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borishaifa [10]
3 years ago
5

Identify the slope (m) and y-intercept (b) of each linear equation. 52. 3x+4y=24

Mathematics
1 answer:
nekit [7.7K]3 years ago
8 0

Answer:

Step-by-step explanation:

  [1]    3x - 4y = -24

  [2]    -x - 16y = -52

Graphic Representation of the Equations :

   -4y + 3x = -24        -16y - x = -52  

 

Solve by Substitution :

// Solve equation [2] for the variable  x

 [2]    x = -16y + 52

// Plug this in for variable  x  in equation [1]

  [1]    3•(-16y+52) - 4y = -24

  [1]     - 52y = -180

// Solve equation [1] for the variable  y

  [1]    52y = 180

  [1]    y = 45/13

// By now we know this much :

   x = -16y+52

   y = 45/13

// Use the  y  value to solve for  x

   x = -16(45/13)+52 = -44/13

Solution :

{x,y} = {-44/13,45/13}

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schepotkina [342]

(1) Recall the angle sum identity for cosine:

cos(<em>x</em> + <em>y</em>) = cos(<em>x</em>) cos(<em>y</em>) - sin(<em>x</em>) sin(<em>y</em>)

So

cos(<em>π</em>/3) cos(5<em>π</em>/6) - sin(<em>π</em>/3) sin(5<em>π</em>/6) = cos(<em>π</em>/3 + 5<em>π</em>/6)

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= -√(3)/2

(2) Recall the half-angle identity:

cos²(<em>x</em>) = (1 + cos(2<em>x</em>))/2

Since <em>π</em>/2 < 7<em>π</em>/12 < <em>π</em>, you should expect cos(7<em>π</em>/12) < 0. So solving for cos(<em>x</em>) above, we have

cos(<em>x</em>) = -√[(1 + cos(2<em>x</em>))/2]

Then

cos(7<em>π</em>/12) = -√[(1 + cos(7<em>π</em>/6))/2]

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You could stop there, or continue and try to de-nest the radicals to end up with

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(3) Recall the angle sum formula for tangent:

tan(<em>x</em> - <em>y</em>) = (tan(<em>x</em>) - tan(<em>y</em>))/(1 + tan(<em>x</em>) tan(<em>y</em>))

Then

(tan(122°) - tan(32°))/(1 + tan(122°) tan(32°)) = tan(122° - 32°)

= tan(90°)

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(4) Recall the double angle identity for sine:

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cos(2<em>x</em>) = 2 cos²(<em>x</em>) - 1

Then

12 cos²(<em>θ</em>) - 6 = 6 (2 cos²(<em>θ</em>) - 1)

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