Answer:
x−2x4+2x3−7x2−8x+12=x3+4x2+x−6
The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that x=-2x=−2 is a root, since (-2)^3+4(-2)^2+(-2)-6=0(−2)3+4(−2)2+(−2)−6=0 , so x+2x+2 is also a factor and we have
\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3(x−2)(x+2)x4+2x3−7x2−8x+12=x2+2x−3
Finally, we can factorize the remaining quotient easily:
x^2+2x-3=(x+3)(x-1)x2+2x−3=(x+3)(x−1)
so the other factors are x+2x+2 , x+3x+3 , and x-1x−1 .
Answer:
Elimination (multiplication and subtraction)
There is 1 solution
Step-by-step explanation:
The only way to solve this system of equations is by elimination (multiplication). Let's say that we want to cancel out the x. You multiply the first equation by 5 and you multiply the second equation by 2.
Your equations now are:
10x-5y=55 and 10x+6y=-22
You can subtract these equations to get -11y = 77.
Now that we know that y = -7, we can substitute y in to solve x.
10x-5(-7) = 55
10x=20
x=2
Final answer (2,-7)
Answer: 5 km walking and 30 km by bus
Step-by-step explanation:
Yochanan walked from home to the bus stop at an average speed of 5 km / h. He immediately got on his school bus and traveled at an average speed of 60 km / h until he got to school. The total distance from his home to school is 35 km, and the entire trip took 1.5 hours. How many km did Yochanan cover by walking and how many did he cover by travelling on the bus?
walking - 5km/h bus - 60km/h
distance walking - d₁ distance bus - d₂
time walking - t₁ time bus - t₂
d₁ + d₂ = 35
t₁ + t₂ = 1.5
v = d/t
vwalking = d₁/t₁
5 = d₁/t₁ ⇒ d₁ = 5t₁
vbus = d₂/t₂
60 = d₂/t₂ ⇒ d₂ = 60t₂
d₁ + d₂ = 35 ⇒ 5t₁ + 60t₂ = 35
_________________________
5t₁ + 60t₂ = 35
t₁ + t₂ = 1.5 (*-5)
5t₁ + 60t₂ = 35
-5t₁ -5t₂ = -7.5 (+)
__________________________
55t₂ = 27.5
t₂ = 27.5/55 = 0.5 h
t₁ + t₂ = 1.5 ⇒ t₁ = 1.5 - 0.5 = 1h
d₁ = 5t₁ ⇒ d₁ = 5.1 = 5 km
d₂ = 60t₂ ⇒ d₂ = 30.0.5 = 30 km
