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prisoha [69]
3 years ago
12

What is the solution of the linear equation? 4b+6=2-b+4

Mathematics
1 answer:
masya89 [10]3 years ago
4 0
4b+b=2+4-6
5b=0
b=0/5
b=0
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Identify the simplest form of each ratio.
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7 0
3 years ago
9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.
kherson [118]

Answer:

a) (7,8)

b) r = 10

c) (x-7)^2+(y-8)^2=100

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as (x_m,y_m)

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

(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)

(x_m, y_m) = (7,8)

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

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

in our case the equation changes to: (selecting the centre and point B)

r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}

r = \sqrt{(7-17)^2+(8-8)^2}

r = 10

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all <u>since in this particular case</u> all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the

  1. coordinates of the center: (x_m,y_m) = (7,8)
  2. radius of the circle: r = 10

we can put this in the formula of the circle:

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

in our case the equation changes to:

(x-x_m)^2+(y-y_m)^2=r^2

(x-7)^2+(y-8)^2=(10)^2

(x-7)^2+(y-8)^2=100

this is the equation of the circle!

6 0
3 years ago
A 1-mile hiking path has signs placed every 240 feet.there are signs placed at the beginning and end of the mile.how many signs
Fed [463]

Answer: 23


Step-by-step explanation:

1 mile = 5280 feet

So,

There are 5280/240 = 22  240 ft. in 1 mile


So, there will be 22 signs in that 1 mile road. Notice that when we divide 5280 by 240 we get an integer. So, we can say that the sign placed at the end of the mile is included in that 22. Now, all we need to do is add one sign that is at the start of the mile. Therefore, the toal signs is 23


5 0
3 years ago
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