Well lets have x be the side perpendicular to the barn. You will have two sides of length "x". Which means the side parallel to the barn has the length of (200 -2x)
So we know the area of the pasture is length * width or x * (200 - 2x)
This means we are seeking to maximize x * (200 - 2x).
This is actually a parabola with zeroes that are at x = 0 and x = 100 which means the vertex is at x = 50.
So when x = 50 > (200 - 2x) = 100
So that means the maximum area of the pasture is 50 * 100 = 5000 square feet.
Answer:
The final cost for him is;
![\text{ \$154.44}](https://tex.z-dn.net/?f=%5Ctext%7B%20%5C%24154.44%7D)
Explanation:
Given that the ipod costs $220;
![C=\text{ \$220}](https://tex.z-dn.net/?f=C%3D%5Ctext%7B%20%5C%24220%7D)
The store gives a 35% discount, which means he will only pay 65% of the original cost;
![100\text{\%- 35\% = 65\%}](https://tex.z-dn.net/?f=100%5Ctext%7B%5C%25-%2035%5C%25%20%3D%2065%5C%25%7D)
The store price is;
![\begin{gathered} P=\text{ 65\% of \$220} \\ P=\frac{65}{100}\times\text{ \$220} \\ P=\text{ \$143} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%3D%5Ctext%7B%2065%5C%25%20of%20%5C%24220%7D%20%5C%5C%20P%3D%5Cfrac%7B65%7D%7B100%7D%5Ctimes%5Ctext%7B%20%5C%24220%7D%20%5C%5C%20P%3D%5Ctext%7B%20%5C%24143%7D%20%5Cend%7Bgathered%7D)
Also he will need to pay additional 8% sales tax on the discounted price P;
![\begin{gathered} t=8\text{\% of P} \\ t=8\text{\% of \$143} \\ t=\frac{8}{100}\times\text{ \$143} \\ t=\text{ \$11.44} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D8%5Ctext%7B%5C%25%20of%20P%7D%20%5C%5C%20t%3D8%5Ctext%7B%5C%25%20of%20%5C%24143%7D%20%5C%5C%20t%3D%5Cfrac%7B8%7D%7B100%7D%5Ctimes%5Ctext%7B%20%5C%24143%7D%20%5C%5C%20t%3D%5Ctext%7B%20%5C%2411.44%7D%20%5Cend%7Bgathered%7D)
The final cost he need to pay is the sum of the discounted price and the sales tax;
![\begin{gathered} F=P+t \\ F=\text{ \$143 + \$11.44} \\ F=\text{ \$154.44} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20F%3DP%2Bt%20%5C%5C%20F%3D%5Ctext%7B%20%5C%24143%20%2B%20%5C%2411.44%7D%20%5C%5C%20F%3D%5Ctext%7B%20%5C%24154.44%7D%20%5Cend%7Bgathered%7D)
Therefore, the final cost for him is;
Answer:
w=6
Step-by-step explanation:
Simplifying
3(2w + 8) = 60
Reorder the terms:
3(8 + 2w) = 60
(8 * 3 + 2w * 3) = 60
(24 + 6w) = 60
Solving
24 + 6w = 60
Solving for variable 'w'.
Move all terms containing w to the left, all other terms to the right.
Add '-24' to each side of the equation.
24 + -24 + 6w = 60 + -24
Combine like terms: 24 + -24 = 0
0 + 6w = 60 + -24
6w = 60 + -24
Combine like terms: 60 + -24 = 36
6w = 36
Divide each side by '6'.
w = 6
Simplifying
w = 6
Answer:
Both versions of the expression equal the exact same amount;one is just much shorter.Simplifying algebraic expressions is the same idea,except you have variables in your expression.So,Basically you're turning a long expression into something you can easily make sense of
Perpendicular to a slope of 1/2 is the negative reciprocal slope -1/(1/2) = -2.
y = - 2 x + b
y + 2 x = b
b = 4 + 2(6) = 16
y = -2x + 16
Check:
-2(6)+16=4 good
Answer: y = -2x + 16