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3 years ago

What is the remainder when the function f(x)=x^4 - 3x^3 +7x - 1 is divided by (x-2)

Mathematics

2 answers:

GaryK [48]3 years ago

7 0

For this case we have:

To divide polynomials, we must construct a quotient in which each term (constructed per step) multiplied by the divisor, yields the first term of the dividend, thus changing its sign and eliminating the terms of the dividend.

When solving, following the previous steps and shown in the attached image, we have as quotient $x ^ 3-x ^ 2-2x + 3$ and as remainder 5.

Answer:

Option B

See attached image

astraxan [27]3 years ago

5 0

Im gonna say 25, but im not completely sure.

tell me if it was correct

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locate the point on the line segment A (3,-5) and B (13,-15) given that the point is 4/5 of the way from A to B. Show your work

rjkz [21]

Answer:

The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

Step-by-step explanation:

As the line segment has the points:

A(3, -5)

B(13, -15)

Let (x, y) be the point located on the line segment which is 4/5 of the way from A to B.

Using the formula

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

Here, the point (x , y) divides the line segment having end points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ from the point (x₁, y₁).

As (x, y) be the point located on the line segment which is 4/5 of the way from A to B, meaning the distance from $A$ to $(x , y)$ is $4$ units, and the

distance from $(x , y)$ to B is 1 unit, as $5 - 4 = 1$ .

Thus

m : n = 4 : 1

Finding x-coordinate:

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

$x=\frac{\left(3\right)\left(1\right)+\left(13\right)\left(4\right)}{4+1}$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$x=\frac{3\cdot \:1+13\cdot \:4}{4+1}$

$x=\frac{55}{4+1}$ ∵ $3\cdot \:1+13\cdot \:4=55$

$x=\frac{55}{5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{55}{5}=11$

$x=11$

Finding y-coordinate:

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

$y=\frac{\left(-5\right)\left(1\right)+\left(-15\right)\left(4\right)}{4+1}$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$y=\frac{-5\cdot \:\:1-15\cdot \:\:4}{4+1}$

$=\frac{-65}{4+1}$ ∵ $-5\cdot \:1-15\cdot \:4=-65$

$=\frac{-65}{5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$y=-\frac{65}{5}$

$y=-13$

The x-coordinate = 11

The y-coordinate = -13

Therefore, the coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be: (11 , -13)

7 0

3 years ago

If x-1/3=k and k=3, what is the value of x?

inna [77]

The answer is 9 just reciprocate the 1/3 and the multiply the 9 by 3

3 0

3 years ago

What is the sum of (2x+4)+(-3x+9)

Levart [38]

Answer:

-x + 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Combining Like Terms

Step-by-step explanation:

Step 1: Define expression

(2x + 4) + (-3x + 9)

Step 2: Simplify

Combine like terms (x): -x + 4 + 9
Combine like terms (Z): -x + 13

7 0

2 years ago

Read 2 more answers

Enter the sum of numbers as a product of their GCF.75 + 90

Semmy [17]

The gcf of the numbers are 15

5 0

3 years ago

PLEASE HELP ME I REALLY NEED HELP

borishaifa [10]

Answer:

2226

Step-by-step explanation:

3 0

3 years ago