Answer:
y = 2/3x + 1/3
Step-by-step explanation:
Standard form of a line looks like y=mx+b. We already know that m is 2/3, but we don't know b. b is our y-int. With the given information, we can write this equation is point-slope form. That looks like y - y1 = m(x-x1). (x1, y1) = (1, 1) - the point given to us. So if you plug in that point to the equation, and the slope - m, it'll look like y - 1 = 2/3 (x - 1).
From here, you can just solve for y, and it'll be in standard form. I would distribute 2/3 first.
y - 1 = 2/3x - 2/3
Then, add 1 to both sides.
y = 2/3x + 1/3
Answer:
a) x1 = 6 and x2 = -2
b) -2
Step-by-step explanation:
a)
To find the roots of the quadratic equation, we can use the Bhaskara's formula:
Delta = b^2 - 4ac
Delta = (-4)^2 - 4*1*(-12) = 64
sqrt(Delta) = 8
x1 = (-b + sqrt(Delta)) / 2a
x1 = (4 + 8) / 2
x1 = 6
x2 = (-b - sqrt(Delta)) / 2a
x2 = (4 - 8) / 2
x2 = -2
b)
The roots are 6 and -2, so the smaller root is -2
Answer
D. 3m - 4/3 -2/m
<u>Explanation</u>
(9m²-4m-6) ÷ 3m = 9m²/3m - 4m/3m - 6/3m
Carry out the division, each term is divided by 3m.
9m²/3m = 3m
- 4m/3m = -4/3
- 6/3m = - 2/m
Finally you will get,
<em>3m - 4/3 -2/m</em>
Cost of kg of apples = £1.08
cost of an orange = £0.12
hi, the solution is in the pic below. sorry for the messy working!
Answer:
![\[3x+\frac{2}{3}\]](https://tex.z-dn.net/?f=%5C%5B3x%2B%5Cfrac%7B2%7D%7B3%7D%5C%5D)
Step-by-step explanation:
![\[f(x)=x-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%28x%29%3Dx-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
![\[g(x)=3x+1\]](https://tex.z-dn.net/?f=%5C%5Bg%28x%29%3D3x%2B1%5C%5D)
Hence, ![\[(f o g)(x)=f(3x+1)\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3Df%283x%2B1%29%5C%5D)
But, ![\[f(3x+1)=(3x+1)-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D%283x%2B1%29-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
Simplifying,
![\[f(3x+1)=3x+(1-\frac{1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%281-%5Cfrac%7B1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{3-1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B3-1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
Hence, ![\[(f o g)(x)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
