How many and what type of solutions does the equation have?

2c2=16c−32

two rational solutions

two irrational solutions

one rational solution

two nonreal solutions

One rational solution.

Just took the test.

The answer is (C).

Step-by-step explanation: The given quadratic equation is

We know that the type of the solution of a quadratic equation depends upon the discriminant.

Here, the discriminant is given by

Since the discriminant is zero, so the two roots are real and equal.

Thus, we can say that the equation has one rational solution.

Hence, (C) is the correct option.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.