V = x³ - 6x²y + 12xy² - 8y³
V = (x - 2y)³
= (x - 2y)(x - 2y)(x - 2y) ( start by expanding the first pair of factors )
= (x² - 4xy + 4y²)(x - 2y) ( multiply the terms from the first group with those in the second )
= x³ - 4x²y + 4xy² - 2x²y + 8xy² - 8y³ ( combine similar terms )
= x³ - 6x²y + 12xy² - 8y³
Answer:
________{0.50 if x < 3
________{1.00 if 3 ≤ x < 6
f(x) = ____{1.50 if 6 ≤ x < 9
________{2.00 if 9 ≤ x < 12
Step-by-step explanation:
Based on the details provided:
Employees with less than 3 years receive an increase of $0.50 hourly
Employees with at least 3 years but under 6 years receive $1.00 increase hourly
Employees with a minimum of 6 years and less than 9 get $1.50 increase hourly
Employees with at least 9 years but below 12 years receive $2.00 increase hourly
This information can be expressed as a piecewise function:
________{0.50 if x < 3
________{1.00 if 3 ≤ x < 6
f(x) = ____{1.50 if 6 ≤ x < 9
________{2.00 if 9 ≤ x < 12
The conditions are outlined in the piecewise function above with x indicating the number of years employed.
Health inspector visits once a week.
Fire inspector comes every 12 days.
a) health inspector fire inspector.
day 7. day 12.
day 14. day 24.
day 21. day 36.
day 28. day 48.
day 35. day 60.
b) 12 x 7 = 84.
Both will coincide on day 84.
Utilizing the Law of Sines (sinA/a=sinB/b=sinC/c) and recognizing that the angles in a triangle add up to 180°.
The angle C calculates to 180-53-17=110°
Thus, we have 27/sin53=b/sin17=c/sin110
This leads to b=27sin17/sin53, c=27sin110/sin53
The perimeter is defined as a+b+c, so
p=27+27sin17/sin53+27sin110/sin53 units
p≈68.65 units (rounded to the nearest hundredth of a unit)
The result I found is 32.761%. Percentage represents any fraction expressed out of 100. It's calculated using the formula: If A is to be expressed as a percentage of B, the formula is A/B * 100. In this case, the paid price for the sweater is $36.20 and the original price is $90.50. We endeavor to find out what percentage reflects the sale price of the sweater. Mathematically, this can be framed as what is 36.20% of 90.5, which translates to (price paid/original price) * 100, and mathematically results in ($36.20/$90.50) * 100 = 32.761. Thus, this indicates that the sweater was sold for 32.761% off its original price.
