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sp2606 [1]
3 years ago
5

Simplify expression (5xy^-6/x^4 y^-2)^2

Mathematics
1 answer:
ipn [44]3 years ago
4 0
Here it is...........................

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Simplify and answer the boxes.
s2008m [1.1K]

Answer:

\huge\boxed{\dfrac{x^2+9^2}{x-3y}+\dfrac{6xy}{3y-x}=x-3y}

Step-by-step explanation:

Domain:

x-3y\neq0\Rightarrow x\neq3y

\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{3y-x}=\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{-(x-3y)}\\\\=\dfrac{x^2+9y^2}{x-3y}-\dfrac{6xy}{x-3y}=\dfrac{x^2+9y^2-6xy}{x-3y}\\\\=\dfrac{x^2-2(x)(3y)+(3y)^2}{3y-x}=\dfrac{(x-3y)^2}{3y-x}\\\\=\dfrac{\bigg[-1(3y-x)\bigg]^2}{3y-x}=\dfrac{(-1)^2(3y-x)^2}{3y-x}\\\\=\dfrac{1(x-3y)(x-3y)}{x-3y}=x-3y

Used:

The distributive property: a(b + c) = ab + ac

(a - b)² = a² - 2ab + b²

6 0
3 years ago
Help again for the last time ;-;
lys-0071 [83]

Answer:

1) Star: (-5,9) 2) Lightning (0,8)

3) Circle: (4,-7) 4) Heart (-3,-8)

5) Cross (6,9) 6) Triangle (0,6)

7) Moon (-4,9) 8) Square (-4,6)

9) Diamond (-1,-4) 10) Music Note (8,1)

Step-by-step explanation:

The way that I solved this was I first set up (x,y). You must find the placement of the x-axis or the horizontal line. Then you find the 7-axis or the vertical line. For example, with the star, the shape is 5 to the left which is -5 and then goes 9 lines upward.

7 0
3 years ago
Mr.wilson wrote the fuction f(x)=7x-15 on the chalkboard.What is the value of this function for f(6)?
bixtya [17]

By plunging 5 into the equation as x, you have the equation

7(5) - 15

7 * 5 = 35 so

35 - 15

f(5) = 20

4 0
3 years ago
What is a ratio? (In your own words,don't get off internet.)
mars1129 [50]

Answer:

a ratio is a rate is something left to right like a book so say if a Problem say there's a rate 14 boys to 12 girls then he says rate girls to boys then it would be 12:14 or 12 to 14

Step-by-step explanation:

Please give me brainlyest.

6 0
3 years ago
Read 2 more answers
If the sum of first n terms of an AP is 3n² + 5n find the AP.
ollegr [7]

Let <em>a</em> (<em>n</em>) denote the <em>n</em>-th term in the progression. Consecutive terms in the sequence differ by a fixed constant - call it <em>c</em> - such that

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + <em>c</em>

Let <em>a</em> = <em>a</em> (1) be the first term in the sequence. We can solve for <em>a</em> (<em>n</em>) in terms of <em>a</em> alone:

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + <em>c</em>

<em>a</em> (<em>n</em>) = (<em>a</em> (<em>n</em> - 2) + <em>c</em>) + <em>c</em> = <em>a</em> (<em>n</em> - 2) + 2<em>c</em>

<em>a</em> (<em>n</em>) = (<em>a</em> (<em>n</em> - 3) + <em>c</em>) + <em>c</em> = <em>a</em> (<em>n</em> - 3) + 3<em>c</em>

and so on, down to

<em>a</em> (<em>n</em>) = <em>a</em> + (<em>n</em> - 1) <em>c</em>

The sum of the first <em>n</em> terms is then

\displaystyle\sum_{k=1}^n a(k)=\sum_{k=1}^n(a+(k-1)c)=a\sum_{k=1}^n1+c\sum_{k=1}^n(k-1)=an+\frac{cn(n-1)}2=\frac c2n^2+\left(a-\frac c2\right)n

Since this is equal to 3<em>n</em> ^2 + 5<em>n</em>, it follows that

<em>c</em>/2 = 3   =>   <em>c</em> = 6

<em>a</em> - <em>c</em>/2 = 5   =>   <em>a</em> = 8

So the sequence is

<em>a</em> (<em>n</em>) = 8 + (<em>n</em> - 1) 6 = 6<em>n</em> + 2

3 0
3 years ago
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