Line segment BD is a diameter of circle E.

Circle E is inscribed with triangle B C D. LIne segment B D is a diameter. Line segments D C and C B are secants. Angle D B C is 51 degrees.
What is the measure of arc B C?

39°
78°
102°
129°

78 degrees

Step-by-step explanation:

Mainly because the measure of the arcs intercepted by the interior angles equals 2 times those interior angles.

so arc DC =  2 * angle DBC = 2 * 51 degrees = 102 degrees.

We also see that because BD is a diameter the angle  BCD that intercepts it is 90 degrees because   half-circle arc BD = 2 * angle BCD

180 degrees = 2 * angle BCD

also we want arc BC.

we know that the total circle is the sum of all 3 arcs.

arc BC + (half-circle) arc BD + arc DC = 360 degrees

arc BC + 180  + 102 = 360 degrees.

arc BC =  360 - 180 - 102 = 78 degrees

did you get the answer yet?

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places