Answer:
see explanation
Step-by-step explanation:
Given
x² - 3x - 40 = 0
Consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term (- 3)
The factors are - 8 and + 5, since
- 8 × 5 = - 40 and - 8 + 5 = - 3, thus
(x - 8)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x + 5 = 0 ⇒ x = 5
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Given
4x² - 81 = 0 ← this is a difference of squares and factors in general as
a² - b² = (a + b)(a - b), thus
4x² - 81
=(2x)² - 9²
= (2x + 9)(2x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 9 = 0 ⇒ 2x = - 9 ⇒ x = - 
2x - 9 = 0 ⇒ 2x = 9 ⇒ x =
Answer:
y = 2
Step-by-step explanation:
Given
y + (4 - 2y) = 2 ← remove parenthesis on left side
y + 4 - 2y = 2, that is
- y + 4 = 2 ( subtract 4 from both sides )
- y = - 2 ( multiply both sides by - 1 )
y = 2
Answer:
The cost of each pair of shoes before the discount=$67.65
Step-by-step explanation:
Step 1
Use the expression below to determine original cost of the 2 pairs of shoes as follows;
A=O-R
where;
A=total bill after discount
O=original cost of 2 pairs of shoe
R=discount amount
In our case;
A=$110.50
O=unknown=x
R=15% of O=(15/100)×x=0.15 x
replacing;
115=x-0.15 x
115=0.85 x
x=115/0.85
x=135.294
Original cost of the 2 pairs of shoes=$135.294
Original cost of a pair of shoes=135.294/2=$67.65
The cost of each pair of shoes before the discount=$67.65
False because the left is statement in the right is reason
