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EleoNora [17]
2 years ago
15

The function f(x) is a cubic function and the zeros of f(x) are -6, -3 and 1. The

Mathematics
1 answer:
jarptica [38.1K]2 years ago
3 0

Answer:

P(x)=-5x^3-40x^2-45x+90

Step-by-step explanation:

<u>Equation of a Polynomial</u>

Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:

P(x)=a(x-x1)(x-x2)(x-x3)

Where a is the leading coefficient.

We know the three roots of the polynomial -6, -3, and 1, thus:

P(x)=a(x+6)(x+3)(x-1)

Since the y-intercept of the polynomial is y=90 when x=0:

90=a(0+6)(0+3)(0-1)

90=a(6)(3)(-1)=-18a

Thus

a = 90/(-18) = -5

The polynomial is:

P(x)=-5(x+6)(x+3)(x-1)

We must write it in standard form, so we have to multiply all of the factors as follows:

P(x)=-5(x^2+6x+3x+18)(x-1)

P(x)=-5(x^2+9x+18)(x-1)

P(x)=-5(x^3-x^2+9x^2-9x+18x-18)

P(x)=-5(x^3+8x^2+9x-18)

\boxed{P(x)=-5x^3-40x^2-45x+90}

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The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will sea
spin [16.1K]

Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = x

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So, number of student tickets = 300 - x

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $15x

Total collection from student tickets =  (300-x)\times 11 = 3300-11x

Given that overall collection = $3630

15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow   x = 82.5

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A factory produces 60005/12
ycow [4]

Answer:

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Step-by-step explanation:

Given the amount of tons of steel produced monthly by a factory to be 6000 5/12 tons, to determine their daily production, we need to use the conversion;

Maximum of 31 days = 1 month

This means that the steel company produces 6000 5/12 tons of steel in 31 days.

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in a day, the company will therefore produce approx. (72,005/12)/31 tons of steel.

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= 72,005/12*31

= 72,005/372

= 193  209/372 tons of steel.

Hence, the factory produces about 193 \frac{209}{372} tons of steel daily

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3 years ago
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