The following table shows the relationship between the time taken to perform the jumps by maria. determine whether the number of jumps is proportional to the number of seconds. if the relationship is proportional, identify the constant of proportionality.
time (seconds)
45
60
105
141
174
jumps completed by maria
15
20
35
47
58
question 8 options:
not proportional; 3
proportional; 3
not proportional;
proportional;

The correct option is B) proportional; 3

Step-by-step explanation:

Consider the provided table.

The constant of proportionality (k) is equal to y/x.

For the provided table the constant of proportionality will be:

Now find the proportionality as shown:

Time (seconds)     Jumps     proportionality

45                             15          

60                             20          

105                            35          

141                             47          

174                             58          

That means Maria can jump once in 3 second.

Hence, the above table is proportional; 3

Therefore, the correct option is B) proportional; 3

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°