Answer:

Step-by-step explanation:
Given the rational expression:
, to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator





Thus, we now have: 
Step 2: Apply the concept of Partial Fraction
Let,
= 
Multiply both sides by (x - 1)(x - 4)
= 

Step 3:
Substituting x = 4 in 





Substituting x = 1 in 





Step 4: Plug in the values of A and B into the original equation in step 2


Answer:
- Walnuts - $1.25, chocolate chips - $3.25
Step-by-step explanation:
Let walnuts = x, chocolate chips = y
<u>Set a system and solve:</u>
<u>Double the first equation and subtract the second one from it:</u>
- 6x + 10y - 6x - 2y = 40 - 14
- 8y = 26
- y = 26/8
- y = 3.25
<u>Find the value of x:</u>
- 6x + 3.25*2 = 14
- 6x = 14 - 6.5
- 6x = 7.5
- x = 7.5/6
- x = 1.25
Answer:
21 square units
Step-by-step explanation:
The sides of the rectangle are aligned with the coordinate grid, so we can easily find its dimensions.
AB lies on the line y = -2, so the horizontal extent is the difference in x-values:
6 - 3 = 3
BC lies on the line x = 6, so the vertical extent is the difference in y-values:
5 -(-2) = 7
The area is the product of these two dimensions:
A = LW = (7)(3) = 21 . . . . square units
The area of the rectangle is 21 square units.
-2(-5)^2 + 7
-2 • 5^2 + 7
-2 • 25 + 7
-50 + 7
-43
Factor out -1
-1(x^2+x-6)
Factor the inner trinomial
-1(x+3)(x-2)
Final answer: B