What is 119/3 as a mixed number?

What is the least common multiple of 6x^2+39x-21 and 6x^2+54x+84?

SOVA2 [1]

Answer:

$12x^3+102x^2+114x-84$

Step-by-step explanation:

Given polynomials:

$\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}$

Factor the polynomials:

Polynomial 1

$\implies 6x^2+39x-21$

$\implies 3(2x^2+13x-7)$

$\implies 3(2x^2+14x-x-7)$

$\implies 3[2x(x+7)-1(x+7)]$

$\implies 3(2x-1)(x+7)$

Polynomial 2

$\implies 6x^2+54x+84$

$\implies 6(x^2+9x+14)$

$\implies 6(x^2+7x+2x+14)$

$\implies 6[x(x+7)+2(x+7)]$

$\implies 6(x+2)(x+7)$

$\implies 2 \cdot 3(x+2)(x+7)$

The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.

Therefore, the LCM of the two polynomials is:

$\implies 2 \cdot 3(x+7)(x+2)(2x-1)$

$\implies (6x^2+54x+84)(2x-1)$

$\implies 12x^3+108x^2+168x-6x^2-54x-84$

$\implies 12x^3+102x^2+114x-84$

8 0

2 years ago

Read 2 more answers

- f(x) = 3x3 – 21×² – 54x Zero Multiplicity Effect

xenn [34]

Answer:

x = 9 or x = 0 or x = -2

Step-by-step explanation:

Solve for x:

3 x^3 - 21 x^2 - 54 x = 0

The left hand side factors into a product with four terms:

3 x (x - 9) (x + 2) = 0

Divide both sides by 3:

x (x - 9) (x + 2) = 0

Split into three equations:

x - 9 = 0 or x = 0 or x + 2 = 0

Add 9 to both sides:

x = 9 or x = 0 or x + 2 = 0

Subtract 2 from both sides:

Answer: x = 9 or x = 0 or x = -2

3 0

3 years ago

Which statement is NOT true? A –69 > –425 A , –69 > –425 B –64 > –78 B , –64 > –78 C 23 < –39 C , 23 < –39 D –

sleet_krkn [62]

Answer:

The answer is "Option C".

Step-by-step explanation:

Given value:

$A) -69 > -425 \\\\B) -64 > -78 \\\\C) \ \ 23 < -39 \\\\D) -898 < 501 \\\\$

In this question, the choice C is not true because 23 is greater than the -39.

4 0

3 years ago

Traveling at 55 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 145 miles from San

Lina20 [59]

55 miles = 1 hour

145 miles = 1/55 x 145 = 2.64 hours = 158 mins

5 0

3 years ago

Read 2 more answers

What is the simplified form of the expression k^3(K^7/5)^-5

Vladimir79 [104]

$\bf k^3\left( \cfrac{k^7}{5} \right)^{-5}\implies k^3\left( \cfrac{5}{k^7} \right)^5\implies k^3\left( \cfrac{5^5}{k^{7\cdot 5}} \right)\implies k^3\cdot \cfrac{5^5}{k^{35}}
\\\\\\
k^3\cdot 5^5\cdot k^{-35}\implies 5^5\cdot k^{3-35}\implies 5^5k^{-32}\implies \cfrac{5^5}{k^{32}}\implies \cfrac{3125}{k^{32}}$

3 0

4 years ago