Answer:
Q1) Final cost = y*0.85*1.05
Q2) Perimeter = 0.1*x - 16
Q3) One over five ( m - 100)
Explanation:
We are given three question as follows:
Q1) Jamie purchased a DVD that was on sale for 15% off. The sales tax in her county is 5%. Let y represent the original price of the DVD. Write an expression that can be used to determine the final cost of the DVD.
Solution:
Note: The effect of each percentage on original price is as follows, where y is the original price of the DVD:
Discount of 15 % = Price reduced by 0.15*y
Sales Tax of 5% = Price increased by 0.05*y
- The resulting prices from each percentage is:
Amount left after discount = y - 0.15*y = 0.85*y
Amount after tax = y + 0.05*y = 1.05*y
- The factors of each affect are:
Factor of discount = 0.85
Factor of Tax = 1.05
Hence, The factors are multiplied by the original cost to get the combined effect as follows:
Answer: Final cost = y*0.85*1.05
Q2) Write an expression for the perimeter of the triangle shown below: A triangle is shown with side lengths labeled 0.5*x + 9, 3x, and - 3.4*x - 25.
Solution:
The perimeter of the triangle is the sum of all 3 sides given:
Perimeter = (0.5*x + 9) + (3x) + ( -3.4*x - 25 )
Perimeter = (0.5*x + 3x - 3.4x) + ( 9 - 25 )
Answer: Perimeter = 0.1*x - 16
Q3) Which expression is equivalent to one over five*m − 20?
Solution:
- Re-write expression:
(1 / 5)*m - 20
Take LCM of the denominator:
(m - 100) / 5
Answer: One over five ( m - 100)