M ABD = 10x - 7 and m2DBC = 3x + 5. What is the numerical value of m_ABD?
D
1
B

 71/7

Step-by-step explanation:

No picture is provided so I am assuming that BD is an angle bisector.

1. ∠ABD=10x-7, ∠DBC=3x+5           Given

2. ∠ABD = ∠DBC                             Definition of angle bisector

3. 10x-7 = 3x+5                                Substitution

4. 7x - 7 = 5                                      Subtraction Property of Equality

5. 7x = 12                                          Addition Property of Equality

6. x = 12/7                                         Division Property of Equality

7. ∠ABD = 10(12/7) - 7                      Substitution

8. ∠ABD = 71/7                                 Adding like terms

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

nswer: a   y-axis

step-by-step explanation: