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4 years ago

Help?!!!!!! ASAP PLEASEE

Mathematics

1 answer:

Tatiana [17]4 years ago

6 0

Answer:

Step-by-step explanation:

Circumference of a circle is given by: 2 $\pi$ r

The radius in this circle is 4 so filling in the equation

2pi(4)

= 25.132 which is most like the third answer in your picture.

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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

4 years ago

What is the value of z in the equation 2z + 6 = −4? 5 1 −1 −5

daser333 [38]

1. Subtract 6 from both sides now you would get..

2z=-10

Now divide each side by 2z and you get

z= -5

So the answer is -5

5 0

4 years ago

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Solve systems of equations algebraically x+4y=3 and 2x-3y=17 what is the system of equations

Snezhnost [94]

Type the equations to a website called maths papa-using their algebra calculator, i highly recommend it, it shows all the working clearly and the answers are always correct

6 0

4 years ago

The average Yorkshire terrier is 6 inches tall. However the

Klio2033 [76]

Answer:

4x6= 24inches tall

.............

3 0

3 years ago

Someone please tell me and maybe ill pay you

rjkz [21]

4x = 6x -10
2x = 10
x = 5

answer
x = 5

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4 years ago