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Flura [38]
3 years ago
14

13 (04.07)

Mathematics
1 answer:
zzz [600]3 years ago
3 0

Step-by-step explanation:

Coefficient of 3x⁴ is positive (concave upwards)

Power of x⁴ is even (both ends go upwards)

Hence the answer is Up on the left, up on the right.

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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
3 years ago
Read 2 more answers
Soit trois nombres consécutifs. Lorsque l’on soustrait le double du deuxième nombre du quadruple du
irina [24]

Answer:

Les trois nombres sont 5, 6 et 7.

Step-by-step explanation:

Soit x le premier nombre.

x + 1 sera le second et x + 2 sera le troisième.

On pose l'équation :

2x + 3(x + 1) = 4(x + 2)

2x + 3x + 3 = 4x + 8

5x - 4x = 8 - 3

x = 5

4 0
3 years ago
Please help me with this. I give brainliest and give ratings. Don't answer just to take my points or your getting reported
lesantik [10]

Answer:

by 3/4ftmrs torrer is shorter than her husband

6 1/4-5 1/2=25/4-11/2=3/4ft

4 0
3 years ago
The sum of two numbers is 65 one is 4 times as large as the others.what are the numbers?​
bixtya [17]
<h3><em>Hey! </em></h3>

<u>let the numbers be n and m</u>

<u>n+m=65</u>

<u>n=4m</u>

<em>So when we put our work in:</em>

<u>4m+m=65</u>

<u>5m=65</u>

<u>m=13</u>

<u>n=52</u>

So therefore your two numbers are 52 and 13!

<em>Hope this helped! °ω°</em>

6 0
3 years ago
50 points!<br><br> What is the value of x?<br><br><br> Enter your answer in the box.<br><br> x =
frosja888 [35]

Answer:

x = 3

Hope this helps!

Step-by-step explanation:

ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6\sqrt{2} ) can be x\sqrt{2} while AB and CB are x. Because 6\sqrt{2} is equal to x\sqrt{2}, you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = x\sqrt{3}. CB is equal to 6 so 2x = 6, x = 3.

8 0
1 year ago
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