Answer/Step-by-step explanation:
2. a. 5y - 3 = -18
Add 3 to both sides
5y - 3 + 3 = -18 + 3
5y = -15
Divide both sides by 5
5y/5 = -15/5
y = -3
b. -3x - 9 = 0
Add 9 to both sides
-3x - 9 + 9 = 0 + 9
-3x = 9
Divide both sides by -3
-3x/-3 = 9/-3
x = -3
c. 4 + 3(z - 8) = -23
Apply the distributive property to open the bracket
4 + 3z - 24 = -23
Add like terms
3z - 20 = -23
Add 20 to both sides
3z - 20 + 20 = - 23 + 20
3z = -3
Divide both sides by 3
3z/3 = -3/3
z = -1
d. 1 - 2(y - 4) = 5
1 - 2y + 8 = 5
-2y + 9 = 5
-2y + 9 - 9 = 5 - 9
-2y = -4
-2y/-2 = -4/-2
y = 2
3. First, find the sum of 3pq + 5p²q² + p³ and p³ - pq
(3pq + 5p²q² + p³) + (p³ - pq)
3pq + 5p²q² + p³ + p³ - pq
Add like terms
= 3pq - pq + 5p²q² + p³ + p³
= 2pq + 5p²q² + 2p³
Next, subtract 2pq + 5p²q² + 2p³ from 3p³ - 2p²q² + 4pq
(3p³ - 2p²q² + 4pq) - (2pq + 5p²q² + 2p³)
Apply distributive property to open the bracket
3p³ - 2p²q² + 4pq - 2pq - 5p²q² - 2p³
Add like terms
3p³ - 2p³ - 2p²q² - 5p²q² + 4pq - 2pq
= p³ - 7p²q² + 2pq
4. Perimeter of the rectangle = sum of all its sides
Perimeter = 2(L + B)
L = (5x - y)
B = 2(x + y)
Perimeter = 2[(5x - y) + 2(x + y)]
Perimeter = 2[5x - y + 2x + 2y]
Add like terms
Perimeter = 2(7x + y)
Substitute x = 1 and y = 2 into the equation
Perimeter = 2(7(1) + 2)
Perimeter = 2(7 + 2)
Perimeter = 2(9)
Perimeter = 18 units
5. First let's find the quotient to justify if the value we get is greater than or less than 2.25
7⅙ ÷ 3⅛
Convert to improper fraction
43/6 ÷ 25/8
Change the operation sign to multiplication and turn the fraction by the left upside down.
43/6 × 8/25
= (43 × 8)/(6 × 25)
= (43 × 4)/(3 × 25)
= 172/75
≈ 2.29
Therefore, the quotient of 7⅙ ÷ 3⅛ is greater than 2.25
