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3 years ago

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The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically a

re shown in the table.Which represents the solution(s) of this system of equations? (4, 4) (–4, –12) (4, 4) and (–4, 12) (–4, 4) and (4, 12)

2 answers:

olchik [2.2K]3 years ago

3 0

Answer:

y = 2x - 4....so sub in 2x - 4 for x in the other equation

y = x^2 - 6x + 12

2x - 4 = x^2 - 6x + 12

x^2 - 6x - 2x + 12 + 4 = 0

x^2 - 8x + 16 = 0

(x - 4)(x - 4) = 0

x - 4 = 0

x = 4

x - 4 = 0

x = 4

solution is (4,4)

(2, −1) and (−4, 17)

Step-by-step explanation:

DedPeter [7]3 years ago

3 0

Answer:

wrong up top

Step-by-step explanation:

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At a hot dog stand they serve regular hot dogs and footling hot dogs at a ratio of 5 to 3. Based on this ratio how many footlong

natta225 [31]

Answer:
45
Step-by-step explanation:
Ratio is 5:3
So total ratio "parts" is 5 + 3 = 8
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3 * 15 = 45 footlong hotdogs

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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

What is 5x minus 5 factored

AveGali [126]

Answer:

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Step-by-step explanation:

5 0

3 years ago

Ami'yan runs every day for exercise at a rate of 1 kilometer every 15 minutes. How many meters does he run in 1 hour? - Thank yo

Alona [7]

Answer:

The total distance covered in 1 hour is 4000 meters.

Step-by-step explanation:

The distance Ami'yan runs is 15 minutes = 1 kilometer

Using the unit formula,

The distance ran in 1 minute = $(\frac{1}{15} ) \textrm{Kilometer}$

Now, 1 hour = 60 minutes

⇒The distance covered in 60 minutes = 60 x (Distance run in 1 minute)

= $60 \times \frac{1}{15} = 4$

So, the distance covered in 1 hour = 4 kilometer

1 kilometer = 1000 meters

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Hence, the total distance covered in 1 hour = 4000 meters.

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