Answer:The answer is choice B
Step-by-step explanation: (3x-2y)2-(2x-3y)2
Final result :
5 • (x + y) • (x - y)
Step by step solution :
Step 1 :
1.1 Evaluate : (3x-2y)2 = 9x2-12xy+4y2
1.2 Evaluate : (2x-3y)2 = 4x2-12xy+9y2
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
5x2 - 5y2 = 5 • (x2 - y2)
Trying to factor as a Difference of Squares :
2.2 Factoring: x2 - y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (x + y) • (x - y)
Final result :
5 • (x + y) • (x - y)
Answer:
81
Step-by-step explanation:
(Refer to image)
Plug in x and z and follow order of operations to simplify the expression
4 pairs of pants for $18.
Divide price by quantity to get the cost of 1 pair of pants:
18 / 4 = 4.50 per pair.
Divide 27 by 4.50 to find number of pairs:
27 / 4.5 = 6
6 pairs of pants can be cleaned for $27.
Answer:
P(B|A)=0.25 , P(A|B) =0.5
Step-by-step explanation:
The question provides the following data:
P(A)= 0.8
P(B)= 0.4
P(A∩B) = 0.2
Since the question does not mention which of the conditional probabilities need to be found out, I will show the working to calculate both of them.
To calculate the probability that event B will occur given that A has already occurred (P(B|A) is read as the probability of event B given A) can be calculated as:
P(B|A) = P(A∩B)/P(A)
= (0.2) / (0.8)
P(B|A)=0.25
To calculate the probability that event A will occur given that B has already occurred (P(A|B) is read as the probability of event A given B) can be calculated as:
P(A|B) = P(A∩B)/P(B)
= (0.2)/(0.4)
P(A|B) =0.5