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3 years ago

Solve for x. (7x - 1)• (6x - 1)•

Mathematics

1 answer:

leonid [27]3 years ago

4 0

Answer:

42x^2 - 7x - 6x + 1

42x^2 - 13x + 1 for FOIL method

To solve for x

7x - 1 = 0

7x = 1

x = 1/7

6x - 1 = 0

6x = 1

x = 1/6

Step-by-step explanation:

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3 years ago

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3^x.2x = 3^x + 2x-1

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Answer:

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2 years ago

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

1 2 3 4 5 6 7 8 9 10 11

alexandr402 [8]

1) PEMDAS: 12 * 5 + 6 / 6

12 * 5 = 60

60 + 6 / 6

6 / 6 = 1

60 + 1 = 61

61 is the final answer.

2) Absolute Value: |-2 - 4| = -6 HOWEVER, because it is in the absolute value signs, it becomes 6. 6 - 4 = 2

2 in the final answer.

3) 4 + 4 + 2 = 10 Because they are all negatives, we add back the negative sign.

-10 is the final answer.

4) 15x + 1 = 26

Subtract 1 from each side.

15x = 25.

25/15 = 1.6...

x = 1.6...

5) 2x -4 + 3x = - 1

2x + 3x = 5x

5x - 4 = -1

Add 4 to each side

5x = 3

3/5 = 0.6

x = 0.6

6) x-2/3 = x+4/5

I don't remember the steps, but the answer is x = 11

7) Finding the relationship between x:4 and 5:20

20/5 = 4

x = 1

The smaller rectangle has a reduction of 5 times.

8) Mean is found by adding all the number, then dividing by the amount added.

18 + 27 + 15 + 24 + 18 + 26 + 19 + 24 = 171

171/8 = 21.375

Mean = 21.375

Median is found by putting the numbers in increasing order, then finding the middle number, 15, 18, 18, 19, 24, 24, 26, 27. 24 + 19 = 43. 43/2 = 21.5

Median = 21.5

9) Circumference of a circle = 2(pi)(r)

Circumference = 30πin (thats the pi symbol)

If you use the typical pi fill-in (3.14) the its 2 * 3.14 * r then it would = 94.5in.

10) Combing Like Terms: 5x + 7y - 8y^2 + 2x - y

5x + 2x = 7x

7x + 7y - 8y^2 - y

-y + 7y = 6y

Answer: -8y^2 + 7x + 6y

5 0

3 years ago

Two numbers rolled can be added to get a sum. Find P(sum is even.)

azamat

When you roll two numbers you have four kinds of outcomes: EE, EO, OE, OO (where E = even, O = odd).

You get an even sum only if you sum two numbers that are both even or both odd, therefore the outcomes wanted are two: EE and OO.

Therefore:
P(sum is even) = 2 / 4 = 0.5

Hence, there is a 50% probability that, when you roll two numbers, their sum will be even.

6 0

3 years ago