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s344n2d4d5 [400]
3 years ago
14

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 <u>180 degrees around point E</u>, therefore, A maps to <u>D</u>, B maps to <u>C</u>, and C maps to <u>B</u>.

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

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.

<u>Step-by-step explanation</u>:

  • Gilbert averaged = 45 miles per hour
  • Brain averaged = 65 miles per hour
  • Total hours = 11.6 hours
  • 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)

 45x+45y = 522

-(<u>45x+65y = 604</u>)

 <u>      -20y = -82 </u>

y = 82/20

y = 4.1 hours

The length of hours Brian drove = 4.1 hours

Substitute y=4.1 in (1)

x+4.1 = 11.6

x = 7.5 hours

The length of hours Gilbert drove = 7.5 hours

3 0
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}

Read more about hyperbolas at:

brainly.com/question/15697124

7 0
3 years ago
Read 2 more answers
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