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4vir4ik [10]
3 years ago
8

The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
7 0

Answer:  The speed of the motorboat is 70 miles per hour

Step-by-step explanation:  Subtract the initial distance, 35, from the distance at any given time, then divide the remainder by the hours.

For example, at 2 hours, the distance shown on the graph is 175 miles

Subtract: 175 -35 = 140.  Then divide 140/2 = 70

At 4 hours, the distance shown is 315 miles.

Subtract: 315 - 35 = 280. Then divide  280/4 = 70

70 mph is the speed.

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Tan(arcsin(x)) and its domain ...?
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- \frac{\pi}{2} < \arcsin{x} < \frac{\pi}{2} &#10;\\&#10;\\\sin(- \frac{\pi}{2}) < \sin(\arcsin{x}) < \sin(\frac{\pi}{2} )&#10;\\&#10;\\-1 < x < 1
6 0
3 years ago
PLEASE HELP I HAVE NO IDEA HOW TO ANSWER THIS :(
dolphi86 [110]

The other 2 angles of given right angles are 61.93° and 28.072°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

Step-by-step explanation:

The given is,

                 Right angled triangle,

                 Side lengths are 8, 15, and 17  

Step:1

                The given triangle is right angle triangle by the converse of Pythagorean theorem, so the trigonometric ratio,

               Ref the attachment,

               For angle a,

                            ...................................................(1)

                 Where,  Opp - 8

                                Hyp - 17

                 From equation (1),

                                      

                                      = 0.470588

                                      (0.470588)

                                   a = 28.072°

                    For angle b,

                                  ...................................................(1)

                 Where,  Opp - 15

                                Hyp - 17

                 From equation (1),

                                      

                                      = 0.882352

                                      (0.882352)

                                   b = 61.93°

Step:2

          Check for solution for right angle triangle,

                        90 ° = Other 2 angles

                        90 ° = a + b

                        90 ° = 28.072° + 61.93°

                        90 ° = 90 °

Result:

          The other 2 angles of given right angles are 61.93° and 28.07°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

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add the term that makes the given expression into a perfect square. write the result as the square of a bracketed expression c s
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<h2>Perfect Squares</h2>

Perfect square formula/rules:

  • a^2+2ab+b^2=(a+b)^2
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Trinomials are often organized like ax^2+bx+c.

The <em>b</em> value in this case is <em>c</em>, and it will always equal the square of half of the <em>b</em> value.

  • Perfect square trinomial: ax^2+bx+(\dfrac{b}{2})^2
  • or ax^2-bx+(\dfrac{b}{2})^2

<h2>Solving the Question</h2>

We're given:

  • c^2-4c

In a trinomial, we're given the ax^2 and bx values. <em>a</em> in this case is 1 and <em>b</em> in this case is 4. To find the third value by dividing 4 by 2 and squaring the quotient:

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Therefore, the term that we can add is + 4.

c^2-4c+4

To write this as the square of a bracketed expression, we can follow the rule a^2-2ab+b^2=(a-b)^2:

(c-2)^2

<h2>Answer</h2>

c^2-4c+4

(c-2)^2

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¼ is equal to 0.25 because when you times by 4 you get a whole :)
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