Answer:
1/7
Step-by-step explanation:
The bag contains 2 red balls, 3 blue balls and 10 green balls.
The total number of balls in the bag is:
2 + 3 + 10 = 15 balls
The probability of picking a green ball is:
10/15 = 2/3
There are now 14 balls left in the bag.
The probability of picking a blue ball is:
3/14
Therefore, the probability of picking a green ball and a blue ball is:
2/3 * 3/14 = 2/14 = 1/7
8+(x/-9)=9 subtract 8
x/-9= 1 multiply by -9
x= -9
The inverse of f(x)=2x−3 is f(x)=(x+3)/2, the inverse of the function <span>f(x)=4x+10 is f(x)=(x-10)/4.
The 3rd question is not clear. What is x4 and where is the function g?</span>
Answer: The correct line is
![\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.](https://tex.z-dn.net/?f=%5Ctextup%7BLine%201%20%3A%7Dx%5E2%2B3x%2B2%3D%28x%2B1%29%28x%2B2%29%3D%28x%2B1.5%29%5E2-0.25.)
Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:
![\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.](https://tex.z-dn.net/?f=%5Ctextup%7BLine%201%3A%20%7Dx%5E2%2B3x%2B2%3D%28x%2B1%29%28x%2B2%29%3D%28x%2B1.5%29%5E2-0.25%2C%5C%5C%5C%5C%5Ctextup%7BLine%202%20%3A%7Dx%5E2%2B5x%2B6%3D%28x%2B2%29%28x%2B3%29%3D%28x%2B2.5%29%5E2%2B6.25.)
We are to select one of the lines from above that represent three equivalent expressions.
We can see that there are three different forms of a quadratic expression in each of the lines:
First one is the simplified form, second is the factorised form and third one is the vertex form.
So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.
We have
![\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),](https://tex.z-dn.net/?f=%5Ctextup%7BLine%201%3A%20%7D%5C%5C%5C%5Cx%5E2%2B3x%2B2%5C%5C%5C%5C%3Dx%5E2%2B2x%2Bx%2B2%5C%5C%5C%5C%3Dx%28x%2B2%29%2B1%28x%2B2%29%5C%5C%5C%5C%3D%28x%2B1%29%28x%2B2%29%2C)
and
![x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.](https://tex.z-dn.net/?f=x%5E2%2B3x%2B2%5C%5C%5C%5C%3Dx%5E2%2B2%5Ctimes%20x%5Ctimes%201.5%2B%281.5%29%5E2-%281.5%29%5E2%2B2%5C%5C%5C%5C%3D%28x%2B1.5%29%5E2-2.25%2B2%5C%5C%5C%5C%3D%28x%2B1.5%29%5E2-0.25.)
So,
![\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.](https://tex.z-dn.net/?f=%5Ctextup%7BLine%201%20%3A%7Dx%5E2%2B3x%2B2%3D%28x%2B1%29%28x%2B2%29%3D%28x%2B1.5%29%5E2-0.25.)
Thus, Line 1 contains three equivalent expressions.
Now,
![\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),](https://tex.z-dn.net/?f=%5Ctextup%7BLine%202%3A%20%7D%5C%5C%5C%5Cx%5E2%2B5x%2B6%5C%5C%5C%5C%3Dx%5E2%2B3x%2B2x%2B6%5C%5C%5C%5C%3Dx%28x%2B3%29%2B2%28x%2B3%29%5C%5C%5C%5C%3D%28x%2B2%29%28x%2B3%29%2C)
and
![x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.](https://tex.z-dn.net/?f=x%5E2%2B5x%2B6%5C%5C%5C%5C%3Dx%5E2%2B2%5Ctimes%20x%5Ctimes%202.5%2B%282.5%29%5E2-%282.5%29%5E2%2B6%5C%5C%5C%5C%3D%28x%2B2.5%29%5E2-6.25%2B6%5C%5C%5C%5C%3D%28x%2B2.5%29%5E2-0.25%5Cneq%20%28x%2B2.5%29%5E2%2B6.25.)
So,
![\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.](https://tex.z-dn.net/?f=%5Ctextup%7BLine%202%20%3A%7Dx%5E2%2B3x%2B2%3D%28x%2B1%29%28x%2B2%29%3D%28x%2B1.5%29%5E2%2B6.25.)
Thus, Line 2 does not contain three equivalent expressions.
Hence, Line 1 is correct.
Answer:
2 over 3
Step-by-step explanation:
.