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3 years ago

Solve the following inequality using the algebraic approach:

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

Answer:

b. x less-than StartFraction 10 Over 3 End fraction

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

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

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

3 0

3 years ago

Is the following shape a square? How do you know?

Basile [38]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Determine the solution to the system of equation below, algebraically. 5x+3y=28 x+y=8

VladimirAG [237]

Is this what you're asking for?

5 0

3 years ago

Is an imaginary "line" from the Earth to the Moon a line, a ray, or a segment? and WHY?

sesenic [268]

Answer:

Segment

Step-by-step explanation:

It is a segment because it has two endpoints (the Earth and Moon). If it was a ray, it would go on forever in one direction. It doesn't, so the imaginary line is a segment.

The first image is a segment, the second is a ray.

Hope this helps. :)

7 0

4 years ago

Solve the system of equations 13х – 6у = 22 x=y+6

Mrrafil [7]

Answer:

x = -2, y = -8

Step-by-step explanation:

13(y + 6) - 6y = 22

=> 13y + 78 - 6y = 22

=> 7y = -56

=> y = -8

x = -8 + 6

=> x = -2

4 0

3 years ago