Here's the picture, if anyone still needs it.
Answer:
see below
Step-by-step explanation:
Angle ACE = DCE since they are vertical angles
Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles
Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles
When all three angles are equal, the triangles are similar.
We can use ratios to find DE
DE CE
------- = ----------
AB AC
DE 8
------- = ----------
12 10
Using cross products
10 DE = 8*12
10 DE = 96
Divide by 10
DE = 9.6
Answer: 1/4 or 0.25
Step-by-step explanation: We will solve log256 4 in several steps to solve for x.
Step 1: Log256 4 = x
Step 2: 256x = 4 ( Next, Use exponents )
Step 3: (2^8)x = 2^2
Step 4: 2^8x = 2^2
Step 5: 8x = 2 (Solve for x0
Step 6: 8x/8 = 2/8 = x = 1/4
Step 7 (The Answer) x, or log256 4 = 1/4 or 0.25
The given equation is ⇒⇒⇒ 2y - 4x = 6
∴ 2y = 4x + 6 ⇒ divide all the equation over 2
∴ y = 2x + 3 and it can be written as ⇒⇒⇒ y - 2x = 3
The last equation represents a straight line with a slope = 2 and y-intercept = 3
To construct a system of equations with definitely many solutions and the equation ( 2y-4x=6 ) is one of the equations, the other equation must have the same slope and the same y-intercept.
so, the general solution of the other equation is ⇒ a ( y - 2x ) = 3a
Where a is constant and belongs to R ( All real numbers )
The system of equations which has definitely many solutions is consisting of <u>Coincident lines.</u>
