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3 years ago

Compute the series 1 2/3 4/9 8/27 16/81

1 answer:

6 0

The pattern is multiplying the top by two and multiplying the bottom by 3.
16*2/81*3
32/243
64/729
128/2189
if you need more you can just use a calculator

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2x^3-x^2+x-2 factorize

bekas [8.4K]

Answer:

$(x-1)(2x^2+x+2)$

Step-by-step explanation:

Factorize:

$f(x)=2x^3-x^2+x-2$

Factor Theorem

If f(a) = 0 for a polynomial then (x - a) is a factor of the polynomial f(x).

Substitute x = 1 into the function:

$\implies f(1)=2(1)^3-1^2+1-2=0$

Therefore, (x - 1) is a factor.

As the polynomial is cubic:

$\implies f(x)=(x-1)(ax^2+bx+c)$

Expanding the brackets:

$\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c$

$\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c$

Comparing coefficients with the original polynomial:

$\implies ax^3=2x^3 \implies a=2$

$\implies (b-a)x^2=-x^2 \implies b-2=-1 \implies b=1$

$\implies -c=-2 \implies c=2$

Therefore:

$\implies f(x)=(x-1)(2x^2+x+2)$

Cannot be factored any further.

4 0

2 years ago

Read 2 more answers

(Please help) What is the rate of change of y with respect to x?

dolphi86 [110]

answer will be 2÷18=9

and the answer is 9

please mark this answer as brainlist

7 0

2 years ago

Use the discriminant to describe the roots of each equation. Then select the best description. 2 = x2 + 5x. A) Double root B) Re

fredd [130]

$\bf 2=x^2+5x\implies 0=x^2+5x-2\\\\\\\qquad \qquad \qquad \textit{discriminant of a quadratic}\\\\\\0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{-2}~~~~~~~~\stackrel{discriminant}{b^2-4ac}=\begin{cases}0&\textit{one solution}\\positive&\textit{two solutions}\\negative&\textit{no solution}\end{cases}\\\\\\(5)^2-4(1)(-2)\implies 25+8\implies 33$

so we have a 33, namely two real solutions for that quadratic.

usually that number goes into a √, if you have covered the quadratic formula, you'd see it there, namely that'd be equivalent to √(33), now 33 is a prime number, and √(33) is yields an irrational value, specifically because a prime number is indivisible other than by itself or 1.

so 33 can only afford us two real irrational roots.

3 0

2 years ago

Simplify the expression -2x^2(4x − 3). -8x3 − 6x2 -8x3 + 6x2 8x3 − 6x2 8x3 + 6x2

Digiron [165]

To simplify the expression we are going to use the distributive property of multiplication: $a(b+c)=ab+ac$ .
We can infer from our problem that $a=-2x^2$ , $b=4x$ , and $c=-3$ . So lets apply the property to simplify our expression:
$-2x^2(4x-3)=(-2x^2)(4x)+(-2x^2)(-3)$
$(-2x^2)(4x)+(-2x^2)(-3)=-8x^3+6x^2$

We can conclude that the correct answer is -8x3 + 6x2

8 0

3 years ago

1 Sales last year were $88,319. Percent of Increase 0.14. What will it be next year?

Valentin [98]

Answer:

$100,683.66

Step-by-step explanation:

88319 = last years sales

.14 = percent increase

88319 * .14 = 12364.66

12364.66 + 88319 = 100,683.66

next years sales = $100,683.66

7 0

2 years ago