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julia-pushkina [17]
3 years ago
11

Factor completely 9xy + 36x − 10y − 40.

Mathematics
2 answers:
Harlamova29_29 [7]3 years ago
6 0
9x(y+4)-10(y+4)
(9x-10)(y+4)
Fittoniya [83]3 years ago
6 0

Answer:

(9x-10)(y+4)

Step-by-step explanation:

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Use trigonometric identities to solve each equation within the given domain.
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Recall that the tangent function is defined by

tan(<em>x</em>) = sin(<em>x</em>)/cos(<em>x</em>)

Also recall the double angle identity for sine,

sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)

Then the equation is the same as

3 sin(<em>x</em>)/cos(<em>x</em>) = 4 sin(<em>x</em>) cos(<em>x</em>)

Move everything to one side to prepare to factorize:

3 sin(<em>x</em>)/cos(<em>x</em>) - 4 sin(<em>x</em>) cos(<em>x</em>) = 0

sin(<em>x</em>)/cos(<em>x</em>) (3 - 4 cos²(<em>x</em>)) = 0

As long as cos(<em>x</em>) ≠ 0, we can omit the term in the denominator, so we're left with

sin(<em>x</em>) (3 - 4 cos²(<em>x</em>)) = 0

and so

sin(<em>x</em>) = 0   <u>or</u>   3 - 4 cos²(<em>x</em>) = 0

sin(<em>x</em>) = 0   <u>or</u>   cos²(<em>x</em>) = 3/4

sin(<em>x</em>) = 0   <u>or</u>   cos(<em>x</em>) = ±√3/2

On the interval [0, 2<em>π</em>),

• sin(<em>x</em>) = 0 for <em>x</em> = 0 and <em>x</em> = <em>π</em>

• cos(<em>x</em>) = √3/2 for <em>x</em> = <em>π</em>/6 and <em>x</em> = 11<em>π</em>/6

• cos(<em>x</em>) = -√3/2 for <em>x</em> = 5<em>π</em>/6 and <em>x</em> = 7<em>π</em>/6

(None of these <em>x</em> make cos(<em>x</em>) = 0, so we don't have to omit any extraneous solutions.)

6 0
3 years ago
David is watching maria and alma race electric trains around track. Maria train can go around the track in 10 seconds. Almas tra
Nady [450]

Answer:

60 seconds.  

Step-by-step explanation:  

We have been given that Maria train can go around the track in 10 seconds. Alma train can go around the track in 12 seconds.

To find the number of seconds after which both trains will cross the finish line together the first time we will find LCM of 10 and 12. LCM will give us the smallest positive integer that is divisible by both 10 and 12.  

Multiples of 10 are: 10, 20, 30, 40, 50, 60, 70,...    

Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,..  

We can see that least common multiple of 10 and 12 is 60, therefore, it will take 60 seconds for both trains to cross the finish line together the first time.

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3 years ago
The equation of a circle is (x+2)2 + (y-3)2 =9. What are the coordinates of the center of this circle?
Setler [38]

Answer:

Step-by-step explanation:

center is (-2,3)

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3 years ago
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Free_Kalibri [48]

Answer:

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Step-by-step explanation:

6 0
3 years ago
Rewrite 1/5and1/2 as a unit rate
denpristay [2]

Answer:

1/2 = 0.5

1/5 = 0.2

Step-by-step explanation:

Hope this helps!!!

4 0
3 years ago
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