Answer:
-2 (2 x^2 - 2 x + 5)
Step-by-step explanation:
Factor the following:
-4 x^2 + 4 x - 10
Factor -2 out of -4 x^2 + 4 x - 10:
Answer: -2 (2 x^2 - 2 x + 5)
Each lap = 4.02 km
200 laps x 4.02 = 804 km total
804 km / 240 km/h = 3.35 hours = 3 hours and 21 minutes
Answer:
see below
Step-by-step explanation:
by rewriting the function we can see that it has a minimum at
![y=7x^2+7x-7\Rightarrow y=7(x^2+x-1)\Rightarrow y=7[(x+\frac{1}{2})^2-\frac{1}{4}-1]\Rightarrow](https://tex.z-dn.net/?f=y%3D7x%5E2%2B7x-7%5CRightarrow%20y%3D7%28x%5E2%2Bx-1%29%5CRightarrow%20y%3D7%5B%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2-%5Cfrac%7B1%7D%7B4%7D-1%5D%5CRightarrow)
![y=7[(x+\frac{1}{2})^2-\frac{5}{4}]\Rightarrow minimum \ (-\frac{1}{2}, -\frac{35}{4})](https://tex.z-dn.net/?f=y%3D7%5B%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2-%5Cfrac%7B5%7D%7B4%7D%5D%5CRightarrow%20minimum%20%5C%20%28-%5Cfrac%7B1%7D%7B2%7D%2C%20-%5Cfrac%7B35%7D%7B4%7D%29)
bye.
The diagonals are:
diagonal₁=2x+3y
diagonal₂=(x+8)+(2y+5)
We have to solve the following system of equations:
2x=3y
(x+8)=(2y+5)
We solve this system by substitution method:
2x=3y ⇒x=3y/2
(3y/2 +8)=2y+5
3y+16=4y+10
-y=-6
y=6
x=3y/2=3*6/2=9
we obtain the measure of the diagonals:
diagonal₁=2x+3y=2*9+3*6=18+18=36
diagonal₂=(x+8)+(2y+5)=(9+8)+(2*6+5)=17+17=34
Answer: The longest diagonal is 36 units.
