It would be 9 1/3 divided by 7/1 or 28/3 * 1/7
It would give you 28/21 which would simplify to 4/3 and still leave you with an improper fraction
Answer:
<span>y ≤ 0.13x² + 0.38x
</span>y ≤ 766.33 - 2.90x² - 8.69x
Your question doesn't say which are the systems of inequlities, but we can find the correct one.
We can call:
x = width of the grass
y = radius of the dispenser
Now, let's translate into mathematical language the statements given in the question:
- "the length of the grassy area for the lion must be 3 feet greater than its width":
l = x + 3
- "the area of the grass must be at least 8 times greater than the radius of the parakeets' food dispenser":
A ≥ 8 · y
The area of a rectangle is given by:
A = l · w = (x + 3) · x
therefore, we can write the first inequality:
(x + 3) · x ≥ 8 · y
x² + 3x ≥ 8y
and solving for y:
y ≤ 0.13x² + 0.38x (rounded to two decimal digits)
- "The food dispenser for the parakeets is … 4 feet tall. It is exactly half-way full" means that the empty height of the dispenser is:
h = 4 : 2 = 2 ft
- "The cost of the parakeets' food is $0.49 times the length of the radius for every foot of height of food missing from the dispenser":
P = 0.49 · y · h
<span> = 0.49 · y · 2
</span>= 0.98y
- "They could put the grass in the lion's habitat for $2.84 per square foot of grass":
G = 2.84 · A
= 2.84 · (x² + 3x)
= 2.84x² + 8.52x
- "Andrea cannot spend more than $751.00 on both projects":
P + G ≤ 751.00
We can now write the second inequality:
(0.98y) + (2.84x² + 8.52x) ≤ 751.00
Solving for y:
0.98y + 2.84x² + 8.52x ≤ 751.00
0.98y ≤ 751.00 - 2.84x² - 8.52x
y ≤ 766.33 - 2.90x² - 8.69x (rounded to two decimal digits)
