Answer:
a. The constant = 45
b. The unit rate is 45 miles per hour
c. d = 45t
Step-by-step explanation:
a. ∵ d ∝ t
∴ d = kt
∵ d = 90 at t = 2
∴ 90 = k(2)
∴ k = 90 ÷ 2 = 45
∴ The constant of proportionality is 45
b. ∵ k = d(miles) ÷ t(hours) = 45
∴ The unit rate is 45 miles per hour
c. The equation is ⇒ d = 45t
Answer:
slope of M'N' = 1
Explanation:
First, we will need to get the coordinates of points M' and N':
We are given that the dilation factor (k) is 0.8
Therefore:
For point M':
x coordinate of M' = k * x coordinate of M
x coordinate of M' = 0.8 * 2 = 1.6
y coordinate of M' = k * y coordinate of M
y coordinate of M' = 0.8 * 4 = 3.2
Therefore, coordinates of M' are (1.6 , 3.2)
For point N':
x coordinate of N' = k * x coordinate of N
x coordinate of N' = 0.8 * 3 = 2.4
y coordinate of N' = k * y coordinate of N
y coordinate of N' = 0.8 * 5 = 4
Therefore, coordinates of M' are (2.4 , 4)
Then, we can get the slope of M'N':
slope = (y2-y1) / (x2-x1)
For M'N':
slope = (3.2-4) / (1.6-2.4)
slope = 1
Hope this helps :)
64 has two square roots, namely 8 and −8 , since:
82=(−8)2=64.
When we say "the square root", what is usually intended is "the principal square root", which in the case of the Real square root of a positive number is the positive one. Any non-zero number n has two square roots.
Answer:
angle of depression = 24°
Step-by-step explanation:
The angle between BA and the horizontal broken line = 90°
Thus the angle of depression ? = 90° - 66° = 24°
Answer:
Karl could have saved $2.50
Step-by-step explanation:
Cost of folders without the sale: 2.5*5 = $12.50
Cost of folders with the sale: 0.8*2.5 = $2 per folder * 5 folders = $10.00
Difference between prices: 12.5-10 = $2.50