G^5 -g = g(g^4 -1)=g(g^2 -1)(g^2 +1) = g(g-1)(g+1)(g^2 +1)
24g^2 -6g^4 = 6g^2(4 -g^2) = 6g^2(2 -g)(2 +g)
Step-by-step explanation:
x = number hours dog walking
y = number hours tutoring
x + y <= 11
6x + 10y >= 80
the solution is the common area below the first line and above the second line.
the first line is above the second line (due to the y-intercept of 11 vs. 8) until the crossing point.
for the crossing point we use the regular equations :
from the first we get
x = 11 - y
using this in the second
6×(11 - y) + 10y = 80
66 - 6y + 10y = 80
4y = 14
y = 14/4 = 7/2 = 3.5
x = 11 - y = 11 - 3.5 = 7.5
so, she has to do at least 3.5 hours tutoring (and then 7.5 hours dog walking) for the minimum of $80 earning, all the way up to the maximum of 11 hours tutoring (and 0 dog walking) for $110 earning.
The length of the flagpole is x - 5 yards
<h3>Area of a square</h3>
The formula for calculating the area of the flagpole is expressed as:
A = L²
Given that;
A = x² - 10 + 25
Factorize
A = x² - 5x - 5x + 25
A =(x - 5) - 5(x - 5)
A = (x-5)²
Compare
L = x - 5 yards
Hence the length of the flagpole is x - 5 yards
Learn more on area of a square here: brainly.com/question/13389992
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Answer:
work is shown and pictured
