He bikes 4/10 of a mile in 1/5 of an hour
That is 4/10 miles in 1/5 hours
Average speed = Distance/ time = 4/10 ÷ 1/5 = 4/10 × 5/1 = 2 miles/hour
Hello,
6x²+2x-20=0
==>6x²+12x-10x-20=0
==>6x(x+2)-10(x+2)=0
==>(x+2)(6x-10)=0
==>x=-2 or x=5/3
Answer:
a) 3 hrs 35 mins
b) 2 hrs 45 mins
c) 4 hrs 30 mins
d) 4 hrs 5 mins
Step-by-step explanation:
x² - 14x + 46 = 0
subtract 46 from both-side
x² - 14x = -46
Add the square of the half of the co-efficient of x
x² - 14x + (-7)² = -46 + 7²
(x-7)² = -46 + 49
(x-7)² =3
Take the square root of both-side
x-7 = ±√3
x-7= ±1.732
Add 7 to both-side of the equation.
x= 7 ± 1.732
Eithe x= 7 + 1.732 or x= 7 - 1.732
x=8.732 or x=5.268
Therefore x = 8.732 , 5.268
Answer:
![-2,\ -1,\ -\dfrac{1}{2},\ 3.](https://tex.z-dn.net/?f=-2%2C%5C%20-1%2C%5C%20-%5Cdfrac%7B1%7D%7B2%7D%2C%5C%203.)
Step-by-step explanation:
Consider polynomial
If x=-2 is its zero, then you can divide the polynomial
by
and get
![2x^4+x^3-14x^2-19x-6=(x+2)(2x^3-3x^2-8x-3).](https://tex.z-dn.net/?f=2x%5E4%2Bx%5E3-14x%5E2-19x-6%3D%28x%2B2%29%282x%5E3-3x%5E2-8x-3%29.)
If x=-1, then the polynomial
can be rewritten as
![2x^4+x^3-14x^2-19x-6=(x+2)(x+1)(2x^2-5x-3).](https://tex.z-dn.net/?f=2x%5E4%2Bx%5E3-14x%5E2-19x-6%3D%28x%2B2%29%28x%2B1%29%282x%5E2-5x-3%29.)
The quadratic polynomial has roots
![x_{1,2}=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\cdot2\cdot(-3)}}{2\cdot 2}=\dfrac{5\pm \sqrt{25+24}}{4}=\dfrac{5\pm \sqrt{49}}{4}=3,-\dfrac{1}{2}.](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%3D%5Cdfrac%7B-%28-5%29%5Cpm%5Csqrt%7B%28-5%29%5E2-4%5Ccdot2%5Ccdot%28-3%29%7D%7D%7B2%5Ccdot%202%7D%3D%5Cdfrac%7B5%5Cpm%20%5Csqrt%7B25%2B24%7D%7D%7B4%7D%3D%5Cdfrac%7B5%5Cpm%20%5Csqrt%7B49%7D%7D%7B4%7D%3D3%2C-%5Cdfrac%7B1%7D%7B2%7D.)
Then the polynomial
has zeros ![-2,\ -1,\ -\dfrac{1}{2},\ 3.](https://tex.z-dn.net/?f=-2%2C%5C%20-1%2C%5C%20-%5Cdfrac%7B1%7D%7B2%7D%2C%5C%203.)