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Luda [366]
3 years ago
15

Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point. (2, 3)

Mathematics
1 answer:
lozanna [386]3 years ago
8 0
Standard equation of a circle: <em>(x-h)² + (y-k)² = r²</em> where <em>(h, k)</em> is the center and <em>r </em>is the radius. In the case of our equation here, <em>(x-5)² + (y+3)² = 25</em>, we can conclude that our circle has a center at (5, -3) and a radius of 5 units.

We can use the distance formula with the center (5, -3) and our point (2, 3) to see how far away they are...if the distance between them is less than the radius of the circle, it is on the interior. If it's equal, it's on the circle. If it's greater, it's on the exterior.

Distance = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Distance = \sqrt{(-3-3)^2+(5-2)^2}

Distance = \sqrt{(-6)^2+3^2}

Distance = \sqrt{36+9}

Distance = \sqrt{45}\approx6.7082

6.7082>5,\ so\ (2,3)\ is\ on\ the\ \boxed{exterior}
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Vitek1552 [10]

Answer:

1. $33.00

2. $48.00

3. $3.00

4. $36.40

Step-by-step explanation:

44.00 - 25% = 33 —> $33.00

80.00 - 40% = 48 —> $48.00

9.99 - 70% = 2.997 —> (round the 7 up because it's above 5) $3.00

52.00 - 30% = 36.4 —> $36.40

6 0
2 years ago
The grid you see below is in the shape of a rectangle. What is the area, in square units, of the shaded part?
kherson [118]

Answer:

8 units²

Step-by-step explanation:

The area (A) of the shaded part (right triangle ) is calculated as

A = \frac{1}{2} × area of rectangle

   = 0,5 × 4 × 4 = 0.5 × 16 = 8 units²

5 0
2 years ago
Read 2 more answers
A hypothesis will be used to test that a population mean equals 10 against the alternative that the population mean is more than
PilotLPTM [1.2K]

Answer:

A) 2.58

B) 1.96

C) 1.65

Step-by-step explanation:

A hypothesis used to test that

H_o : \mu  = 10

against the alternatives H1 : \mu not equal to 10

if null hypothesis is true, then distribution of test statics follow

Zo = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}

for two sided alternatives  hypothesis ( H1: \mu \neq 7), then P value is

P = 2[1- \phi(\left | Zc \right |)]                          (1)

a)significance level  \alpha = 0.01

from 1 eq we get

\pi (\left | Zc \right |) = P(Zo

Therefore  \left | Zc \right | = 2.58    FROM Z TABLE

B) significance level  \alpha = 0.05

from 1st equation we get

\pi (\left | Zc \right |) = P(Zo < \left | Zc \right |) = 1 - \frac{0.05}{2}  = 0.975

Therefore  \left | Zc \right | = 1.96    FROM Z TABLE

C) significance level  \alpha = 0.10

from 1 eq we get

\pi (\left | Zc \right |) = P(Zo

Therefore  \left | Zc \right | = 1.65    FROM Z TABLE

3 0
3 years ago
The quadrilateral shown is a parallelogram. If m∠ADC = 125° and m∠1 = 30°, what is m∠2? A) 15° B) 25° C) 35° D) 55°
Ganezh [65]

Answer:

B) 25°

Step-by-step explanation:

Assuming the quadrilateral is the one shown in the picture attached, then a triangle ADC is form, where m∠ADC = 125° and m∠1 = 30°. The addition of the three angles of a triangle is equal to 180°, so:

m∠ADC + m∠1 + m∠2 = 180°

Replacing with the known values and isolating m∠2 we get:

125° + 30° + m∠2 = 180°

m∠2 = 180° - 125° - 30°

m∠2 = 25°

3 0
3 years ago
5/7x1/9 is approximately
Alexxandr [17]

Answer:

5/63 is the answer I gotten.

Step-by-step explanation:

Hope you like :)

3 0
3 years ago
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