Problem 3-66 Examine each diagram below. Which diagrams are possible? Which are impossible? Justify each conclusion
Hint:

All of them is impossible in mathematics

Step-by-step explanation:

In the first diagram we see a right triangle, which we can use pythagorean theorem to verify , but 20^2-14^2 does not equal to 5^2

IN the second diagram, According to the corresponding angles theorem, the statement “If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent” is true either way. But in the diagram we see 50 isn't equal to 48, hence it's a false statement too.

In the third diagram, we see we can verify it using the summation of triangle a+b+c=180, we clearly see 63+59+57 isn't equal to 180

So, indeed, all of the three diagram is impossible to exist in mathematics

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1