All categories

1 year ago

Solve the equation 4n2 − 16n − 84 = 0 by completing the square.

Mathematics

1 answer:

melomori [17]1 year ago

8 0

4n² - 16n - 84 = 0

Multiply both sides by 1/4 :

n² - 4n - 21 = 0

Add 21 to both sides:

n² - 4n = 21

Complete the square by adding 4 to both sides:

n² - 4n + 4 = 25

(n - 2)² = 25

Solve for n :

n - 2 = ± √25

n - 2 = ± 5

n = 2 ± 5

Then n = 2 + 5 = 7 or n = 2 - 5 = -3.

You might be interested in

Find the surface area of composite figures

Aleonysh [2.5K]

Answer:

429 cm²

Step-by-step explanation:

A(blue) =

= 2×6cm×10cm + 2×6cm×8cm + 8cm×10cm + (8cm×10cm - 5cm×4cm)

= 120cm² + 96cm² + 80cm² + 60cm²

= 356 cm²

A(green) =

= 4cm×5cm + 2×5cm×5cm/2 + 4cm×7cm

= 20cm² + 25cm² + 28cm²

= 73 cm²

A(total) =

= A(blue) + A(green)

= 356 cm² + 73 cm²

= 429 cm²

6 0

2 years ago

Read 2 more answers

Find the distance between C & D. C = (6,-5) and D = (-1, -4) (please show work)

NeTakaya

Answer:7.0711

Step-by-step explanation:

8 0

1 year ago

Graph the solution of the inequality on a number line c<5

polet [3.4K]

C < 5

there will be an open circle on 5....it is open because there is no equal sign in the problem.....the shading will be to the left....because less then is shaded to the left

5 0

2 years ago

the function intersects its midline at (-pi,-8) and has a maximum point at (pi/4,-1.5) write an equation

Tcecarenko [31]

The equation that represents the sinusoidal function is $x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3} \right)\right]$ , $i\in \mathbb{Z}$ .

<h3>Procedure - Determination of an appropriate function based on given information</h3>

In this question we must find an appropriate model for a periodic function based on the information from statement. Sinusoidal functions are the most typical functions which intersects a midline ( $x_{mid}$ ) and has both a maximum ( $x_{max}$ ) and a minimum ( $x_{min}$ ).

Sinusoidal functions have in most cases the following form:

$x(t) = x_{mid} + \left(\frac{x_{max}-x_{min}}{2} \right)\cdot \sin (\omega \cdot t + \phi)$ (1)

Where:

$\omega$ - Angular frequency
$\phi$ - Angular phase, in radians.

If we know that $x_{min} = -14.5$ , $x_{mid} = -8$ , $x_{max} = -1.5$ , $(t, x) = (-\pi, -8)$ and $(t, x) = \left(\frac{\pi}{4}, -1.5 \right)$ , then the sinusoidal function is: