Answer:
AB and CD are parallel lines
Step-by-step explanation:
• Parallel lines have equal slopes
• The slopes of perpendicular lines are negative reciprocals
Calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
let (x₁, y₁ ) = A(1, 4) and (x₂, y₂ ) = B(3, 8)
m = 
= 
= 2
let (x₁, y₁ ) = C(- 1, 6) and (x₂, y₂ ) = D(3, 14)
m = 
= 
= 2
Since slope of AB and CD are equal then lines are parallel
Best to find the equation of the parabola first:
Its equation is y+12.5 = (x+1.5)^2, or y = -12.5 + (x+1.5)^2
Check the first possible x-intercept: let x = -2. Does y come out to 0?
y = -12.5 + (-0.5)^2 = -12.5 + 0.25. This is not equal to 0, so (-2,0) is not an x-intercept of this parabola. Continue checking each possible x-intercept until you find the right one (or ones).
Simplifying
3x + 4 = 7 + -2x
Reorder the terms:
4 + 3x = 7 + -2x
Solving
4 + 3x = 7 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
4 + 3x + 2x = 7 + -2x + 2x
Combine like terms: 3x + 2x = 5x
4 + 5x = 7 + -2x + 2x
Combine like terms: -2x + 2x = 0
4 + 5x = 7 + 0
4 + 5x = 7
Add '-4' to each side of the equation.
4 + -4 + 5x = 7 + -4
Combine like terms: 4 + -4 = 0
0 + 5x = 7 + -4
5x = 7 + -4
Combine like terms: 7 + -4 = 3
5x = 3
Divide each side by '5'.
x = 0.6
Answer: x = 0.6
Answer:
In a certain Algebra 2 class of 30 students, 22 of them play basketball and 18 of them play baseball. There are 3 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
I know how to calculate the probability of students play both basketball and baseball which is 1330 because 22+18+3=43 and 43−30 will give you the number of students plays both sports.
But how would you find the probability using the formula P(A∩B)=P(A)×p(B)?
Thank you for all of the help.
That formula only works if events A (play basketball) and B (play baseball) are independent, but they are not in this case, since out of the 18 players that play baseball, 13 play basketball, and hence P(A|B)=1318<2230=P(A) (in other words: one who plays basketball is less likely to play basketball as well in comparison to someone who does not play baseball, i.e. playing baseball and playing basketball are negatively (or inversely) correlated)
So: the two events are not independent, and so that formula doesn't work.
Fortunately, a formula that does work (always!) is:
P(A∪B)=P(A)+P(B)−P(A∩B)
Hence:
P(A∩B)=P(A)+P(B)−P(A∪B)=2230+1830−2730=1330
Answer:
Step-by-step explanation:
lets eliminate the parenthesis,
-2x-2=2x-2
-4x=0
x=0
