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2 years ago

_______ samples are used to ensure representation from different types of subgroups in a population.

Mathematics

1 answer:

atroni [7]2 years ago

5 0

Answer:

Step-by-step explanation:

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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 $c$ .

$4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3)$ .

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:

$4x^3 + 2x + 7 = 4x^3 + 12x^2 + (b\,x + c)(x + 3)$

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:

$\begin{aligned}&\left(-12 x + c\right)(x + 3) \cr =& \left(-12 x+ c\right)(x + 3) \cr =& (-12x)(x + 3) + c(x + 3) \cr =& -12x^2 -36x + (bx + c)(x + 3)\end{aligned}$ .

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 $(4x^2 - 12x + 38)$ .

6 0

3 years ago

Megan is sitting in her car in a parking lot. The car next to her pulls forward. If Megan is looking only at the car next to her

Zina [86]

Answer:Backward

Step-by-step explanation:

If the car next to Megan is being Pulled Forward and Megan is seeing only the pulled car then her car appears to be moving backward.

This can be said by using the concept of relative velocity which states that the speed of the body with respect to the other is considered to be at rest.

Here Megan's car appears to move backward with respect to the car next to her due to the existence of relative velocity.

6 0

2 years ago

Which of the following sets of numbers could not represent the three sides of a right<br> triangle?

umka21 [38]

Answer:

{48, 64, 81}

Step-by-step explanation:

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3 years ago

Consider that point A is located at (x, y) in Quadrant I of the coordinate plane. In which quadrant is point B with coordinates

Aleonysh [2.5K]

C) quadrant IV

it is saying I need more echaractes but I wrote the answer so I am writing this

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3 years ago

a youth ice hockey team scores 14 goals in September. in that month, colin scored 6 of the goals for his team. draw additional p

kifflom [539]

Cccccctttttttt

or

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6 0

3 years ago