Given: △abc, m∠b=90° ab=12, bc=16, bk ⊥ ac . find: ac and bk.

Since m∠B = 90°, then ΔABC is a right triangle, so Pythagorean Theorem can be used to solve for AC.

AB² + BC² = AC²

12² + 16² = AC²

144 + 256 = AC²

400 = AC²

20 = AC

The placement of point K is not given.  Is it on AC, inside the triangle, or outside the triangle?  In order to find the length, you need to know where it is placed.

AC = 20, BK = 35/3 ≈ 11.67

is only a line? i think so

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct