Answer:
43.75%
Step-by-step explanation:
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
<h3>How to determine the missing coefficients of a quartic equation</h3>
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
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P = 5 .............................................
this is how=
first you expand the second equation
<span>25 + 4p = -18 + -12 + 6p + 9p
</span>
then you add the like terms in the second equation:
25 + 4p = -30 + 15p
then this is how=
25+30 = 15p -4p
55=11p
p= 5
a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
---------------------------------
We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 <em>subtract 140 from both sides</em>
AB > -40 → AB > 0
----------
(2) a + c > b
AB + 100 > 140 <em>subtract 100 from both sides</em>
AB > 40
-----------
(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
<h3>Answer: 40 < AB < 240</h3>
