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3 years ago

Graph the solution of the inequality: 3/7 (35x-14) ≤ 21x/2 + 3

Mathematics

1 answer:

hammer [34]3 years ago

5 0

Hello there!

In order to graph the solution, we need to solve it first.

So let's start....

3/7(35x - 14) ≤ 21x/2 + 3

15x -6 ≤ 21x/2 + 3

15x - 21x/2 ≤ 3 + 6

9x/2 ≤ 9

x ≤ 9* 2/9

x ≤ 18/9

x ≤ 2

See the picture for the graph

Please let me know if you have questions about the answer.

Thanks!

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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!

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