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3 years ago

This circle is centered at the origin, and the length of its radius is 8. what is the equation of the circle?

2 answers:

8 0

Hello :
note :

an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =0 b = 0 r =8
the equation of the circle is : x²+y² = 64

klasskru [66]3 years ago

8 0

Answer: The required equation of the circle is $x^2+y^2=64.$

Step-by-step explanation: We are given to find the equation of a circle with center at the origin and radius of length 8 units.

We know that

the equation of a circle with center at the point (g, h) and radius of length r units is given by

$(x-g)^2+(y-h)^2=r^2.$

Here,

center, (g, h) = (0, 0) and radius, r = 8 units.

Therefore, the equation of the circle will be

$(x-0)^2+(y-0)^2=8^2\\\\\Rightarrow x^2+y^2=64.$

Thus, the required equation of the circle is $x^2+y^2=64.$

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Determine the measure of an interior angle of the named regular polygon. If a side of the polygon is extended, determine the sup

ladessa [460]

Answer:

A) Each interior angle of the Regular Hexagon = 120°

B)The measure of the supplementary angle of an interior angle is 60°

Step-by-step explanation:

Regular Hexagon : A 6 sided polygon which has all 6 interior angles as EQUAL is called a regular hexagon.

So, here are 6 interior angles of the hexagon are equal.

Also, Sum of all interior angles of an hexagon = 720°

Let us assume the each angle of the hexagon = m

⇒ m + m + m + m + m + m = 720°

or, 6 m = 720°

or, m = 720° / 6 = 120°

⇒ Each interior angle of the Regular Hexagon = 120°

Now, a side is extended to form an exterior angle.

Let us assume the measure of that exterior angle = k

⇒ k + m = 180 ° ( as k and m are SUPPLEMENTARY ANGLES)

or, k = 180 - 120 = 60 °

or, k = 60 °

Hence, the measure of the supplementary angle of an interior angle is 60°

6 0

3 years ago

K=6x+10, solve for k

kicyunya [14]

Answer:

x=(10-k)÷6

Step-by-step explanation:

6x=10-k

x=(10-k)÷6

4 0

2 years ago

-3x^2+6x+1=4 find the discriminant of each quadratic equation then state the number and type solutions

ipn [44]

Answer:

S={( 1 )}

Step-by-step explanation:

-3x²+6x+1=4

-3x²+6x+1-4=0

-3x²+6x-3=0

∆=b²-4.a.c

∆=(6)²-4.(-3).(-3)

∆=36-36

∆=0

x'=x"=-b/2a=-(+6)/2.(-3)=-6/-6=1

3 0

3 years ago

Read 2 more answers

The fuel efficiency in miles per gallon of all bmw 320i's is (approximately) normally distributed with a mean of 25 and a standa

grigory [225]

Given:
μ = 25 mpg, the population mean
σ = 2 mpg, the population standard deviation

If we select n samples for evaluation, we should calculate z-scores that are based on the standard error of the mean.
That is,
$z= \frac{x-\mu}{\sigma / \sqrt{n} }$

The random variable is x = 24 mpg.

Part (i): n = 1
σ/√n = 2
z = (24 -25)/2 = -0.5
From standard tables,
P(x < 24) = 0.3085

Part (ii): n = 4
σ/√n = 1
z = (24 -25)/1 = -1
P(x < 24) = 0.1587

Part (iii): n=16
σ/√n = 0.5
z = (24 - 25)/0.5 = -2
P(x < 24) = 0.0228

Explanation:
The larger the sample size, the smaller the standard deviation.
Therefore when n increases, we are getting a result which is closer to that of the true mean.

6 0

3 years ago

Write an equation In slope intercept form for the line that is parallel to the given line and that passes through the given poin

ludmilkaskok [199]

The equation of the parallel line in slope-intercept form is;

y = $\frac{5}{2}$ x - $\frac{25}{2}$

Step-by-step explanation:

Let us revise some facts about parallel lines

The equations of two parallel lines have:

Same slopes
Different y-intercept

The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept

The given line has equation 5x - 2y = 10

Put it in the form of y = m x + b to find its slope

∵ 5x - 2y = 10

- Subtract 5x from both sides

∴ -2y = 10 - 5x

- Divide to sides by -2

∴ y = -5 + $\frac{5}{2}$ x

∴ y = $\frac{5}{2}$ x - 5

- The value of m is the coefficient of x

∴ m = $\frac{5}{2}$

∴ The slope of the given line is $\frac{5}{2}$

∵ Parallel lines have same slopes

∴ The slope of the parallel line is m = $\frac{5}{2}$

- Substitute the value of m in the form of the equation

∴ The equation of the parallel line is y = $\frac{5}{2}$ x + b

To find b substitute x and y in the equation by the coordinates of any point lies on the line

∵ The parallel line passes through point (3 , -5)

- Substitute x and y by the coordinates of the point (3 , -5)

∵ x = 3 and y = -5

∴ -5 = $\frac{5}{2}$ (3) + b

∴ -5 = $\frac{15}{2}$ + b

- Subtract $\frac{15}{2}$ from both sides

∴ b = $\frac{-25}{2}$

∴ The equation of the parallel line is y = $\frac{5}{2}$ x + $\frac{-25}{2}$

∴ The equation of the parallel line is y = $\frac{5}{2}$ x - $\frac{25}{2}$

The equation of the parallel line in slope-intercept form is;

y = $\frac{5}{2}$ x - $\frac{25}{2}$

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/8628615

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5 0

3 years ago