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konstantin123 [22]

3 years ago

8

Someone help me please I can’t solve this

1 answer:

Dmitry_Shevchenko [17]3 years ago

3 0

Answer:

b=36

Step-by-step explanation:

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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

You are planning to invest $500 at 12% compounded annually. How much money would you have after 10 , 20 and 30 years?

Serjik [45]

$A=P(1+r)^t$

where A=final amount

P=principal

r=rate in decimal form

t=time in years

we are given that P=500, r=12%=0.12

we want to find A when t=10, 20, and 30

so

$A=500(1+0.12)^t$

$A=500(1.12)^t$

when t=10, $A=500(1.12)^{10}=$1552.92$

when t=20, $A=500(1.12)^{20}=$4823.15$

when t=30, $A=500(1.12)^{30}=$14980.96$

7 0

3 years ago

Read 2 more answers

Let f(x) = 7x² + 19x + 21 and g(x) = 4x² + 4x + 3 . Identify the solution(s) of f(x) = g(x).

tresset_1 [31]

Answer:

-3 and -2

Step-by-step explanation:

7x² + 19x + 21 = 4x² + 4x + 3

combine like terms:

3x² + 15x + 18 = 0

3(x² + 5x + 6) = 0

(x + 3)(x + 2) = 0

x = -3

x = -2

7 0

3 years ago

What is the measure of angle a

rewona [7]

Review the meaning of "straight angles."

Here 110 and A are "straight angles," and so 110 + A = 180 (degrees).

Then A = 70 degrees.

4 0

3 years ago

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Is the area of the shaded rectangle 6(2−m) or 6(m−2)?<br>Explain how you know.

Rzqust [24]

Answer:

6(2-m)

Step-by-step explanation:

the m could not be times only two so the answer would have been 12-m no matter what you don't add or subtract or times the letter because unless if the number had the same letter!

Hope this helps!! if it doesnt i apalogize!! god bless!! - Natalia

6 0

3 years ago

Read 2 more answers