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Zielflug [23.3K]
3 years ago
5

Help me please and thanks

Mathematics
1 answer:
leva [86]3 years ago
3 0

Answer:

  A.  (1, -4)

Step-by-step explanation:

You can try the answers to see which works. (The first one does.)

Or, you can solve the equations algebraically. Equating y-values works well here:

  2x -6 = -2x -2

  4x = 4 . . . . . . . add 2x+6 to both sides; next divide by 4

  x = 1 . . . . . . . . shows you selection A is correct

___

A graphing calculator can show you the point of intersection. Perhaps this is the way to go, since the unit seems to be on graphing systems of equations. Both of these equations are in slope-intercept form (y=mx+b), so are easily graphed by starting from the y-intercept (b) and using the slope (m=rise/run) to find another point on the line.

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3 years ago
A hiker starting at point P on a straight road wants to reach a forest cabin that is 2 km from a point Q, 3 km down the road fro
pantera1 [17]

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

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(24 − 8x) / 3 = (13 − 6x + x²)^½

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576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

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x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

7 0
3 years ago
I need help on this. An answer and an explanation would be great!!
charle [14.2K]

Answer:

60 & 55

Step-by-step explanation:

1. the sum of the angles 1; 2 and 3 is 180°, then

m∠1=m∠2=m∠3; ⇒m∠3=60°;

2. m∠3=m∠r; ⇒ m∠r=60°;

3. m∠α= 180-(m∠r+65°)°; ⇒ m∠α=55°

all the details are in the picture.

4 0
3 years ago
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