3. determine k so that the given equation will have the stated property, and write the resulting equation:
(a) x
2 + 4kx + k + 2 = 0 has one root

The values of k are

Step-by-step explanation:

we know that

In a quadratic equation of the form

The discriminant D is equal to

If D=0 ----> The quadratic equation has only one real solution

If D>0 ----> The quadratic equation has two real solutions

If D<0 ----> The quadratic equation has no solutions (complex solutions)

in this problem we have

so

Find out the discriminant D

substitute the values

For D=0

Solve for k

Factor 16 left side

Complete the square

Rewrite as perfect squares

square root both sides

therefore

The values of k are

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.