Answer:
9 and 10
Step-by-step explanation:
The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.
<h3>Which expression can be used to find the sum of the given polynomials?</h3>
It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).
Hence, the sum can be evaluated as follows;
= 9 - 3x² + -8x² + 4x + 5
= -11x² +4x +14.
Consequently, the required expression is; -11x² +4x +14.
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Answer:
k = 106 2/3
Step-by-step explanation:
Solve for k by simplifying both sides of the equation, then isolating the variable.
Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h