Answer:
Width of rectangular piece = x = 8 inches
Step-by-step explanation:
Perimeter of rectangular piece = 62 inches
Let width of rectangular piece= x
and length of rectangular piece = x+15
We need to find width i.e value of x
The formula used for perimeter of rectangle is:
Putting values in formula and finding Width:
After solving we get value of x = 8
So, Width of rectangular piece = x = 8 inches
Answer:
40 miles
Step-by-step explanation:
let distance be d and time be t
Since d varies directly with t, then the equation relating them is
d = kt ← k is the constant of variation
To find k use the condition d = 75 when t = 3
k = =
= 25
d = 25t ← equation of variation
when t = 1.6, then
d = 25 × 1.6 = 40 miles
We have to identify the transformations that take △ABC to △A"B"C".
The first transformation takes △ABC to △A'B'C'. We can see that the triangle is reflected over the x-axis (horizontal axis).
For example, as C is located on the x-axis, C' is also located on the x-axis. For A and B, its vertical coordinates change sign but mantain its absolute value.
We can write this transformation as:
This transformation shows that the horizontal coordinates are mantained and the vertical coordinates have their sign inverted.
The second transformation is a translation. The orientation stays the same but the points are translated a fixed number of units in both the horizontal and vertical direction.
We can take any point and its transformed point and compare its coordinates. For example B'' is 6 units to the right and 2 units up.
Then, we can write:
We can generalize this to the rule:
as the x-coordinate will increase 6 units and the y-coordinate will increase 2 units.
Answer: the transformations are a reflection over the horizontal axis (y=0) and a translation of (x+6,y+2) [First option].
