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vovikov84 [41]
3 years ago
14

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

Mathematics
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.

4 0
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:

5 0
3 years ago
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