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2 years ago

The original quantity is 10 and the new quantity

Mathematics

1 answer:

kobusy [5.1K]2 years ago

7 0

Answer:

30 %

Step-by-step explanation:

Assumption: the increase is to be expressed as a percentage of 10.

We change from 10 to 13 so the increase is 3 We now need to change this into a percentage.

In fraction form we have increase Original value → 3 10 But we need to change this into the form some number 100 Let the unknown value be x giving: 3 10 ≡ some number 100 = x 100 To change the 10 from 3 10 into 100 we multiply by 10 Multiply by 1 and you do not change the value.

However, 1 comes in many forms.

3 10 × 1 = 3 10 × 10 10 = 30 100 This is the same as 30 × 1 100 but 1 100 is the same as %.

So 30 100 → 30 %

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

Arte-miy333 [17]

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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.

The degree-three term on the left-hand side is $4 x^3$ . On the right-hand side, that would be $a\, x^3$ . Hence $a = 4$ .

Now, given that $a = 4$ , rewrite the right-hand side:

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

Hence:

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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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Subtract $-12x^2 -36x$ from both sides of the equation:

$38x + 7 = c(x + 3)$ .

By the same logic, $c = 38$ .

Hence the quotient would be $(4x^2 - 12x + 38)$ .

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