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3 years ago

Hello! Please help with this fill in the blank, thanks!

Mathematics

1 answer:

Ivenika [448]3 years ago

7 0

<h3>Answer:</h3>

Triangle ABC is rotated 180 degrees around point E, therefore, A maps to D, B maps to C, and C maps to B.

===================================================

Explanation:

If you were to rotate triangle ABC 180 degrees around point E, then it would line up perfectly with triangle DCB

Point A lands on point D
Point B lands on point C
Point C lands on point B

Note how in the sequence ABC we have A first, B second, then C third

Then for the sequence DCB we have D first, C second, then B third

This order matters so we can pair up the points properly

A goes to D (A is first of ABC; D is first of DCB)
B goes to C (B is second in ABC; C is second in DCB)
C goes to B (C is third in ABC; B is third in DCB)

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2 years ago

Gilbert and Brian drove 604 miles in 11.6 hours. Gilbert drove the first part of the trip and averaged 45 miles per hour. Brian

AVprozaik [17]

The length of hours Gilbert drove is 7.5 hours.

The length of hours Brian drove is 4.1 hours.

Step-by-step explanation:

Gilbert averaged = 45 miles per hour
Brain averaged = 65 miles per hour
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Total distance = 604 miles

Let 'x' be the hours Gilbert drove.

Let 'y' be the hours Brian drove.

x+y = 11.6 -----(1)

45x+65y = 604 -----(2)

Multiply (1) by 45 and subtract (2) from (1)

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-20y = -82

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3 years ago

LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (6

USPshnik [31]

LORAN follows an hyperbolic path.

The equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

The coordinates are given as:

$\mathbf{(x,y) = (-60,0)\ (60,0)}$

The center of the hyperbola is

$\mathbf{(h,k) = (0,0)}$

The distance from the center to the focal points is given as:

$\mathbf{c = 60}$

Square both sides

$\mathbf{c^2 = 3600}$

The distance from the receiver to the transmitters is given as:

$\mathbf{2a = 100}$

Divide both sides by 2

$\mathbf{a = 50}$

Square both sides

$\mathbf{a^2 = 2500}$

We have:

$\mathbf{b^2 = c^2 - a^2}$

This gives

$\mathbf{b^2 = 3600 - 2500}$

$\mathbf{b^2 = 1100}$

The equation of an hyperbola is:

$\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}$

So, we have:

$\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}$

$\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Hence, the equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$