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3 years ago

14

The equation x2 − 6x − 27 = 0 when solved is:

1 answer:

Amiraneli [1.4K]3 years ago

8 0

Answer:

-3 , 9

Step-by-step explanation:

Sum = - 6

Product = -27

Factors = 3, -9

x² - 6x-27 = 0

x² + 3x - 9x - 9*3 = 0

x(x + 3) - 9(x + 3) = 0

(x + 3) (x - 9) = 0

x +3 = 0 ; x - 9 = 0

x = - 3 ; x = 9

Solution: x = -3 , 9

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A circle is centered at the point (5, -4) and passes through the point (-3, 2).

zepelin [54]

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

$\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10$

The standard form of equation of circle is:

$(x-h)^{2}+(y-k)^{2}=r^{2}$

where h and k are the coordinates of the center. So putting in the value:

$(x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100$

8 0

3 years ago

How do I solve this? It says solve each right angle and then to round answers to the nearest tenth.

mariarad [96]

Answer:

19.2

Step-by-step explanation:

Add 12 squared to 15 squared(144+225)

Square root the answer( $\sqrt{369}$ )

Round to the nearest tenth(19.209)

7 0

3 years ago

If 12 less than 4 times a number is 8, the number is 5. Write a different sentance where the unknown number is also 5.

anastassius [24]

Two times a number minus 4 is six. (2*5-4=6)

7 0

3 years ago

Read 2 more answers

What are the amplitude, period, and phase shift of the given function? f(t)=-2/3 cos (3t-3pi)

dybincka [34]

Answer:

amplitude; $\frac{2}{3}$

Phase shift; $\pi$ units right

Period; $\frac{2\pi}{3}$

Step-by-step explanation:

The given function is

$y=-\frac{2}{3}\cos(3t-3\pi)$

This function is of the form;

$y=A\sin (Bt+C)$

The period is given by:

$|A|=|-\frac{2}{3}|= \frac{2}{3}$

The period is given by:

$T=\frac{2\pi}{|B|}= \frac{2\pi}{|3|}=\frac{2\pi}{3}$

The phase shift is given by;

$\frac{C}{B}=\frac{-\3pi}{3}=- \pi$ or $\pi$ units right.

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3 years ago

In 56 years ,Kevin will be 9 times as old as he is right now.<br><br> How old is he right now?

m_a_m_a [10]

Answer:

7

Step-by-step explanation:

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3 years ago