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3 years ago

Help!!!!!! show all work

Mathematics

2 answers:

Gnom [1K]3 years ago

8 0

Hi There!

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Part A:

Slope Intercept Form: y = mx + b

m = slope (slope = $\frac{y2 - y1}{x2 - x1}$ )

b = y intercept

$m=\frac{4 - 6}{(-2)- (-6)} = \frac{-2}{4} = \frac{-1}{2}$

b = 3

Answer: y = -1/2x + 3

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Part B:

Just substitue f(x) for y.

Function Notation = f(x) -1/2 + 3

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Part C:

This function given looks almost the same but the slope is different while the one stated in the question has a slope of +2 and the equation given at the start with the slope being -1/2.

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Hope This Helps :)

Kobotan [32]3 years ago

8 0

Answer:

Part A:

Slope Intercept Form: y = mx + b

m = slope (slope = )

b = y intercept

b = 3

Answer: y = -1/2x + 3

----------------------------------------------

Part B:

Just substitue f(x) for y.

Function Notation = f(x) -1/2 + 3

----------------------------------------------

Part C:

This function given looks almost the same but the slope is different while the one stated in the question has a slope of +2 and the equation given at the start with the slope being -1/2.

Step-by-step explanation:

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3 years ago

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:

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