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3 years ago

Solving these quadratics for x using complete the square 3x^2-4x-1=0. Show your work.

1 answer:

6 0

Answer: x = (sqrt(7) + 2)/3 and
x = ( – sqrt(7) + 2)/3

Explanation:

3x^2 - 4x - 1 = 0

Divide both sides by 3:

3x^2/3 - 4/3x - 1/3 = 0/3
x^2 - 4/3x - 1/3 = 0
x^2 - 4/3x = 1/3
x^2 - 4/3x + (2/3)^2 = 1/3 + (2/3)^2
(x - 2/3)^2 = 1/3 + 4/9
(x - 2/3)^2 = 7/9

Sqrt both sides:

x - 2/3 = sqrt (7/9)
x - 2/3 = |sqrt(7)/3|

Set x -2/3 = sqrt(7)/3

=> x = (sqrt(7) + 2)/3

Set x - 2/3 = - sqrt(7)/3

=> x = ( - sqrt(7) + 2)/3

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If 2/5n+4=20, what is the value of n?

Dimas [21]

2/5n + 4 = 20
/5 /5
2n + 4 = 100
- 4 -4
2n = 96
/2 /2
n = 48

The answer to your question is 48

6 0

3 years ago

Find the angles between -pi and pi that satisfy: (−√3) sin(v)+cos(v)=√3

MAXImum [283]

Observe that

$\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v$

In the original equation, divide both sides by $\dfrac12$ :

$-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2$

$\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2$

Next,

$\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi$

where $n$ is any integer. Then

$\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi$

Fix $n=0$ to ensure $-\pi$ , so that

$v=-\dfrac\pi6,v=-\dfrac\pi2$

3 0

3 years ago

Eric prepared 45 kilograms of dough after working 9 hours. How many hours did Eric work if he prepared 55 kilograms of dough? As

EastWind [94]

45 / 9 = 5

55 / 5 = 11

Eric worked 11 hours to prepare 55 kilograms of dough.

4 0

3 years ago

Find the total surface area.

Ede4ka [16]

Hey love! <3

Answer:

The right answer is A = 49.6 π ft^2

Step-by-step explanation:

(Let pi = 3.1415926535898)

The formula for calculating the surface area of a cylinder is A=2πrh+2πr^2

So if r = 4 ft

and h = 2.2 ft

A= 2π(4)(2.2)+2π(4)^2

Once we've plugged in our formulas our final surface area is A = 49.6 π ft2

Hope this helped you calculate the surface area! ◃┆◉◡◉┆▷ Sincerely, Kelsey from Brainly.

~ #LearnWithBrainly ~

8 0

3 years ago

Read 2 more answers

In the year 1987, an investment was worth $29,800. In the year 1997, this

Veseljchak [2.6K]

Answer:

a) 46.98%

b) increasing rate of change

Step-by-step explanation:

In year 1987, investment worth $29800

In year 1997, investment worth $43800

Rate of change = 1997investment - 1987investment / 1987investment × 100

Rate of change = 43800 - 29800/29800 × 100

= 14000/29800 × 100

= 0.46979 × 100

= 46.98%

Therefore, the rate of change of the investment during the time period is 46.98%.

b) The rate of change of the investment is increasing. This is as a result of the following reasons. First, the value of rate of change is positive. Second, there is no value for rate of change for period before the time period so we cannot compare rate of change.

8 0

4 years ago