Well for answer 23 is -6 √(5) + 6 √(2).
The answer for 25 is -3 √(5) - 2 √(6)
And the answer for 27 is -15 √(5) + 4 √(3) + 3 √(6)
Hope this helps :)
Simply put,
If you find a common denominator between 12 and 16, and multiply them to fit,
You should end up with a proportion giving you the correct answer. Whichever is lower is the better deal
Ex: a box of cereal from target costs $2
Two box deal from Costco costs $5
Which is cheaper for the money.
Assuming they are the same size, all you have to do is take the dollar amount from the one from target and multiply it by two, giving you the cost of two boxes.
$4<$5
Angles of the parallelogram which is given in the problem are:α = 49° + 17 °= 66°
β = 180° - 66° = 114°
x - length of the longest side of the parallelogram;
Use the Sine Law:x / sin 49° = 20/ sin 17°
x / 0.7547 = 20 / 0.2924
0.2924 x = 15.094
x = 15.094 : .2924
x = 51.62 is the longest side of the parallelogram.
(a) x = 4
First, let's calculate the area of the path as a function of x. You have two paths, one of them is 8 ft long by x ft wide, the other is 16 ft long by x ft wide. Let's express that as an equation to start with.
A = 8x + 16x
A = 24x
But the two paths overlap, so the actual area covered will smaller. The area of overlap is a square that's x ft by x ft. And the above equation counts that area twice. So let's modify the equation by subtracting x^2. So:
A = 24x - x^2
Now since we want to cover 80 square feet, let's set A to 80. 80 = 24x - x^2
Finally, let's make this into a regular quadratic equation and find the roots.
80 = 24x - x^2
0 = 24x - x^2 - 80
-x^2 + 24x - 80 = 0
Using the quadratic formula, you can easily determine the roots to be x = 4, or x = 20.
Of those two possible solutions, only the x=4 value is reasonable for the desired objective.
(b) There were 2 possible roots, being 4 and 20. Both of those values, when substituted into the formula 24x - x^2, return a value of 80. But the idea of a path being 20 feet wide is rather silly given the constraints of the plot of land being only 8 ft by 16 ft. So the width of the path has to be less than 8 ft (the length of the smallest dimension of the plot of land). Therefore the value of 4 is the most appropriate.
