Which veal represents the functions ?

6- 3/4x + 1/3 = 1/2 x + 5

Wittaler [7]

Answer: Solve for

x

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

x

=

16

15

x

=

16

15

Decimal Form:

x

=

1.0

¯

6

x

=

Mixed Number Form:

x

=

1

15

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

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

coordinates of the center: $(x_m,y_m) = (7,8)$
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

I’d ABCD is dilated by a scale factor of 2 about point E, which of the following is true about line segment E’F’

PilotLPTM [1.2K]

Answer:

Line Segment EF passes through the center of the dilatation

Step-by-step explanation:

I just know...

3 0

3 years ago

Consider the function f(x)=x^2+bx-49 where b is a constant. if the function has an axis of symmetry at x = 8, what is the value

Jlenok [28]

For this case we have the following equation:
f (x) = x ^ 2 + bx-49
Deriving we have:
f '(x) = 2x + b
We match zero:
0 = 2x + b
We clear x:
x = -b / 2
The axis of symmetry is at x = 8, therefore:
x = -b / 2 = 8
Clearing b:
b = -2 * (8)
b = -16
Answer:
the value of b is:
b = -16

3 0

3 years ago

The ordered pair (0,4) is a soultion of which system

Anettt [7]

<span>This question is asking you to substitute 0 for X and 5 for y in both equations. If the right hand value is equal to the left hand value after making the substitution, the answer is "yes". Otherwise, the answer is "no".
Substitute 0 for x and 5 for y in the first equation and then the second equation. Since 0 + 5 = 5 and -5*0 + 2*5 = 10 the answer </span>

5 0

3 years ago