In the diagram, point O is the center of the circle and AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E. If m∠AOB = 90° and

Short Answer: Current speed = 3 miles per hour. Given details for downstream distance of 4.48 miles at time 0.32 hours and upstream distance of the same 4.48 miles taking 0.56 hours. Using the equation d = r*t, we equate distances for both directions leading to a function in terms of the current speed. With each correction to solve ultimately yields the current speed as 3 mph.

The least number of times that two planes can cross is zero, since parallel planes do not intersect. A good example would be a floor and a ceiling, which run parallel, hence they do not meet. Conversely, if two planes occupy the same space, they can intersect at infinitely many points, as could happen with a line within that plane.

Explanation:

Step-by-step clarification:

Referring to step 6

(b² — 4ac) / 4a² = (x + b/2a)²

The mistake in the question is that it should be (x + b/2a)²

According to step 7

±√(b² —4ac) /2a = x + b/2a

The error in the question is that it should be divided by 2a, not 1a.

1. The transition from step 6 to step 7 involves taking the square roots of both sides

(b² — 4ac) / 4a² = (x + b/2a)²

Taking the square of both sides

√(b²—4ac) / √4a² = √(x + b/2a)²

√(b²—4ac) / 2a = x + b/2a

This forms step 7 correctly.

Next, subtracting b/2a from both sides

√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a

√(b²—4ac) / 2a — b/2a = x

(√(b²—4ac)  — b)/2a = x

x = [—b ± √(b²—4ac)] / 2a

This gives the desired formula.

The discriminant is D = b²—4ac.

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Answer:

(B) There is a single solution: x = 0.

Step-by-step explanation:

The equation that Kate is attempting to solve is:

Consequently, this equation results in one solution: x = 0.