Is the square root of 1.69 rational or irrational?
1 answer:
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Answer:
Step-by-step explanation:
2x³+ 6x² - x - 10 = 0
(1) Possible roots
The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In your function, the constant term is -10 and the leading coefficient is 2, so
Factors of 10 = ±1, ±2, ±5, ±10
Factors of 2 = ±1, ±2
(2) Synthetic division
Rather than work through all 12 possibilities, I will do one that works.
So, x = -2 is a root, and the quotient is 2x² + 2x - 5.
(3) Check for other rational roots
2x² + 2x - 5 = 0
D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44
√44 = 2√11, which is irrational.
Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.
= 0.41667
= 0.375
You are correct! 0.41667>0.375
9514 1404 393
Answer:
- 3 rides
- $16.50
Step-by-step explanation:
The plan 1 cost for x rides will be ...
y = 6 + 3.50x
The plan 2 cost for x rides will be ...
y = 12 + 1.50x
These costs will be equal when ...
y = y
6 + 3.50x = 12 + 1.50x . . . . . substitute for y
2.00x = 6 . . . . . . . . . . . . . subtract 6+1.50x
x = 3 . . . . . . . . . . . . . . . divide by 2
For 3 rides, the cost will be the same.
__
For 3 rides the cost is ...
y = 6 + 3.50(3) = 6 + 10.50 = 16.50
The cost for 3 rides will be $16.50 for either plan.
