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marissa [1.9K]
3 years ago
12

Sry the picture is blurry ask me of want to right it out.​

Mathematics
1 answer:
bixtya [17]3 years ago
3 0
The one that has multiplication
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The graphs below have the same shape. Complete the equation of the blue
aleksklad [387]

Answer:

(x+2)^2+1

Step-by-step explanation:

G is shifted 2 to the left and one up. 2 to the left is represented by changing the input by adding 2 to it (as the original is 2 more than the edited), and adding 1 to the end of it adds 1, so our answer is (x+2)^2+1

8 0
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
6.8 dollars. How do you write the decimal 6.8 when it refers ti money
Rainbow [258]
$ 6.80.


hope that helped
7 0
3 years ago
Read 2 more answers
What is the line of best fit for these points?<br> (0,6)(2, 10)(-2, 2)(-1,4)
Likurg_2 [28]

Answer:

Connect the dots, just label them on the graph and draw a line almost like connecting the dots

7 0
3 years ago
The biology faculty at a college consists of 9 full professors, 14 associate professors, 13 assistant professors, and 4 instruct
-Dominant- [34]
32 total
9/32 -professor
9/32 -instructor
9/32+9/32=18/32=9/16
5 0
3 years ago
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