Ophelia spins each of the three shown spinners once. What is the

Answer:

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7 0

2 years ago

Find an equation of the circle that satisfies the given conditions.

hodyreva [135]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

$P(-1,1) \\
x_1=-1 \\ y_1=1 \\ \\ Q(5,9) \\ x_2=5 \\ y_2=9 \\ \\
\frac{x_1+x_2}{2}=\frac{-1+5}{2}=\frac{4}{2}=2 \\ \frac{y_1+y_2}{2}=\frac{1+9}{2}=\frac{10}{2}=5$

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(-1,1) \\ x_1=-1 \\ y_1=1 \\ \\ (2,5) \\ x_2=2 \\ y_2=5 \\ \\ d=\sqrt{(2-(-1))^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

The radius is 5.

$(x-2)^2+(y-5)^2=5^2 \\
\boxed{(x-2)^2+(y-5)^2=25}$

4 0

2 years ago

The library is halfway between your house and your school. If your house is located at (-4,-3) and the library is at (2,-1), wha

aleksandrvk [35]

I believe it would be (-2,-2) i may be wrong though i dont have my graphing papers

6 0

3 years ago

Recall that two angles are complementary if the sum of their measures is 90 degrees°. find the measures of two complementary ang

Julli [10]

Let x represent the smaller angle. Then the larger one is 20+4x. Since they are complementary, their sum is 90. (All measures are degrees.)

90 = x + (20+4x)
90 = 5x +20
70 = 5x
14 = x

The smaller angle is 14°.
The larger angle is 76°.

8 0

3 years ago

Theo deposits $2,000 deposit in a savings account earning compound interest at an annual rate of 5% compounded annually. He make

Arada [10]

The amount in the account after 10 years would be $3257.79

4 0

2 years ago