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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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In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, _____. a. a Type
lara31 [8.8K]

Answer:(c)

Step-by-step explanation:

Given : In a hypothesis testing the null hypothesis has been rejected when the alternative hypothesis has been true.

Find : to find that the given decision is create type I error , type II error or right decision has been taken

Step by step :

In hypothesis testing there are 2 types of error.

(1)Type I error :- if the null hypothesis is rejected when it is true, is known has Type I error .

(2)Type II error:- if the null hypothesis is accepted when alternative hypothesis is true, is known as type II error.

Since here null hypothesis has been rejected when alternative hypothesis has been true,i.e., the correct decision has been made

Hence option (c) is correct.

4 0
3 years ago
Based on the picture below:<br><br> Solve for AB
Fiesta28 [93]

Answer:

AB ≈ 35.93

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos3.5° = \frac{adjacent}{hypotenuse} = \frac{AB}{AC} = \frac{AB}{36}

Multiply both sides by 36

36 × cos3.5° = AB, thus

AB ≈ 35.93 ( to 2 dec. places)

3 0
3 years ago
Not sure about these either...
harina [27]
5 is a and 6 is also a
6 0
3 years ago
(a) 95% of what is 57?<br><br> (b) What number is 35% of 40?
frosja888 [35]

Answer:

a=54.15 and b=14

Step-by-step explanation:

6 0
2 years ago
HELP ASAP
dalvyx [7]
So,

All we have to do is multiply all three dimensions together.

First, convert all fractions into improper fractions.

3 \frac{1}{5}--\ \textgreater \  \frac{16}{5}

1 \frac{3}{4} --\ \textgreater \  \frac{7}{4}

2 \frac{1}{4} --\ \textgreater \ \frac{9}{4}

Now multiply the fractions together.

<span>\frac{16}{5}*\frac{7}{4}*\frac{9}{4}= \frac{2*2*2*2*3*3*7}{2*2*2*2*5}
</span>
\frac{3*3*7}{5}--\ \textgreater \ \frac{63}{5}\ or\ 12 \frac{3}{5}\ ft.^3

The correct option is C.
4 0
3 years ago
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