Answer:
a = 1
Step-by-step explanation:
(x²+x-1)(x-1) = x³+x²-x-x²-x+1 = x³-2x+1
Answer:
Choice C: Lauren is faster than Kevin, slower than Jeremy.
Step-by-step explanation:
Ok, so it directly says that Jeremy is going at y=12x, or 12 miles per hour. To find how fast Kevin is riding, take two points of the table and use the slope formula to get the speed(.
Slope Formula: (y2-y1) / (x2-x1)
So lets take the table plots (2, 22) and (4, 33) to do this.
(y2-y1) / (x2-x1)
(33-22) / (4-2)
(11) / (2)
The speed of Kevin is 5.5 miles by hour.
Then, it asks for how fast Lauren is going, saying she is twice as fast as Kevin. Therefore, simply do:
5.5 * 2 = 11 miles per hour
To get the third biker's speed.
Now, with all of the speeds of the bikers, we can now compare them. Here's a listing of their speeds to make things easier to compare:
Jeremy: 12 mph
Kevin: 5.5 mph
Lauren: 11 mph
From this, we can see that Lauren is the second fastest. She is slower than Jeremy but faster than Kevin. Therefore, the correct answer choice is C.
Answer: The numbers are 1 and 3.
Step-by-step explanation:
Let x = smaller number , y= larger number.
As per given,
...(i)
...(ii)
Put value of x from (i) in (ii)
![\dfrac{y}{3}+y=y^2-5\\\\\Rightarrow\ \dfrac43y=y^2-5\\\\\Rightarrow\ 3y^2-4y-15=0\\\\\Rightarrow\ 3y^2-9y+5y-15=0\\\\\Rightarrow\ 3y(y-3)+5(y-3)=0\\\\\Rightarrow\ (y-3)(3y+5)=0\\\\\Rightarrow\ y=3 \ \ or\ y=\dfrac{-5}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7By%7D%7B3%7D%2By%3Dy%5E2-5%5C%5C%5C%5C%5CRightarrow%5C%20%5Cdfrac43y%3Dy%5E2-5%5C%5C%5C%5C%5CRightarrow%5C%203y%5E2-4y-15%3D0%5C%5C%5C%5C%5CRightarrow%5C%203y%5E2-9y%2B5y-15%3D0%5C%5C%5C%5C%5CRightarrow%5C%203y%28y-3%29%2B5%28y-3%29%3D0%5C%5C%5C%5C%5CRightarrow%5C%20%28y-3%29%283y%2B5%29%3D0%5C%5C%5C%5C%5CRightarrow%5C%20y%3D3%20%5C%20%5C%20or%5C%20y%3D%5Cdfrac%7B-5%7D%7B3%7D)
Since numbers are positive , so y=3 is correct.
And x will be 1 [from (i)]
Hence, the numbers are 1 and 3.
When you plug the equation into a graphing calculator the x-intercept is -5
Or you can set the equation equal to 0 and solve for x.
Mmm, x is equals to -7....