$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{3}{5}x+10\to m_1=\dfrac{3}{5}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{3}{5}}=-\dfrac{5}{3}.\\\\\text{The equation of the searched line:}\ y=-\dfrac{5}{3}x+b.\\\\\text{The line passes through }(15,\ -5).$

$\text{Put thecoordinates of the point to the equation.}\ x=15,\ y=-5:\\\\-5=-\dfrac{5}{3}(15)+b\\\\-5=(-5)(5)+b\\\\-5=-25+b\qquad\text{add 25 to both sides}\\\\b=20\\\\\boxed{y=-\dfrac{5}{3}x+20}$

8 0

3 years ago

Which of the following is a polynomial with roots 2, 3i, and -3i?

solniwko [45]

Since the roots are 2,3i, and -3i, you can write it as

(x-2)(x-3i)(x+3i)=(x-2)(x^2+9)=x^3-2x^2+9x-18.

3 0

4 years ago

If you have 10 red, 10 blue, 10 orange and 10 black socks in a drawer, how many socks must you pull out of the drawer (assume it

Orlov [11]

Answer:

Step-by-step explanation:

The probability of u choosing two orange socks from the sock drawer WITHOUT REPLACEMENT:

= P(the first one is Orange) * P(the second one is Orange)

= 10/40 * 9/39 = 3/52.

6 0

3 years ago