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Len [333]
2 years ago
13

Perform the indicated operation. (3a2 - 7xy)(3a2 + 7xy)

Mathematics
2 answers:
Naily [24]2 years ago
8 0

(3a² - 7xy)(3a² + 7xy) =

= (3a²)² - (7xy)²

= 9a⁴ - 49x²y²

Use

a² - b² = (a - b)(a + b)

raketka [301]2 years ago
8 0

Answer:

9a^4 - 49x^2y^2.

Step-by-step explanation:

(3a^2 - 7xy)(3a^2 + 7xy)

This is example of the difference of 2 squares:

(a + b)(a - b) = a^2 - b^2,  so the answer is:

(3a^2)^2 - (7xy)^2

= 9a^4 - 49x^2y^2.

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Answer the question in the picture
Svet_ta [14]
<h3>Answer:</h3>
  • left picture (bottom expression): -cot(x)
  • right picture (top expression): tan(x)
<h3>Step-by-step explanation:</h3>

A graphing calculator can show you a graph of each expression, which you can compare to the offered choices.

_____

You can make use of the relations ...

... sin(a)+sin(b) = 2sin((a+b)/2)cos((a-b)/2)

... cos(a)+cos(b) = 2cos((a+b)/2)cos((a-b)/2)

... cos(a)-cos(b) = -2sin((a+b)/2)sin((a-b)/2)

Then you have ...

\dfrac{\cos{2x}-\cos{4x}}{\sin{2x}+\sin{4x}}=\dfrac{2\sin{3x}\sin{x}}{2\sin{3x}\cos{x}}=\dfrac{\sin{x}}{\cos{x}}=\tan{x}

and ...

\dfrac{\cos{2x}+\cos{4x}}{\sin{2x}-\sin{4x}}=\dfrac{2\cos{3x}\cos{x}}{-2\cos{3x}\sin{x}}=\dfrac{-\cos{x}}{\sin{x}}=-\cot{x}


6 0
3 years ago
What is 1-2sin^2x=sinx <br> Please show steps and find all solutions in interval [0,2pi)
Svetlanka [38]

Answer:

\large\boxed{x=\dfrac{3\pi}{2}\ \vee\ x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}

Step-by-step explanation:

1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}

\sin x=-1\to x=-\dfrac{\pi}{2}+2k\pi,\ k\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}\\\\x\in[0,\ 2\pi)

x=-\dfrac{\pi}{2}\notin[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+2\pi=\dfrac{3\pi}{2}\in[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+4\pi=\dfrac{7\pi}{2}\notin[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}+2\pi=\dfrac{13\pi}{6}\notin[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}+2\pi=\dfrac{17\pi}{6}\notin[0,\ 2\pi)

4 0
3 years ago
Gwen has 3 red erasers, 4 green erasers, 2 black erasers, 5 purple erasers, and 6 yellow erasers in her book bag.
son4ous [18]
I think the probability that Gwen will reach in her book bag purple eraser is 5/20 or 1/4
5 0
2 years ago
12 rounded to the nearest tenth in between 167
Alex777 [14]

No, 12 rounded to the nearest tenth is 12.0


3 0
2 years ago
What is (5y+6)-(10y+3)
melisa1 [442]

5y + 6 - 10y  -  3 \\  - 5x + 3
6 0
3 years ago
Read 2 more answers
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