Let's use 50 cents as the price of the item
Two for the price of one = $.50 for two (or $.25 each)
Three for the price of two = $1.00 for 3 or approximately $.33 each
Buy one get 25% off the 2nd means $.50 + (.125 which is 25% of $.50) for a total of $.625 or about $.63 ($.315 or about $.32 each)
Buy Two get 50% off the 2nd means $.50 for the first and $.25 for the 2nd for a total of $.75 or $.375 - about $.38 each
We can see that two for the price of one is the best value since you save $.25 off of $.50 (that's half) and that buy two get 50% off the 2nd is the smallest price reduction since the $.50 item only goes down to $.38 or twelve cents off.
This would work no matter what the cost of the item. The savings would still be in the same proportions.
Answer:
123.948 km²
Step-by-step explanation:
We can use the equation: <em>AΔ = 1/2*ab*sinθ</em>, where a and b are the lengths of the sides next to the known angle, and θ is the angle itself.
Plugging in the numbers we know, we get: <em>AΔ = 1/2*22*24*sin(28°)</em>
Simplify: <em>AΔ = 264*.4695</em> (0.4695 is approximately sin(28°))
Simplify: 123.948 km²
<h3>5x - y = 27 and 2x + y = 8 are the system of equations with a solution of (5,-2)
</h3>
<em><u>Solution:</u></em>
Given that,
create a system of equations with a solution of (5,-2)
<em><u>The equation for a line in slope intercept form:</u></em>
y = mx + b
Where, m is the slope and b is the y intercept
For (x, y) = (5, -2)
-2 = 5m + b
<em><u>When m = 5</u></em>
-2 = 5(5) + b
-2 = 25 + b
b = -2 - 25
b = -27
<em><u>When m = -2</u></em>
-2 = 5(-2) + b
-2 = -10 + b
b = 8
<em><u>Thus equations are:</u></em>
y = 5x - 27
y = -2x + 8
<em><u>Rearranging to standard form,</u></em>
5x - y = 27 --- eqn 1
2x + y = 8 ---- eqn 2
Thus the system of equations are found
<h3><u>Verify:</u></h3>
Solve eqn 1 and eqn 2
Add both eqn 1 and eqn 2
7x = 35
<h3>x = 5</h3>
Substitute x = 5 in eqn 2
2(5) + y = 8
y = 8 - 10
<h3>y = -2</h3>
Thus solution is (5, -2) and the found system of equations are correct
Answer:
#1: -2 ≤ y ≤ ∞
#2: -2 ≤ x ≤ 2
#3: -4 ≤ y ≤ 3
#4: -5 ≤ y ≤ ∞
#5: 0 ≤ x ≤ ∞
Step-by-step explanation:
To do these, you must understand what range and domain are:
Range: all the values that y can be
Domain: all the values that x can be
#1: It's asking for range, so look at the posible y values. The smallest y value is -2, and the largest is actually infinity. So, the range is: -2 ≤ y ≤ ∞.
#2: It's asking for domain, so look at the possible x values. The smallest is -2 and the largest is 2, so: -2 ≤ x ≤ 2.
#3: Again, it's asking for range, so look at the possible y values. The smallest is -4, and the largest is 3, so: -4 ≤ y ≤ 3.
#4: It's asking for range. The smallest value is -5, and the largest goes to infinity (from the arrows), so: -5 ≤ y ≤ ∞.
#5: It's asking for domain. The smallest x value is 0, and it goes to infinity. So: 0 ≤ x ≤ ∞.
