Answer:
G=39, F=141
Step-by-step explanation:
Let us set up equations, with G and F as variables.
Since G and F are supplementary, they must add up to 180.
G+F=180
Given the equation, we can set it up too
F = 4 * G - 15
Here, we can solve for this equation by plugging the second equation into the first one with substitution
G+4*G-15=180
simplify and solve
5G=195
G=39
Plug this into the first equation to solve for F:
39+F=180
F=141
We can plug both answers into the second equation to check and find that we are indeed right.
Since n=5, take the 6th row of Pascal Triangle: (a+b)⁵:
(a+b)⁵ = a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵.
But a= 2x and b=y, plug in:
(2x)⁵ + 5(2x)⁴y + 10(2x)³y² + 10(2x)²y³ + 5(2x)y⁴ +y⁵
32x⁵ + 80x⁴y +80x³y² + 40x²y³ + 10xy⁴ + y⁵
The 3rd term has a:
coefficient = 80
power of x= 3
power of y =2
Answer:
25 minutes 42 seconds
Step-by-step explanation:
The tub will fill at the rate of ...
2.25 gal/min - 0.50 gal/min = 1.75 gal/min
It will take ...
45 gal/(1.75 gal/min) ≈ 25.714 min
for the tub to fill.
You can shower for about 25 minutes 42 seconds.
Answer:
c = 20 ft
Step-by-step explanation:
The largest square will be 14 sqrt(2) ft long
To figure out the side length of the square
use the pythagorean theorem
a^2 + b^2 =c^2
we are limited by the shortest side of the rectangle
28 ft
each side of the triangle is 1/2 the length of the short side of the rectangle or 14 ft
a^2 + b^2 =c^2
14^2 + 14^2 = c^2 where c is the side of the square
196 + 196 = c^2
392 = c^2
take the square root of each side
sqrt(392) = sqrt(c^2)
c = 14sqrt(2)
c = 19.799ft
to the nearest whole number
c = 20 ft
