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tamaranim1 [39]
3 years ago
6

Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of th

e circle. In your final answer, include all formulas and calculations used to find Point O, x, y), the center of circle O.
Mathematics
1 answer:
balandron [24]3 years ago
7 0
The answer:

the main formula of the circle's equation is 
(x-a)²+ (y-b)² = R²
where C(a, b) is the center of the circle
R is the radius

if a point A(x', y') passes through the circle, so the equation of the circle can be written as 
(x'-a)²+ (y'-b)² = R², and that is  a main formula.


<span>Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2), so we have exactly three equation:
</span>
(0-x)² + (0-y)² = R², circle O passes through A
x²+y²= R²
(-3 -x)² + (0-y)² = R², circle O passes through B
(-3 -x)² + (y)² = R²
(1-x)² + (2-y)² = R², circle O passes through A
(1-x)² + (2-y)² = R²

and we know that R= OA = OC= OB, 
OA=R= sqrt( (0-x)² + (0-y)² ) = OB = sqrt((-3 -x)² + (0-y)²), this implies

x²+y² = (-3 -x)² + (0-y)² , it implies x² = 9+ x² + 6x , and then -9/6=x, x= -3/2
and when OA = OC
x²+y² =(1-x)² + (2-y)²  so, x²+y² =1+x²-2x +4+y²-4y, therefore -5= -2x -4y
 -5= -2x -4y, when x = -3 /2   we obtain y = 2

the center is C(-3/2, 2)
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natita [175]

Answer:

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Step-by-step explanation:

we know that

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I=P(rt)

where

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P is the Principal amount of money to be invested

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t is Number of Time Periods

in this problem we have

First account

t=1 years\\ P=\$x\\ r=0.03

substitute in the formula above

I=x(0.03*1)

I=0.03x

Second account

t=1 years\\ P=\$(7,000-x)\\ r=0.05

substitute in the formula above

I=(7,000-x)(0.05*1)

I=350-0.05x

Remember that

The interest is equal to \$290

so

Adds the interest of both accounts

0.03x+350-0.05x=\$290

0.05x-0.03x=350-290

0.02x=60

x=\$3,000

therefore

In the first account was invested \$3,000  at 3%

In the second account was invested \$7,000-\$3,000=\$4,000  at 5%

7 0
3 years ago
Write the inequality!! Connie’s dog Fido weighs 35 pounds. Her vet placed Fido on a diet. What inequality can you write to find
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Answer:   \frac{35-28}{x} \leq 6

Step-by-step explanation:

Let x be the average number of pounds Fido must loss.

Since, the initial weight of Fido is 35 pounds.

And, After losing the weight, the new weight of Fido in pounds = 28 pounds.

Then the time taken for losing the weight

= \frac{\text{ The weight it losses}}{\text{ Average of losing weight per month}}

= \frac{35-28}{x}

According to the question,  it must lose weight within 6 months,

Thus,   \frac{35-28}{x}\leq 6

Which is the required inequality to find the average number of pounds per month.

By solving it we, get,    x\geq \frac{7}{6}

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3 years ago
Elijah gave out a survey to some students in his school about their favorite color. 392 of those surveyed said their favorite co
Softa [21]

Answer:

700

Step-by-step explanation:

It was right on my test lol

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2 years ago
the stove and the freezer weigh at least 260kg. the stove weighs 115 kg. How much would the freezer weigh?
Aleks [24]
About 145 I gonna guess I dont know if that's right
7 0
3 years ago
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If f(x)=x+8 and g(x)=-4-3 find (f+g)(x)
Lilit [14]

Answer:

(f+g)(x) = -3x+5

Step-by-step explanation:

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             = -3x+5

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