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Question 1

A) For the direct variation equation
y =38x
The constant of proportionality is .
Question 2
x
, what is the constant of proportionality? (1 point)
A) Donte is told that for a particular math problem, the value of is always 8 times the value of
. Donte writes the equation
y
y =8x
constant of proportionality? (1 point)
to show the relationship between and . What is the
The constant of proportionality is .
Question 3
x
y
A) A group of hikers is packing trail mix. The direct variation equation shows the
relationship between number of hikers, , and number of cups of trail mix, . What is the
constant of proportionality in this situation? (1 point)
y = x
3
4
x
The constant of proportionality is
Question 4
A) A hummingbird flaps its wings 5,000 times a minute when hovering in place. How many
times will it flap its wing in 15 seconds? (1 point)
The hummingbird will flap its wings times.
Question 5
A) In 2 days, Quinesha exercises 50 minutes. At this rate, how many minutes does she
exercise in 4 weeks? (1 point)
Quinesha exercises minutes in 4 weeks

1 answer

Here are the answers to your questions:

Question 1: The direct variation equation is \( y = 38x \). The constant of proportionality is 38.

Question 2: The equation written by Donte is \( y = 8x \). The constant of proportionality is 8.

Question 3: The equation given is \( y = \frac{3}{4}x \). The constant of proportionality is \(\frac{3}{4}\).

Question 4: To find out how many times the hummingbird will flap its wings in 15 seconds, first calculate how many seconds are in a minute and then find the number of flaps in 15 seconds:

  • \( 5,000 \) flaps/minute.
  • \( 1 \) minute = \( 60 \) seconds.
  • In \( 15 \) seconds: \[ \text{Flaps in 15 seconds} = \frac{5,000 \text{ flaps}}{60 \text{ seconds}} \times 15 \text{ seconds} = \frac{5,000 \times 15}{60} = 1,250. \] The hummingbird will flap its wings 1,250 times.

Question 5: Quinesha exercises 50 minutes in 2 days. First, find her daily exercise in minutes:

  • Daily exercise: \[ 50 \text{ minutes}/2 \text{ days} = 25 \text{ minutes/day}. \] Now, calculate how many minutes she exercises in 4 weeks (which is 28 days): \[ 25 \text{ minutes/day} \times 28 \text{ days} = 700 \text{ minutes}. \] Quinesha exercises 700 minutes in 4 weeks.