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[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

[tex] \huge \boxed{\mathfrak{Explanation} \downarrow}[/tex]

To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

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So, let's do the division (steps in the attached picture).

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We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

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x² - 5x + 6

= (x - 3) (x - 2) [use the splitting the middle term method].

So, the zeroes are,

(x - 3)

x - 3 = 0

x = 3 ⇨ 1st zero.

(x - 2)

x - 2 = 0

x = 2 ⇨ 2nd zero.

Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

p(x) = x³ - 6x² + 11x - 6

p(3) = 3³ - 6(3)² + 11 (3) - 6

p(3) = 27 - 54 + 33 - 6

p(3) = 0.

p(x) = x³ - 6x² + 11x - 6

p(2) = 2³ - 6(2)² + 11 (2) - 6

p(2) = 8 - 24 + 22 - 6

p(2) = 0

Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

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Hope it'll help you!

ℓu¢αzz ッ

Answer:

y= [tex]\frac{5}{6} x[/tex] + 4

Step-by-step explanation:

Pick two points: (-6,-10) and (0,4)

Then solve for m (slope): I picked (0,4)

[tex]m= \frac{4-(-1)}{0-(-6)} =\frac{5}{6}[/tex]

Then put in slope intercept form:

4= [tex]\frac{5}{6} (0)[/tex] + b

4=b

Then put in final form:

y= [tex]\frac{5}{6} x[/tex] + 4

Hope this helps!

Answer:

y=5/6x+4

Step-by-step explanation:

9514 1404 393

Answer:

  13.7 N

Step-by-step explanation:

The vertical component of the force is ...

  (15 N)sin(66°) ≈ 13.7 N

Answer:

The percent gain would be 77952515`0%

Answer:

absolute value of n - 29

Step-by-step explanation:

n - 29

Answer:

Answer:

Greatest:

16/5

/5

-3

6/7

I think, I am no t sure

Answer:

Area of rectangle = L x W

Step-by-step explanation:

A = L x W

L = 18

W = 10 + 5

so,

A = 18 x (10+5)

A = 18 x 15

A = 270

The solution of Equation is y=5.

The correct option is C.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

y+ 6 = -3y + 26

Now, solving for y we get

y + 3y= 26 - 6

4y= 20

y= 20/4

y= 5

Thus, the value of y is 5.

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Answer:

Step-by-step explanation:

Kites have one pair of congruent angles.

In this case it is B and D:

Find the measure of B and D:

Find the measure of angle C:

The smallest angle is C

Answer: Slope = 3/2 or 1.5

Answer: y= 1.5 x+2 or y=3/2x+2

Step-by-step explanation:Slope (m) =

ΔY

ΔX

=

3

2

= 1.5

θ =

arctan( ΔY )

ΔX

= 56.30993247402°

ΔX = 4 – 2 = 2

ΔY = 8 – 5 = 3

Distance (d) = √ΔX2 + ΔY2 = √13 = 3.605551275464

y = 1.5x + 2

or

y =

3 x

2

+ 2

When x=0, y = 2

When y=0, x = -1.3333333333333

Answer:

1.8(3) (three is a repeating number)

Step-by-step explanation:

Divide the numerator from the denominator. Add the value of the integer part.

Answer:1.83

Step-by-step explanation:

so the  1 that's a whole number and 5 out of 6 should be around 82-85 but for real its 1.83 but its a repeating decimal so its like 1.83333

Answer:    17

Step-by-step explanation:  

Answer:

(-3.2)^0 = 1

Step-by-step explanation:

Anything to the power of 0 equals 1.

Answer:

1

Step-by-step explanation:

Any number raised to a power of 0 is equal to 1.

Answer:

I think it's A. I may be wrong tho.

Answer: A. Functions f, g, and h

Step-by-step explanation: Plato answer

Answer:

f(x)=x(x-3) x (x+4) x (x-9

Step-by-step explanation:

your function in factored form

The polynomial whose real zeros and degree are given is f(x) = x³ - 3x² - 4x

The given parameters are:

Rewrite the zeros as:

x = -1, x = 0 and x = 4

Set the zeros to 0

x + 1 = 0, x = 0 and x - 4 = 0

Multiply the zeros

(x + 1) * x * (x - 4) = 0 * 0 * 0

Multiply the factors

(x² + x) * (x - 4) = 0

Multiply the factors

x³ - 4x² + x² - 4x = 0

Evaluate the like terms

x³ - 3x² - 4x = 0

Express as a polynomial function

f(x) = x³ - 3x² - 4x

Hence, the polynomial whose real zeros and degree are given is f(x) = x³ - 3x² - 4x

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Answer:

337.5

Step-by-step explanation:

Based on the given conditions, formulate 3 112.5

Calculate the product or quotient: 337.5

Answer:

Slope: - 5/2

Step-by-step explanation:

Answer:

Inc Interest : $16,089

Step-by-step explanation:

1. Let's turn $50 a month into a year, so 50 * 12 = $600

2. Including the annual interest, which is $43.56 out of the $600

3. Add them together, which will be 43.56 + 600 = 643.56

4. Multiply it by 25 to get the full 25 years and you're done!

The value of Amy's investment after 25 years will be $140.75.

Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest. The straightforward crediting of cash flows related to an investment or deposit is referred to as "simple" interest.

Given that, Amy contributes $50 per month to the Lincoln National Bond Fund which earns 7.26% annual interest.

The investment after 25 years will be calculated as,

SI = ( P x R x T)/100

SI = ( 50 x 7.26 x 25 ) / 100

SI = $90.75

The total investment will be calculated as,

A = $90.75 = $50

A = $140.75

Therefore, the value of Amy's investment after 25 years will be $140.75.

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Answer:

a: 00:45

b: 7:30 PM

Step-by-step explanation:

Hope this is right

Answer:

-87

Here ya go :)

Answer:

c. BC

Step-by-step explanation:

It is the possible one

Di ko alam Yan sorry

Step-by-step explanation:

Bobo ako eh ML nalng Joke lang Tanong nalng kayo Ng iba

Answer:

152

Explination:

this is answer

Brainliest answer: thx(:

Answer:

x = 3.236

Step-by-step explanation:

Answer:

Step-by-step explanation:

25- guaranteed

$14 on each table waited on

He waited on 17.

17x14= $238 tips

238+25= $263

1. Marques expects to earn $263 on 17 tables

2. He expects to make 25+14t per day.

Answer:

about 35 mins

Step-by-step explanation:

Answer:

The quotient of 902 divided by 27 equals 33 and the remainder is 11.

Answer:

hope it helps

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