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larisa [96]
3 years ago
5

Please help me Simplify. 3(x + 4)

Mathematics
1 answer:
valentinak56 [21]3 years ago
8 0
Distribute the 3.

3*x + 3*4
3x + 12

Hope this helps :)
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Given cos ⁡ ( θ ) = 5/6 , then sin ⁡ ( θ ) = a/b .<br><br> Determine the values of a and b.
slega [8]

Answer:

a = √11 and b = 6

Step-by-step explanation:

Refer to attached picture for reference

for an right triangle with angle θ

we are given

cos θ = 5/6 = length of adjacent side / length of hypotenuse

hence

adjacent length = 5 units

hypotenuse length = 6 units

the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:

hypotenuse ² = adjacent ² + opposite²   (rearrange)

opposite ² = hypotenuse ² - adjacent ²

opposite ² = 6² - 5²

opposite = √ (6²-5²) = √11

sin θ = opposite length / hypotenuse  (substitute values above)

sin θ = √11 / 6

hence a = √11 and b = 6

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3 years ago
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9514 1404 393

Answer:

  1. 6x +y = -6
  2. 6x -y = 8
  3. 5x +y = 13

Step-by-step explanation:

To rewrite these equations from point-slope form to standard form, you can do the following:

  • eliminate parentheses
  • subtract the x-term
  • subtract the constant on the left
  • if the coefficient of x is negative, multiply by -1

Of course, any operation you do must be done <em>to both sides of the equation</em>.

__

1. y -6 = -6(x +2)

  y -6 = -6x -12 . . . . . eliminate parentheses

  6x +y -6 = -12 . . . . . add 6x

  6x +y = -6 . . . . . . . . add 6

__

2. y +2 = 6(x -1)

  y +2 = 6x -6

  -6x +y +2 = -6

  -6x +y = -8

  6x -y = 8 . . . . . . . . multiply by -1

__

3. y -3 = -5(x -2)

  y -3 = -5x +10

  5x +y -3 = 10

  5x +y = 13

_____

<em>Additional comment</em>

The "standard form" of a linear equation is ax+by=c for integers a, b, c. The leading coefficient (generally, 'a') should be positive, and all coefficients should be mutually prime (have no common factors). That is why we multiply by -1 in problem 2.

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Answer:


Step-by-step explanation:


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