A four sided figure is resized to create a scaled copy. The lengths of its four side’s change as in the table below. Original figure
15. 55
21 77
36. 12
To create a scaled copy of the original figure, we need to determine the scale factor for each side. The scale factor is found by dividing the corresponding lengths of the scaled copy by the lengths of the original figure.
The table presents the lengths of the original figure and the scaled copy:
Original figure:
Side 1: 15
Side 2: 55
Side 3: 21
Side 4: 77
Scaled copy:
Side 1: 36
Side 2: 12
To find the scale factor for each side, we divide the lengths of the scaled copy by the lengths of the original figure:
Scale factor for Side 1 = 36 / 15 = 2.4
Scale factor for Side 2 = 12 / 55 ≈ 0.218
Scale factor for Side 3 = Not provided
Scale factor for Side 4 = Not provided
Since the lengths of Side 3 and Side 4 in the scaled copy are not given, we cannot determine their scale factors.
Find the scale factor as a fraction in reduced terms
To find the scale factor as a fraction in reduced terms, we need to simplify the ratio of the lengths of the scaled copy to the lengths of the original figure.
Original figure:
Side 1: 15
Side 2: 55
Scaled copy:
Side 1: 36
Side 2: 12
To find the scale factor as a fraction, we divide the lengths of the scaled copy by the lengths of the original figure:
Scale factor for Side 1 = 36 / 15 = 12 / 5
Scale factor for Side 2 = 12 / 55
To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and denominator.
For the scale factor of Side 1:
GCD(12, 5) = 1
Therefore, the scale factor for Side 1 as a reduced fraction is 12/5.
For the scale factor of Side 2:
GCD(12, 55) = 1
Therefore, the scale factor for Side 2 as a reduced fraction is 12/55.
The table shows the cost of downloading songs from a website.
Number if songs Total cost
14 $6.50
18 $8.46
20 $9.40
If C represents the total cost in dollars and cents for any number of songs downloaded, s, write a proportional equation for C in terms of s that matches the context
Let's find the constant of proportionality first, which relates the total cost to the number of songs.
We can use any two pairs from the table to calculate the constant of proportionality:
Pair 1: (14, $6.50)
Pair 2: (18, $8.46)
To find the constant of proportionality, we divide the change in cost by the change in the number of songs:
Constant of proportionality = (Change in cost) / (Change in number of songs)
Constant of proportionality = ($8.46 - $6.50) / (18 - 14)
Constant of proportionality = $1.96 / 4
Constant of proportionality = $0.49
Now that we have the constant of proportionality, we can write the proportional equation:
C = ks
Where C represents the total cost in dollars and cents, s represents the number of songs downloaded, and k represents the constant of proportionality.
In this case, the proportional equation for the total cost C in terms of the number of songs downloaded s is:
C = $0.49s
Do i Have to write the s part
No, you don't have to explicitly include the "s" part in the proportional equation. You can simply write:
C = $0.49
This equation represents the total cost (C) in terms of the constant of proportionality, which in this case is $0.49. The "s" part is understood to be the variable that represents the number of songs downloaded.