Answer:
y = x⁴ − 9x² − 50x − 150
Step-by-step explanation:
Complex roots come in conjugate pairs. So if -1 + 3i is a root, then -1 − 3i is also a root.
y = (x − 5) (x + 3) (x − (-1 + 3i)) (x − (-1 − 3i))
y = (x − 5) (x + 3) (x + 1 − 3i) (x + 1 + 3i)
Distribute using FOIL (first, outer, inner, last) to get real coefficients:
y = (x − 5) (x + 3) (x² + (1 + 3i)x + (1 − 3i)x + (1 − 3i)(1 + 3i))
y = (x − 5) (x + 3) (x² + x + 3ix + x − 3ix + 1 + 3i − 3i − 9i²)
y = (x − 5) (x + 3) (x² + 2x + 1 + 9)
y = (x − 5) (x + 3) (x² + 2x + 10)
Distribute to convert from factored form to standard form:
y = (x² + 3x − 5x − 15) (x² + 2x + 10)
y = (x² − 2x − 15) (x² + 2x + 10)
y = x²(x² + 2x + 10) − 2x(x² + 2x + 10) − 15(x² + 2x + 10)
y = x⁴ + 2x³ + 10x² − 2x³ − 4x² − 20x − 15x² − 30x − 150
y = x⁴ − 9x² − 50x − 150
18 ft= 54 yds.
a square has four equal sides, so 54 times 54 equals 2,916
Your answer is 2,916 square yards
Answer:
(addition property of equality)
(multiplication property of equality)
Step-by-step explanation:
Given:
To find: appropriate properties to justify each step
Solution:
According to division property of equality, if both sides of an equation are divided by the same nonzero number, the sides remain equal.
According to multiplication property of equality, if both sides of an equation are multiplied by the same nonzero number, the sides remain equal.
According to addition property of equality, if same number is added to both sides of an equation, the sides remain equal.
According to subtraction property of equality, if same number is from both both sides of an equation, the sides remain equal.
Add 6 to both sides ( addition property of equality )
Multiply both sides by 5 (multiplication property of equality)
Answer:
c and d
Step-by-step explanation:
Answer:
x = 15
Step-by-step explanation:
(4x - 5) = 55
+ 5 + 5 Add 5 to both sides
4x = 60 Divide both sides by 4
x = 15
