The given inequality is 2.5x + 4y ≤ 60. x is the bags of chips and y is the jars of salsa,
Replace x and y in the equation with the possible answers and solve:
A) 10 chips and 2 salsas:
2.5(10) +4(2) = 25 + 8 = 32 This is less than 60 so is a solution.
B) 20 chips, 2 salsas:
2.5(20) + 4(2) = 50 + 8 = 58, this is less than 60 so is a solution.
C) 14 chips, 5 salsas:
2.5(14) + 4(5) = 35 + 20 = 55, this is less than 60 so is a solution.
D) 18 chips , 6 salsas:
2.5(18) + 4(6) = 45 + 24 = 69, this is greater than 60 so is not a solution.
18 bags of chips and 6 jars of salsa is not a solution.
Remark
pi/4 is between 0 and pi/2 which means that pi/4 is in the first quadrant.
5*pi / 4 is between pi and 3/2 pi which means that the angle is in the third quadrant.
So you are talking about one two angles that are in the first and third quadrants.
Step One
Find the Tangent of pi/4 using the unit circle as a reference.
Since pi/4 is 1/2 way between 0 and pi/2 you are referring to something that has and x value of 0.707 for an x value and 0.707 for a y value. (They are equal)
That is the point where the opposite / adjacent = 0.707/0.707 = 1
Step Two
Find the tangent of 5pi/4 using the unit circle.
Using the same argument as pi/4 this time the opposite / adjacent = -0.707/-0.707 = 1 ( the two minus signs cancel out.)
Answer:
$4,116
Step-by-step explanation:
Worth of Mike's car at the start of 2014 = $12,000
If the car is said to depreciates every year by 30% = 30/100 = 0.3
The worth of the car at the start of 2017 is what we are to determine.
This means that the car depreciated by 30% (0.3) for 3 years since 2014 (2017 - 2014 = 3 yrs)
The worth at the start of 2017 would be calculated as follows:
12,000 × (1 - 0.3)³
= 12,000 × (0.7)³
= 12,000 × 0.343
= 4,116
Worth of the car at the start of 2017 would be $4,116
Answer: 20% of 500= 100
So 500-100 = 400
4x100= 400
Step-by-step explanation:
If you call x the total value of the sales, the sale over 12,000 will be: g(x) = 12,000 - x.
And the commission is 4.1% of that = 0.041 * (12,000 - x) = 0.041 * g(x)
So, if f(x) = 0.041x, to calculate the commission you first have to calculate g(x) = 12,000 - x, and the f(g(x))=0.041[12,000 - x].
Which leads you to the solution for the commission as [f o g] (x) = f (g(x)) = 0.041 (12,000 - x).
Answer: [ f o g] (x)
