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aleksklad [387]

3 years ago

10

The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is 10,000 and is i

ncreasing at a rate of 2% per year. The mayor predicts that the population will continue to grow in this manner, and that in "t" years, the population will be at least 15,000.
Write an inequality in terms of "t" that models the situation.

2 answers:

jek_recluse [69]3 years ago

7 0

Answer:

10000*(1.02)^t $\geq$ 15000.

Step-by-step explanation:

mrs_skeptik [129]3 years ago

5 0

10,000 + (0.02 * 10,000) t = 15,000
That's my equation.

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<h3><u>Solution:</u></h3>

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated

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<u><em>Given system of equations are:</em></u>

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What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

Arte-miy333 [17]

Answer:

The quotient of this division is $(4x^2 -12x + 38)$ . The remainder here would be $-26$ .

Step-by-step explanation:

The numerator $4x^3 + 2x + 7$ is a polynomial about $x$ with degree $3$ .

The divisor $x + 3$ is a polynomial, also about $x$ , but with degree $1$ .

By the division algorithm, the quotient should be of degree $3 - 1 = 2$ , while the remainder shall be of degree $1 - 1 = 0$ (i.e., the remainder would be a constant.) Let the quotient be $a\,x^2 + b\, x + c$ with coefficients $a$ , $b$ , and $c$ .

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Start by finding the first coefficient of the quotient.

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$\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}$ .

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Subtract $\left(4x^3 + 12x^2\right$ from both sides of the equation:

$-12x^2 + 2x + 7 = (b\,x + c)(x + 3)$ .

The term with a degree of two on the left-hand side has coefficient $(-12)$ . Since the only term on the right hand side with degree two would have coefficient $b$ , $b = -12$ .

Again, rewrite the right-hand side:

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