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3 years ago

ine segment MN has endpoints M(-5,4) and N(1,-2). Find the equation for the perpendicular bisector of line segment MN.

Mathematics

1 answer:

Gre4nikov [31]3 years ago

4 0

Answer:

y=x-3

Step-by-step explanation:

slope=4+2/-5-1=-1

perpendicular slope= negative reciprical=1

y=x+b

midpoint on perpendicular bisector= (-5+1/2, 4-2/2)=(-2,1)

substitution-2=1+b, b=-3

y=x-3

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3 years ago

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What is the area of the sector with a central angle of 49° and a radius of 11 cm? Use 3.14 for pi and round your final answer to

olga_2 [115]

Answer:

$\boxed{\text{51.71 cm}^{2}}$

Step-by-step explanation:

If the angle θ is in radians, the formula for the area (A) of a sector of a circle is

A = ½r²θ

If θ is in degrees

$A = \dfrac{1}{2}r^{2}\theta \times \dfrac{\pi \text{ rad}}{180^{\circ}}= \pi r^{2}\times\dfrac{\theta }{360}$

Data:

θ = 49°

r = 11 cm

Calculation:

$\begin{array}{rcl}A& = &3.14\times 11^{2}\times\dfrac{49}{360}\\\\ & = &3.14 \times 121 \times 0.1361\\ & = & \mathbf{51.71}\\\end{array}\\\text{The area of the sector is }\boxed{\textbf{51.71 cm}^{2}}$

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2 years ago

Find the area of the following shape,

lord [1]

$\bold{ANSWER:}$
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1 year ago

Please help this is the last problem I need

tangare [24]

Answer:

$sin 54 = \frac{x}{14}$

Step-by-step explanation:

$sine = \frac{opposite}{hypotenuse}$

Side z is the adjacent, since it is next to the angle you are solving for.

Side x is the opposite, since it is opposite the angle you are solving for.

The side measuring 14 is the hypotenuse, since it is across from the right angle.

$sin 54 = \frac{x}{14}$

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2 years ago

Use the parabola tool to graph the quadratic function f(x)=(x-5)^2+1

andrey2020 [161]

Answer:

Look to the attached graph

Step-by-step explanation:

* Lets revise how to graph the quadratic function

- Find the vertex of it

- Find the y-intercept

- Find the x-intercept

∵ f(x) = (x - 5)² + 1 ⇒ the completing square form

- The completing square form for any quadratic is

( x - h)² + k, where h and k are the coordinate of the vertex point

* Lets compare the two forms

∵ (x - h)² + k = (x - 5)² + 1

∴ h = 5 and k = 1

∴ The vertex of the parabola is (5 , 1)

- To find the x-intercept put f(x) = 0

∵ (x - 5)² + 1 = 0 ⇒ subtract 1 from both sides

∴ (x - 5)² = -1 ⇒ the square can not give -ve number

∴ The parabola does not intersect the x-axis

- To find the y-intercept put x = 0

∵ f(0) = (0 - 5)² + 1 = 25 + 1 = 26

∴ The parabola intersects the y-axis at point (0 , 26)

- The parabola is opened upward because the coefficient of x² is +ve

* Now lets graph it

- Look to the attached graph

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3 years ago