In the box containing the 2 plain pencils and 2 pens, there would be a 50% chance of getting a pen. In the other box containing 7 color pencils and 3 crayons there would be a 30% chance of getting a crayon.
The circle equation is in the format (x – h)² + (y – k)² = r², with the center being at the point (h, k) and the radius being "r".
QUESTION 11.
Equation x²+y²+10x-14y-7 =0 can be rewritten as: x²+10x+25 + y² -14y + 49 -7 - 25 - 49=0
It can be factories as (x + 5)² + (y – 7)² = 9²
Therefore the radius equals 9 and the center is (-5,7)
QUESTION 12.
From equation (x + 4)² + y² = 121
The radius equals √121 = 11 and the center is (-4,0)
QUESTION 13.
As there are missing information in the question, I can't assist. However, you can use the general circle equation (x – h)² + (y – k)² = r² to solve the question.
Finally equations 14 & 15 aren't linear.
Hope that helps you :)
The consecutive positive integers would be: x and (x+1),
We would have to solve the following equation to find these numbers:
x(x+1)-[x+(x+1)]=29
x²+x-2x-1=29
x²-x-30=0
x=[1⁺₋√(1+120)]/2
x=(1⁺₋11)/2
We have two possible solutions:
x₁=(1-11)/2=-5 then: (x+1)=-5+1=-4 This is not the solution.
x₂=(1+11)/2=6 then: (x+1)=6+1=7 This solution is right.
Answer: the numbers would be 6 and 7.
Plug in 1 for x
f(1) = |1-3| + 7
|1-3| = |-2| = 2
f(1) = 2 + 7
Solution: f(1) = 9
The answer to this question is A
