1.5/75 = 0.02
0.02 x 100 = $2
Therefore the original price was $2.
20 children can get a serving of popcorn
Since each serving is 1/4 of a cup, each cup can provide for 4 children. Since there are 5 total cups, multiplying 5 by 4 will give you 20.
Answer:
The price is $1.6 per square foot of the land
Step-by-step explanation:
step 1
Find the area of the plot of land
we know that
The area of the plot of land is equal to the area of trapezoid 1 plus the area of trapezoid 2
see the attached figure to better understand the problem
Remember that
The area of a trapezoid is equal to
![A=\frac{1}{2}[b1+b2]h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Bb1%2Bb2%5Dh)
<em>Find the area of trapezoid 1</em>
we have
![b1=125\ ft](https://tex.z-dn.net/?f=b1%3D125%5C%20ft)
![b2=265\ ft](https://tex.z-dn.net/?f=b2%3D265%5C%20ft)
![h=260-150=110\ ft](https://tex.z-dn.net/?f=h%3D260-150%3D110%5C%20ft)
substitute
![A1=\frac{1}{2}[125+265](110)](https://tex.z-dn.net/?f=A1%3D%5Cfrac%7B1%7D%7B2%7D%5B125%2B265%5D%28110%29)
![A1=21,450\ ft^{2}](https://tex.z-dn.net/?f=A1%3D21%2C450%5C%20ft%5E%7B2%7D)
<em>Find the area of trapezoid 2</em>
we have
![b1=150\ ft](https://tex.z-dn.net/?f=b1%3D150%5C%20ft)
![b2=265\ ft](https://tex.z-dn.net/?f=b2%3D265%5C%20ft)
![h=150\ ft](https://tex.z-dn.net/?f=h%3D150%5C%20ft)
substitute
![A2=\frac{1}{2}[150+265](150)](https://tex.z-dn.net/?f=A2%3D%5Cfrac%7B1%7D%7B2%7D%5B150%2B265%5D%28150%29)
![A2=31,125\ ft^{2}](https://tex.z-dn.net/?f=A2%3D31%2C125%5C%20ft%5E%7B2%7D)
The area total of the land is
![A=A1+A2](https://tex.z-dn.net/?f=A%3DA1%2BA2)
![A=21,450+31,125=52,575\ ft^{2}](https://tex.z-dn.net/?f=A%3D21%2C450%2B31%2C125%3D52%2C575%5C%20ft%5E%7B2%7D)
step 2
Find the price per square foot of the land
Divide the total cost by the total area
![\frac{84,120}{52,575}=1.6\frac{\$}{ft^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B84%2C120%7D%7B52%2C575%7D%3D1.6%5Cfrac%7B%5C%24%7D%7Bft%5E%7B2%7D%7D)
Answer:
![(4f)^3 = 64*f^3](https://tex.z-dn.net/?f=%284f%29%5E3%20%3D%2064%2Af%5E3)
![(-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20%5Cfrac%7B9%7D%7B4%7Dt%5E4)
Step-by-step explanation:
Solving (a):
![(4f)^3](https://tex.z-dn.net/?f=%284f%29%5E3)
Apply law of indices:
![x^3 = x * x * x](https://tex.z-dn.net/?f=x%5E3%20%3D%20x%20%2A%20x%20%2A%20x)
So, we have:
![(4f)^3 = 4f * 4f * 4f](https://tex.z-dn.net/?f=%284f%29%5E3%20%3D%204f%20%2A%204f%20%2A%204f)
Rewrite as:
![(4f)^3 = 4 * 4 * 4*f*f*f](https://tex.z-dn.net/?f=%284f%29%5E3%20%3D%204%20%2A%204%20%2A%204%2Af%2Af%2Af)
![(4f)^3 = 64*f^3](https://tex.z-dn.net/?f=%284f%29%5E3%20%3D%2064%2Af%5E3)
Solving (b):
![(-\frac{3}{2}t^2)^2](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2)
Apply law of indices:
![x * x = x^2](https://tex.z-dn.net/?f=x%20%2A%20x%20%3D%20x%5E2)
So, we have:
![(-\frac{3}{2}t^2)^2 = (-\frac{3}{2}t^2) * (-\frac{3}{2}t^2)](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%20%2A%20%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29)
Remove brackets
![(-\frac{3}{2}t^2)^2 = -\frac{3}{2}t^2 * -\frac{3}{2}t^2](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dt%5E2%20%2A%20-%5Cfrac%7B3%7D%7B2%7Dt%5E2)
Rewrite as:
![(-\frac{3}{2}t^2)^2 = -\frac{3}{2}*-\frac{3}{2}*t^2 * *t^2](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%2A-%5Cfrac%7B3%7D%7B2%7D%2At%5E2%20%2A%20%2At%5E2)
![(-\frac{3}{2}t^2)^2 = \frac{3}{2}*\frac{3}{2}*t^4](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20%5Cfrac%7B3%7D%7B2%7D%2A%5Cfrac%7B3%7D%7B2%7D%2At%5E4)
![(-\frac{3}{2}t^2)^2 = \frac{9}{4}*t^4](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20%5Cfrac%7B9%7D%7B4%7D%2At%5E4)
![(-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7Dt%5E2%29%5E2%20%3D%20%5Cfrac%7B9%7D%7B4%7Dt%5E4)
Your answer would be 8n³ + 6n² - 4n - 20.
The horizontal method for simplifying binomials is to simply multiply the terms in the first bracket by the terms in the second bracket. Written out, this looks like:
(2n² × 4n) + (4n × 4n) + (4 × 4n) + (2n² × -5) + (4n × -5) + (4 × -5).
Then, we just need to do the operations in the brackets, which gives us:
8n³ + 16n² + 16n - 10n² - 20n - 20
And finally we collect the like terms to simplify, which means doing 16n² - 10n² = 6n², and 16n - 20n = -4n, so the final answer is 8n³ + 6n² - 4n - 20.
I hope this helps!