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Eva8 [605]
3 years ago
12

Is 2.324324 a rational number

Mathematics
2 answers:
Aleks [24]3 years ago
6 0

Yes it is a rational number.

alekssr [168]3 years ago
5 0

Answer:yes 2.324324 is a rational number

Step-by-step explanation:

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What is the coordinate j(2,-5) after a reflection in the line y=x?​
kenny6666 [7]

Answer:

(- 5, 2 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ), thus

(2, - 5 ) → (- 5, 2 )

7 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
Challenge An arts academy requires there to be 4 teachers for every 76 students and 3 tutors for
klio [65]

Answer:

12. 5

11.

10

10

15. 7

14. 11

2

=

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16

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+

11

17

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4

co

loo

8

Step-by-step explanation:

12. 5

11.

10

10

15. 7

14. 11

3 0
2 years ago
What is the approximate circumference of a circle with a diameter of 14 inches, rounded to the nearest inch? (Use 3.14 as an app
soldi70 [24.7K]

Answer:

44 in.

Step-by-step explanation:

pi = 3.14 (in our case)

circumference = diameter x pi

circ. = 14 x 3.14, which equals to 43.96

round that and you get 44 in.

5 0
2 years ago
please help me answer these 3 questions correctly . u will get 30 pints if you do and the brainlest. please do not answer if you
Marianna [84]

Answer:

6a) B

6b) C

6c) A

7 0
2 years ago
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