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3 years ago

What is the explicit formula for this sequence 2,6,18,54,162

Mathematics

1 answer:

Nina [5.8K]3 years ago

8 0

Answer:

x3 just multiply 2 x 3 and then multiply the 6 from that by 3 to get 18 and so on

Step-by-step explanation:

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1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals n

Andrew [12]

Part 1
We are given $x^2-21x=-4x$ . This can be rewritten as $x^2-18x=0$ .
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}$
$x=\frac{18\pm 18}{2}$

The values of x are
$x_1=\frac{18-18}{2}=0$
$x_2=\frac{18+18}{2}=18$

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function.

Part 3.
The first equation is $y=x^2+2$ .
The second equation is $y=3x+20$ .

We have
$x^2+2=3x+20$
$x^2-3x-18=0$
Factoring, we have
$\left(x-6\right)\left(x+3\right)=0$
Equating both factors to zero.
$x_1-6=0\rightarrow x_1=6$
$x_2+3=0\rightarrow x_2=-3$

When the value of x is 6, the value of y is
$y=3\left(6\right)+20=38$

When the value of x is -3, the value of y is
$y=3\left(-3\right)+20=11$

Therefore, the solutions are (6,38) or (-3,11)

7 0

3 years ago

Find the volume of the prism.

Gemiola [76]

Answer:

Step-by-step explanation:

The volume of the triangular prism, this is an isosceles triangular prism is

V=1/2 * a*b*h

V=1/2 x10x8x14=560 cm^3

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2 years ago

Zelda made 5 gallons of lemonade and gave each of her friends an equal amount. Write an expression that represents how much lemo

enot [183]

Answer:

2.5

Step-by-step explanation:

!!!!!!!!!!hehbeffjjdjdjsjcjjfbdbd

8 0

3 years ago

Plzzzz help like just plzzzzz In Alana's math class, there are 12 boys and 13 girls. What is the ratio of boys to girls?

irakobra [83]

Answer:

12:13 is the ratio of boys:girls.

7 0

3 years ago

Read 2 more answers

Pic is question vuygvcutyfvgt

Furkat [3]

Answer:

Step-by-step explanation:

270/9 = 30

Hope This Helps & Good Luck :)

5 0

3 years ago