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ollegr [7]
3 years ago
6

Simplify the following expression: '5x - 8 + 3y + 10x - 8y'

Mathematics
1 answer:
monitta3 years ago
6 0

Answer:

-5x-8-11y

Step-by-step

Because you shift 10x to -10x and then 5x-10x = -5x

You leave the -8 the same

You do 3y to -3y and  then do -3y -8y = -11y

Hence altogether you get, -5x -8 -11y

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In a 45-45-90 triangle, the hypotenuse is 7, find both the legs
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Answer: If the hypotenuse is 7, the other 2 sides are \sqrt{24.5} 0r about = 4.95

Step-by-step explanation:  in a 45-45-90 triangle, the legs are equal.

a² + b² = c² .   2(a²) = 49  a² = 49/2

So find the square root of 24.5

\sqrt{24.5}   =4.949747468 .round to 4.95

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9514 1404 393

Answer:

  y = -4/3x +23/2

Step-by-step explanation:

The tangent of interest is perpendicular to the radius at the given point on the circle. To find the perpendicular, it helps to know the slope of the radius segment. To find that, we need the center of the circle.

The center of the circle can be found by completing the square for each variable.

  (x^2 -2x) +(y^2 +4y) = 20

  (x^2 -2x +1) +(y^2 +4y +4) = 20 +1 +4

  (x -1)^2 +(y +2)^2 = 25

Comparing this equation to the standard form equation for a circle, we can find the center.

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . . circle of radius r centered at (h, k)

The center of circle P is (1, -2).

__

The slope m' of the line segment between (1, -2) and (5, 1) is given by ...

  m' = (y2 -y1)/(x2 -x1)

  m' = (1 -(-2))/(5 -1) = 3/4

The slope m of the perpendicular line is the opposite reciprocal of this, so is ...

  m = -1/m' = -1/(3/4) = -4/3

The y-intercept of the desired line can be found from ...

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  b = 1 -(-4/3)(5) = 23/3

Then the equation of tangent line AB is ...

  y = mx +b

  y = -4/3x +23/3

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2 years ago
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