If m□ebd=4x-8 and m□ebc=5x+20,find the value of x and m□ebc

The value of x is 18.67° and m∠ebc = 113.33°

Here is the correct question:

If m∠EBD= 4x - 8 and m∠EBC= 5x + 20, find the value of x and m∠EBC.

The diagram that completes the question is shown in the attachment below:

In the diagram, we can observe that dbc is a straight line.

Also ∠ebd and ∠ebc are the angles on the straight line

Since the sum of angles on a straight line is equal to 180°, then we can write that

∠ebd +  ∠ebc = 180°

From the question

m∠ebd = 4x - 8 and  m∠ebc = 5x + 20

∴ 4x - 8 + 5x + 20 = 180°

Solving the linear equation

Then,

Now, divide both sides by 9

∴

∴ x ≅ 18.67°

For the value of m∠ebc

Since, m∠ebc = 5x + 20

∴ m∠ebc =

m∠ebc

m∠ebc =

m∠ebc = 93.33 + 20

m∠ebc = 113.33°

Hence, the value of x is 18.67° and m∠ebc = 113.33°

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55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

step-by-step explanation: