1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
likoan [24]
1 year ago
5

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

Mathematics
1 answer:
olya-2409 [2.1K]1 year ago
7 0

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}

You might be interested in
When triangle ABC is rotated about side AB, what figure is formed?
Ne4ueva [31]

I think it’s a pyramid

3 0
3 years ago
What are the two point plz help me
evablogger [386]

Your first point should always be shown in the y-intercept following the standard form for slope-intercept form

Y = mx + b

b = y - intercept

In this case your first point would be (0,1)

You next point would be following the slope which is -2x. When you graph a equation always know that it is rise over run. For this line, it would be going from left to right since it is a negative line.

Your second point would go down 2 points from your starting point (0,1) and run 1 to the right in the x-axis, which is also called, (1,-3)

5 0
3 years ago
Solve and type in 'ab' 8×a=32,a+26=b+1,a<20<b
Whitepunk [10]
8*a=32
32:8=a
4=a

4+26=b

30=b

3 0
3 years ago
Please help with these math questions part 2
NikAS [45]
5).
and
6).
The volume of a sphere is

               (4/3) (pi) (radius)³ .

In #5, the 'pi' is already there next to the answer window.
You just have to come up with the (4/3)(radius³).

Remember that the radius = 1/2 of the diameter.

7).  The volume of a cylinder is

                         (pi) (radius²) (height) .

Divide the juice in the container by the volume of one can,
to get the number of cans he can fill.

8).  The volume of a cone is

                     (1/3) (pi) (radius of the round bottom)² (height) .

He starts with a small cone, he then adds clay to it to make it higher.
The question is:  How much clay does he ADD to the short one,
to make the bigger one ?

Use the formula to find the volume of the short one.
Use the formula again to find the volume of the bigger one.
Then SUBTRACT the smaller volume from the bigger volume.
THAT's how much clay he has to ADD.

Notice that the new built-up cone has the same radius
but more height than the first cone.
_______________________________________

Don't worry if you don't understand this.

The answer will be this number:

 (1/3) (pi) (radius²) (height of the big one minus height of the small one).
6 0
3 years ago
HELP PLEASE I will give brainlist ​
steposvetlana [31]

Answer:

the second one

Step-by-step explanation:

y = 2/3 (x +6)-5

4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve SA = πrs + π r^2 for s
    7·1 answer
  • Evaluate
    12·2 answers
  • Emily owns 10.2 shares of stock in a company. On Friday, the stock dropped by $1.35/share. What was the total change in value of
    8·1 answer
  • Chords AB and CD intersect at point E, AE = 10, EB = 4, and CE = 8. Therefore, ED =
    10·2 answers
  • What does y=3x to the second power +7
    8·1 answer
  • Given vectors u=7i + 3j and v=-4i + 3j, find 5u-4v in terms of unit vectors i and j
    5·2 answers
  • Someone please help me this is ASAP- please answer c) I don’t understand it
    15·1 answer
  • In ΔQRS, the measure of ∠S=90°, the measure of ∠R=56°, and SQ = 49 feet. Find the length of QR to the nearest tenth of a foot.
    6·2 answers
  • an airplane can travel 550 mph in still air. if it travels 3498 miles with the wind in the same length of time it travels 3102 m
    7·1 answer
  • Take $27.99 from $42.79.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!