, y = (1)^2 + 5 = 6.
- When x is 2, y = (2)^2 + 5 = 9.
- When x is 3, y = (3)^2 + 5 = 14.
So the values in the table match the quadratic rule.
A 154-lb person burns 420 calories per hour riding an exercise bike at a rate of 15 mi/h. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem relates to the function.
can you show how you got the answer ?
thanks
the 2nd question is a ?
correct
Thanks this really helps!
Which function rule represents the data in the table?
x -3, -2, -1, 0, 1
y -17, -14, -11, -8, -5
The rule is y = 3x - 8.
Here's how to check:
- When x is -3, y = 3(-3) - 8 = -17.
- When x is -2, y = 3(-2) - 8 = -14.
- When x is -1, y = 3(-1) - 8 = -11.
- When x is 0, y = 3(0) - 8 = -8.
- When x is 1, y = 3(1) - 8 = -5.
So the values in the table match the function rule.
Let t be the time in hours that the person rides the exercise bike.
The rate of burning calories is 420 calories per hour, so in one hour the person burns 420 calories.
The rate of riding the bike is 15 miles per hour, but we are not given the distance that the person rides. However, we know that the number of calories burned is related to the amount of work done, and work is force times distance. Since the person is riding a bike, the force is the person's weight, or 154 lbs, which we can convert to 689 newtons using the conversion 1 lb = 4.448 N. The distance is the number of miles the person rides, which we don't know, but we can use the formula distance = rate × time. We know the rate is 15 mi/h, and we are given the time t. Therefore, the distance is 15t miles.
The work done is force times distance, or 689 N × (15t miles), which equals 10,335t joules.
The number of calories burned is the work done divided by the conversion factor of 4.184 joules per calorie, or 10,335t ÷ 4.184 = 2470.96t.
Therefore, the function rule that represents the total calories burned over time t is:
y = 2470.96t
where y represents the total number of calories burned.
In other words, for each hour of exercise, the person burns 420 calories. However, the total number of calories burned also depends on the distance the person rides. In this case, since we know the rate of riding the bike but not the actual distance, we used the formula distance = rate × time to express the distance in terms of time, and then used the formula for work to find the total number of calories burned. The resulting function rule relates the total number of calories burned to the time spent riding the bike.