2 years ago

The factors for x2 + 5x + 6 are x + 2 and x + 3.

Mathematics

1 answer:

Nookie1986 [14]2 years ago

5 0

It is true that (x+2)(x+3) = x2 +5x + 6

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A sector has angle 2.5 radians and perimeter of 18cm. find the radius of the sector

babunello [35]

Answer:

4 cm

Step-by-step explanation:

Perimeter = 18cm

θ = 2.5 radian

s = rθ, s = Arc length

Perimeter of Sector, P = arc length, s + 2r

Perimeter = rθ + 2r

r = Radius

18cm = r(2.5) + 2r

18cm = 2.5r + 2r

18cm = 4.5r

r = 18 /4.5

r = 4

8 0

2 years ago

What is the equation of the line that is perpendicular to y= -3x + 1 and passes through (2,3)?

Aleonysh [2.5K]

Answer:

$\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}$

Step-by-step explanation:

$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).$

$\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}$