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mote1985 [20]
3 years ago
6

Can u help me plz ?

Mathematics
1 answer:
natita [175]3 years ago
8 0

Answer:

82 grams

Step-by-step explanation:

each rubber band weighs 3 grams because when 2 bands were added to 88 grams it went up 6 grams and six divided by 2 equals 3.

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Look at the pentagonal numbers. Use finite differences to determine which function represents the pattern.
Ahat [919]

Answer:

f(x) = 1.5x - 0.5x

Step-by-step explanation:

The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.

The triangular number general formula

                      x (x + 1) / 2

For  example,

The sequence

1,     3,     6,      10

                                             *

                          *              *  *

         *           *   *          *   *  *

* ,    *  *,     *   *   *,     *   *   *  *

_____________________________

The pentagonal numbers

The sequence:

1, 5, 12, 22, 35

As shown in the picture can be divided into three triangles

Triangle 2

x (x + 1) / 2

Triangle 1 and 3  (they are triangles one unit smaller than 2)

n (n + 1) / 2

n= x-1

Replacing n

(x-1) ((x-1) + 1) / 2

(x-1) (x) / 2

(x-1) x / 2

______________

Function represents the pattern

Triangle 2  + (Triangle 1  +  Triangle 3)

Triangle 1  = Triangle 3

So then,

Triangle 2 + 2* Triangle 1

x (x +1) /2  + 2* (x -1) x/2

Rearranging

0.5 x (x +1) + x(x -1)

0.5x^2 + 0.5x + x^2 -x

(0.5 x^2 + x^2)  + (0.5x -x )

1.5 x^2 - 0.5 x  

______

3 0
2 years ago
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A boat is marked up 28%. The wholesale cost was $50. What is the dollar amount of the<br> markup?
Vera_Pavlovna [14]
<h2>Step-by-step explanation:</h2>

6 0
3 years ago
Solve the system: <br> 2/x - 3/y =-5; 4/x + 6\y =14
sertanlavr [38]

The solution is x = 2 \text{ and } y = \frac{1}{2}

<em><u>Solution:</u></em>

Let us assume,

a = \frac{1}{x}\\\\b = \frac{1}{y}

<em><u>Given system of equations are:</u></em>

\frac{2}{x} - \frac{3}{y} = -5

\frac{4}{x} + \frac{6}{y} = 14

<em><u>Rewrite the equation using "a" and "b"</u></em>

2a - 3b = -5 ------------ eqn 1

4a + 6b = 14 -------------- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

<em><u>Multiply eqn 1 by 2</u></em>

2(2a - 3b = -5)

4a - 6b = -10 ------------- eqn 3

<em><u>Add eqn 2 and eqn 3</u></em>

4a + 6b = 14

4a - 6b = -10

( - ) --------------------

8a = 4

a = \frac{4}{8}\\\\a = \frac{1}{2}

Substitute a = 1/2 in eqn 1

2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2

Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2

Substitute b = 2 in assumed value

b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}

Thus the solution is x = 2 \text{ and } y = \frac{1}{2}

3 0
2 years ago
How many feet are in 9 meters? <br> 1 m = 3.3 ft<br><br><br>9 m = [?] ft​
sukhopar [10]
9 x 3.3 ft = 29.7 feet
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natima [27]

Answer:

Y=-x+1

Step-by-step explanation:

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