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leva [86]
3 years ago
8

I need help with #11

Mathematics
1 answer:
strojnjashka [21]3 years ago
4 0
You can plug in the numbers
1) (0,3):
3 < 2(0) + 2
3 < 2 this is incorrect, so it is not 1

2) (2,0)
0 < 2(2) + 2
0 < 6 this passed the first one

0 > -(2) - 1
0 > -3 this is also correct

the answer is 2) (2,0)
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30 POINTS AVAILABLE
kherson [118]

Answer:

\large\boxed{(x-2)^2+(y-1)^2=34}

Step-by-step explanation:

The equation of a circle in standard form:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)

Substitute:

h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

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

Substitute the coordinates of the points (2, 1) and (5, -4):

r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}

Finally we have:

(x-2)^2+(y-1)^2=(\sqrt{34})^2

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In the right triangle shown in the diagram below,
adelina 88 [10]

QUESTION :-

what is the value of x to the nearest whole number?

ANSWER :-

\cos( \theta)  =   \frac{base}{hypotenuse}  \\  \cos(30)  =  \frac{x}{24}  \\  \frac{ \sqrt{3} }{ \cancel2}  =  \frac{x}{ \cancel{24}}  =  \frac{x}{12}  \\ 1.732 =  \frac{x}{12}  \\ 12 \times 1.732 = x \\ x = 20.7

SO

the nearest whole number-->

20.7 --> approximately --> 21 units

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