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Vlad1618 [11]
3 years ago
10

David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. after 4 seconds, the rock reaches a maxim

um height of 108 feet. Six seconds later, the rock enters the ocean.
A) Write a function to model the scenario
B) Create a table of at least five values to represent the scenario
C) Identify how you see the X- and Y- intercepts in the table, graph, and equation. ​
Mathematics
1 answer:
lesya692 [45]3 years ago
4 0

Answer:

David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. After 4 seconds, the rock reaches a maximum height of 108 feet. Six seconds later, the rock enters the ocean.  . Create a graph to represent the scenario. The graph should include at least the x- and y-intercepts and the vertex. (A complete graph consists of axis labels and appropriate scales, ordered pairs for each identified point, the function, and appropriate domain/range.)  . Write a function to model the scenario.  Part C. Create a table of values to represent the scenario. Be sure to include at least five values. Values should include at least the x- and y-intercepts and the vertex.  Part D. Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)

Step-by-step explanation:

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Solution 2: 1-1\sqrt{3}

Step-by-step explanation:

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3 years ago
Complete the square to write the quadratic expression in vertex form.
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Answer:

1. (x - 3)² = 8

2. (x + 2)² = 3

3. (x + 6)² = $ \frac{101}{2} $

4. (x + 3)² = 27

5. (x + 4)² = 13

6.  $ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $

Step-by-step explanation:

Completion of Square: $ (x - a) ^2 = x^2 - 2ax + a^2 $

In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.

1. x² - 6x + 1 = 0

Taking the constant term to the other side, we get:

x² - 6x = - 1

⇒ x² - 2(3)x = -1

⇒ x² -2(3)x + 9 = - 1 + 9  [Adding 9 to both the sides]

⇒ x² -2(3)x + 3² = 8

⇒ (x - 3)² = 8 is the answer.

2. 3x² + 12x + 3 = 0

Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.

3x² + 12x = -3

Dividing by 3 through out, x² + 4x = - 1

⇒ x² + 2(2) + 4 = -1 + 4

⇒ x² +2(2) + 2² = 3

⇒ (x + 2)² = 3 is the answer.

3. 2x² + 24x = 29

x² + 12x = $ \frac{29}{2} $

⇒ x² + 2(6)x + 36 = $ \frac{29}{2} $ + 36

⇒ x² + 2(6)x + 6² = $ \frac{29 + 72}{2} $

⇒ (x + 6)² = $ \frac{101}{2} $ is the answer.

4. x² + 6x - 18 = 0

x² + 6x = 18

⇒ x² + 2(3)x = 18

⇒ x² + 2(3)x + 9 = 18 + 9

⇒ x² + 2(3)x + 3² = 27

⇒ (x + 3)² = 27 is the answer.

5. x² + 8x + 3 = 0

x² + 8x = -3

⇒ x² + 2(4)x = -3

⇒ x² + 2(4)x + 16 = - 3 + 16

⇒ x² + 2(4)x + 16 = 13

⇒ (x + 4)² = 13 is the answer.

6. 9x² - 30x + 6 = 0

9x² - 30x = - 6

⇒ x² $ - \frac{30}{9} $ x = - 6

$ \implies x^2 -2 \bigg( \frac{15}{9} \bigg )x + \frac{225}{81} = - 6 + \frac{225}{81} $

$ \implies x^2 - 2\bigg( \frac{15}{9} \bigg ) x + \bigg ( \frac{15}{9} \bigg ) ^2 = \frac{261}{81} $

$ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $ is the answer.

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3 years ago
I need help on 1/2/3/4
vaieri [72.5K]

You may need to sit down with your parents or with your teacher and
go over how to add and subtract fractions.

1).  "Perimeter" means the distance all the way around the square.
With a square, all 4 sides are the same length.  With <u>this</u> square,
every side is 1-1/4 inches long.

Perimeter = length of all 4 sides= (1-1/4) + (1-1/4) + (1-1/4) + (1-1/4) =

                                               (1 + 1 + 1 + 1) + (1/4 + 1/4 + 1/4 + 1/4) =

                                                         4           +             4/4  =  <em>5 inches</em> .

2).  (2-3/8) + (1-7/8) = (2 + 1) + (3/8 + 7/8) =

                                        (3)   +    (10/8) =

                                         3    +      1-1/4 =        <em>4-1/4 .</em>

3).  The difference is  (1-1/6) minus (5/6) .

Before you start to do the subtraction, write the (1-1/6)  as  (7/6) .

Then the subtraction is    (7/6) - (5/6)  =  2/6  =  <em>1/3</em> .

4).  This one is almost the same kind of problem as #3. 
It's another subtraction.

If you need (2-1/4) all together, and you already have (1-3/8),
then the amount you still have to find, or borrow, or buy, is the
difference between those two numbers.

           (2-1/4) minus (1-3/8) .

The trick is to write the (2-1/4) in some form that you'll be able to
subtract (1-3/8) from it.  When I learned how to do that, it was called
'borrowing', but I think now it's called 'regrouping'.

We need to work on (2-1/4):

-- take 1 from the 2, and change it into fourths.
 
                 2-1/4  =  1 and 4/4 and 1/4  =  1 and 5/4

-- Now, take those 5/4, and turn them into eighths.                
   Each fourth makes 2 eighths.  So  5/4  =  10/8.

Now, the (2-1/4) has turned into  1-10/8 .
We did NOT change the value.  It's still the same amount
as 2-1/4 , but it's just written in a different way.
And now the subtraction is easy:

         (2-1/4) minus (1-3/8)  = 

       (1-10/8) minus (1-3/8)  =  (zero and 7/8).

You need  <em>7/8 inch</em>  more string than you already have.

         

5 0
3 years ago
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