If f(2) =20 and f(3) =10F(4) = ,f(5)=
1 answer:
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Answer:
x = 15 or x = -
Step-by-step explanation:
Cross- multiplying gives
(14x + 6)(17x + 5) = 9x(27x + 11) ( expanding factors )
238x² + 172x + 30 = 243x² + 99x
rearrange into standard form : ax² + bx + c = 0
5x² - 73x - 30 = 0 ← in standard form
consider the factors of the product 5 × - 30 = - 150 which sum to the coefficient of the x-term (- 73 )
the factors are - 75 and + 2
Use these factors to split the middle term
5x² - 75x + 2x - 30 = 0 ( factor by grouping )
5x(x - 15) + 2(x - 15) = 0 ← take out the factor (x - 15)
(x - 15)(5x + 2) = 0
equate each factor to zero and solve for x
x - 15 = 0 ⇒ x = 15
5x + 2 = 0 ⇒ x = -
Answer:
a) 1,757,600 different plates possible.
b) 1,404,000 different plates possible.
Step-by-step explanation:
The permutations formula is important to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
(a) can be repeated:
There are 3 letters, each one with 26 possible outcomes.
2 digits, each with 10 possible outcomes
So
T = 26*26*26*10*10 = 1757600
1,757,600 different plates possible.
(b) cannot be repeated:
Here the permutations formula is used.
Three letters, from a set of 26.
Two digits, from a set of 10. So
1,404,000 different plates possible.