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2 years ago

Simplify -8(2-3w) -5w

Mathematics

2 answers:

lord [1]2 years ago

8 0

Answer:

-16 +19w

Step-by-step explanation:

-8(2-3w) -5w

Distribute the -8

-8*2 -8*(-3w) -5w

-16 +24w -5w

-16 +19w

Setler [38]2 years ago

5 0

Answer:

19w - 16

Step-by-step explanation:

distribute the terms in the parenthesis by - 8

-8(2 - 3w) - 5w

= - 16 + 24w - 5w ← collect like terms

= 19w- 16

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QUESTION 1 - 1 POINT

guajiro [1.7K]

Answer + Step-by-step explanation:

the inequality by finding the boundary line, then shading the appropriate area.

y > − 5/2x − 5

(anything in shaded region)

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1 year 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

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

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3 years ago

What percent of campers are over the age of 14?

Ierofanga [76]

Answer: 45%

Step-by-step explanation: There's 9 people over the age of 14. And 9 divided by the total number, 20, gives you 0.45. 0.45 multiplied by 100 is 45.

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3 years ago

Dara has 12 red counters. She has 7 more red counters than yellow counters. How many yellow counters does Dara have?

pantera1 [17]

12 red counters

7 more red counters than yellow counters

12 - 7 = 5 yellow counters

Dara has 5 yellow counters.

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3 years ago

Read 2 more answers

Does anyone know how to do this if so please help immediately!!!