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2 years ago

HELPPP PLEASE I NEED THIS BY FRIDAYYYYY!!!!

Mathematics

1 answer:

Igoryamba2 years ago

5 0

Answer:

<ABD = 44

<DBC = 44

<ABC = 88

Step-by-step explanation:

If an angle bisects another, then the two resulting angles are equal

In this case <ABC is bisected by BD

which means that

<ABD = <DBC

6x + 14 = 3x + 29

simplify and solve using inverse operations

6x + 14 = 3x + 29

-3x -14 -3x -14

3x = 15

/3 /3

x = 5

now substitute into the given values

< ABD = 6x + 14

= 5 * 6 + 14

= 30 + 14

= 44

<DBC = 3x + 29

= 5 * 3 + 29

= 15 + 29

= 44

< ABC = <ABD + <DBC

<ABC = 44 + 44

= 88

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sweet-ann [11.9K]

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Need help with homework

motikmotik

We have two points describing the diameter of a circumference, these are:

$\begin{gathered} A=(-12,-4) \\ B=(-4,-10) \end{gathered}$

Recall that the equation for the standard form of a circle is:

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

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.

For this we use the following equation:

$M=(\frac{x_1+x_2_{}_{}}{2},\frac{y_1+y_2}{2})$

Now, we replace and solve:

$\begin{gathered} M=(\frac{-12+(-4)}{2},\frac{-4+(-10)}{2} \\ M=(\frac{-12-4}{2},\frac{-4-10}{2}) \\ M=(\frac{-16}{2},\frac{-14}{2}) \\ M=(-8,-7) \end{gathered}$

The center of the circle is (-8,-7), so:

$\begin{gathered} h=-8 \\ k=-7 \end{gathered}$

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation: