Ask question

Ask question

All categories

Alekssandra [29.7K]

1 year ago

6

What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?

1 answer:

saveliy_v [14]1 year ago

3 0

Answer: -3/2

Step-by-step explanation:

The axis of symmetry, and thus the x-coordinate of the vertex, is given by $x=-\frac{b}{2a}$

So, the answer is $x=-\frac{9}{2(3)}=\boxed{-\frac{3}{2}}$

You might be interested in

HELP ASAP PLZ i need help !<br>help me :((

kodGreya [7K]

Answer:

(1) $g[f(x)]=\frac{8x-1}{12x-4}$

(2) $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

Step-by-step explanation:

Given functions f(x) = (4x-1)

are $g(x)=\frac{2x+1}{3x-1}$

(1) $g[f(x)]=\frac{2(4x-1)+1}{3(4x-1)-1}$

$=\frac{8x-2+1}{12x-3-1}$

$=\frac{8x-1}{12x-4}$

(2) for $g^{-1}(x)$ , rewrite the function g(x) in terms of an equation

$y=\frac{2x+1}{3x-1}$

Substitute y in place of x and x in place of y, then solve for y.

$x=\frac{2y+1}{3y-1}$

(3y-1)x = 2y+1

3xy - x = 2y + 1

3xy - 2y = x + 1

y(3x-2) = x + 1

$y=(\frac{x+1}{3x-2} )$

⇒ $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $f[g(x)]=(x-1)$

$f[g(x)]=4[\frac{2x+1}{3x-1}] =(x-1)$

⇒ $\frac{(8x+4)-(3x-1)}{3x-1}=(x-1)$

⇒ $\frac{8x-3x+4+1}{3x-1}=(x-1)$

⇒ $\frac{5x+5}{(3x-1)}=(x-1)$

⇒ $5x+5=(3x-1)(x-1)$

⇒ $5x+5=3x^2-3x-x+1$

⇒ $5x+5=3x^2-4x+1$

⇒ $3x^2-9x-4=0$

⇒ $x=\frac{9\pm\sqrt{(-9)^2-4(-4)\times3} }{2\times3}$

$x=\frac{9\pm\sqrt{81+48} }{6}$

$x=\frac{9\pm\sqrt{129} }{6}$

$x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

4 0

3 years ago

Mitchell has a small bag with 12 M&Ms in it. 5 of the M&Ms are yellow. 2 are green. 1 is orange. 4 is brown. what fricti

Sophie [7]

Answer:

1/3

Step-by-step explanation:

There are 4 brown M&Ms and 12 M&Ms in total.

Since both 4 and 12 are divisible by 4,

4/12 = 1/3

6 0

2 years ago

Emma started babysitting her neighbor. After babysitting for 5 hours, she made $37.50. What is her babysitting pay rate?

LUCKY_DIMON [66]

Answer:

$7.50

Step-by-step explanation:

Hourly Pay * 5 = 37.5

Rearrange to find the hourly pay

Hourly pay = 37.5 / 5 = 7.5

5 0

3 years ago

A person noted that the angle of elevation to the top of a tree was 65 degrees at a distance of 11 feet from the tree. Using the

sashaice [31]

Answer:

approximate 23.590 feet

Step-by-step explanation:

tan 65° = x / 11 = 2.145

x = 11 x 2.145 = 23.595

5 0

2 years ago

Read 2 more answers

Help, I wanna pass this iready lesson or im going to get yelled at.

densk [106]

Answer:

1/10 is the correct answer

Step-by-step explanation:

3/5=6/10

7/10-6/10=1/10

7 0

2 years ago

Read 2 more answers