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lana66690 [7]
3 years ago
13

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and

calculations to receive credit.
x2 + 2x + y2 + 4y = 20
Mathematics
1 answer:
Sliva [168]3 years ago
4 0

Answer:

( x+1)^2  + (y+2)^2 = 25

The center is (-1, -2) and the radius is 5

Step-by-step explanation:

x^2 + 2x + y^2 + 4y = 20

Complete the square

2/2 =1  1^2 =1  so add 1 for x     4/2 =2  2^2 = 4 so add 4 for y

x^2 +2x +1   +y^2 +4y+4 = 20 +1 +4

( x+1)^2  + (y+2)^2 = 25

(x+1) ^2 + (y+2)^2 = 5^2

(x - -1) ^2 + (y -  -2)^2 = 5^2

This is in (x-h)^2 + (y-k)^2 = r^2 form where (h,k) is the center and r is the radius

The center is (-1, -2) and the radius is 5

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Use the formula for the cosine of the difference of two angles to find the exact value of the following expression.
Zolol [24]

Answer:

Exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

Step-by-step explanation:

Given:

Cos(45° - 60°)

We have to apply the formula of cosine for difference of the two angles.

Formula:

cos(a-b)=cos(a)\ cos(b)+sin(a)\ sin(b)

Plugging the values.

⇒ cos(45-60)=cos(45)\ cos(60) + sin(45)\ sin(60)

We know that the values :

sin(45) =cos(45) = \frac{1}{\sqrt{2} }

sin(60)=\frac{\sqrt{3} }{2}  and  cos(60)=\frac{1}{2}

So,

⇒ cos(45-60)=(\frac{1}{\sqrt{2} } \times \frac{1}{2} ) + (\frac{1}{\sqrt{2} } \times \frac{\sqrt{3} }{2})

⇒ cos(45-60)=(\frac{1}{2\sqrt{2} }  + \frac{\sqrt{3} }{2\sqrt{2} })

⇒ cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )

⇒ cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )\times \frac{2\sqrt{2} }{2\sqrt{2} }  ...<em>rationalizing </em>

⇒ cos(45-60)=\frac{2\sqrt{2} +2\sqrt{6} }{ 8}

⇒ cos(45-60)=\frac{2(\sqrt{2}+\sqrt{6})}{8}       ...<em>taking 2 as a common factor</em>

<em>⇒ </em>cos(45-60)=\frac{(\sqrt{2}+\sqrt{6})}{4}

To find the exact values we have to put the values of sq-rt .

As<em>, </em>\sqrt{2}=1.41     and   \sqrt{6} =2.44

Then

<em>⇒ </em>cos(45-60)=\frac{( 1.41+2.44)}{4}<em />

<em>⇒ </em>cos(45-60)=\frac{( 3.85)}{4}<em />

⇒ cos(45-60)=0.96

So the exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

3 0
3 years ago
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Keith_Richards [23]
I'm writing this because I need to type extra characters, but the answer is (0,7) because x=0, because there are 0 X's in the equation, and y=7. The equation that comes from is y=Mx+b, where 'b' is the y-intercept, the equation, when not simplified looks like this, Y=0x+7
8 0
3 years ago
After the priest ruled the city who became the 1st king of the city ? ​
cricket20 [7]

Answer:

son of the priest

Step-by-step explanation:

I guess

6 0
3 years ago
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Which two values of x are roots of the polynomial below x^2+3x-5
Elenna [48]

Answer:

Step-by-step explanation:

Given a quadratic equation

ax^2+bx+c=0  

you can find its solutions with the following formula:

x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}  

You equation is identified by the coefficients

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Which means the solutions are

\dfrac{3 \pm \sqrt{9-4\cdot 5}}{2} = \dfrac{3 \pm \sqrt{-11}}{2}

8 0
3 years ago
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Olin [163]

Answer:

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Step-by-step explanation:

The range is the output so the y values, when x = 3 then

y = \frac{2}{3}(3) - 2 so y = 0

y = \frac{2}{3}(4) - 2 so 8/3 - 6/3 is 2/3 so y = 2/3

y = \frac{2}{3}(5) - 2 so 10/3 - 6/3 is 4/3 so y = 4/3 or 1 1/3

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Now you try the rest

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