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3 years ago

What is the name for a function that can be written in the form y=mx+b, where x is the

Mathematics

1 answer:

krok68 [10]3 years ago

5 0

Answer: The formula is meant for slope interception.

m = slope

x = the independent variable

y = the dependent variable

idk if this is the answer you were looking for but I hope it helps!!!

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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

The front face of Josh’s roof is shaped like a triangle. It has a base of 100 feet and a height of 15 feet. What is the area of

sweet-ann [11.9K]

Answer:

750 square feet

Step-by-step explanation:

The area of a triangle is 1/2bh

Now, we can plug our values in.

1/2(100)(15)

Simplify

50(15)

750

7 0

3 years ago

Hi, I need help with this question.

elena-14-01-66 [18.8K]

Answer:

135 steps

Step-by-step explanation:

Each member marches:

50 + 40 = 90 yards

Convert this to feet:

1 yard = 3 feet
90 yards = 3*90 feet = 270 feet

Find the number of steps:

270/2 = 135 steps

7 0

3 years ago

Read 2 more answers

I beg for help where are the geniuses?

KatRina [158]

Answer:

CB = sqrt62

Step-by-step explanation:

The pythagorean theorem will help with this! First take triangle ACD, AD^2 + CD^2 = AC^2. Plug in, AD^2 + 16 = 25. AD^2 = 9. AD = 3. I'm not exactly sure how to find DB, but I can assume it's double of AD< so 6. We know CD is 4, so 4^2 + 6^2 = CB^2. 16 + 36 = CB^2. CB = sqrt62

Sorry if this isn't exactly right, there's no exact way to find DB.

7 0

3 years ago

Five is sixteen more than five times a number Translate to an equation

3241004551 [841]

Answer:

Step-by-step explanation:

5 is 16 more then 5 times a number

let the number be x

5 = 5x + 16

4 0

3 years ago