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:
12 cm x 15 cm
Step-by-step explanation:
if the picture frame thickness is x,
then the frame dimension would be (8+2x) cm by (11+2x) cm
area is (8+2x)(11+2x)=180
solve for x, x= 2, -23/2
x is thickness, so should be >0, so x=2
frame dimension: 12 x 16
Answer:
180
Step-by-step explanation:
For each boy you choose, you choose one of the 15 girls.
This is the counting principle.
12 * 15 = 180
Answer: 180