Can someone help me with these three

Solve the following equation by factoring:9x^2-3x-2=0

olya-2409 [2.1K]

Answer:

The two roots of the quadratic equation are

$x_1= - \frac{1}{3} \text{ and } x_2= \frac{2}{3}$

Step-by-step explanation:

Original quadratic equation is $9x^{2}-3x-2=0$

Divide both sides by 9:

$x^{2} - \frac{x}{3} - \frac{2}{9}=0$

Add $\frac{2}{9}$ to both sides to get rid of the constant on the LHS

$x^{2} - \frac{x}{3} - \frac{2}{9}+\frac{2}{9}=\frac{2}{9}$ ==> $x^{2} - \frac{x}{3}=\frac{2}{9}$

Add $\frac{1}{36}$ to both sides

$x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{2}{9} +\frac{1}{36}$

This simplifies to

$x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{1}{4}$

Noting that (a + b)² = a² + 2ab + b²

If we set a = x and b = $\frac{1}{6}\right)$ we can see that

$\left(x - \frac{1}{6}\right)^2$ = $x^2 - 2.x. (-\frac{1}{6}) + \frac{1}{36} = x^{2} - \frac{x}{3}+\frac{1}{36}$

So

$\left(x - \frac{1}{6}\right)^2=\frac{1}{4}$

Taking square roots on both sides

$\left(x - \frac{1}{6}\right)^2= \pm\frac{1}{4}$

So the two roots or solutions of the equation are

$x - \frac{1}{6}=-\sqrt{\frac{1}{4}}$ and $x - \frac{1}{6}=\sqrt{\frac{1}{4}}$

$\sqrt{\frac{1}{4}} = \frac{1}{2}$

So the two roots are

$x_1=\frac{1}{6} - \frac{1}{2} = -\frac{1}{3}$

and

$x_2=\frac{1}{6} + \frac{1}{2} = \frac{2}{3}$

7 0

2 years ago

What is the value of a in the equation 3Q+b=54, when b = 9?<br> 15<br> 18<br> 21<br> 27

vladimir1956 [14]

Answer: 15

Step-by-step explanation:

3q+9=54

-9 -9

3q = 45

—————-

3

Q=15

4 0

3 years ago

Expand (a+b)^7 using pascal triangle

Inga [223]

(a+b)^7= a^7+ 7a^7b+ 21 a^6b²+ 35a^5b³+ 35 a⁴b⁴+ 21 a³b^5 + 7a²b^6 + b^7

8 0

3 years ago

Suppose you take a sample of 15 pieces of colored fruit snacks and a sample of 60 pieces of colored fruit snacks from one day's

Annette [7]

Answer:

The sample of 15 pieces of colored fruit snacks

Step-by-step explanation:

The sample of 15 pieces of colored fruit snacks. The 60 pieces are from ONE day which means it can be heavily biased. It might be like "BLUE RASPBERRY SPECIAL DAY!" or "PRESIDENTS DAY!! RED BLUE AND WHITE!!". However, 15 pieces, whilst having less of a population, is probably more spaced out.

5 0

2 years ago

What is the slope of y=0.50x+5 and write a sentence to describe the meaning

castortr0y [4]

Answer:

5.5

Step-by-step explanation:

y = 0.5x + 5

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0.5

y-intercept: 5

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding values.

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y.

y = 0.5(0) + 5

y = 5

To graph the y intercept using the equation of the line, plug in 1 for the x variable and solve for y.

y = 0.5(1) + 5

y = 5.5

Which means when x is 0, y intercept at 5 and when x is 1 y intercept at 5.5. Graph the line using the slope and the y-intercept, or the points.

This tells us, in practical terms, that, for every one unit that the x-variable increases (that is, moves over to the right), the y-variable increases (that is, goes up) by 50% of a unit.

6 0

4 years ago