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Mathematics

2 answers:

shusha [124]2 years ago

7 0

Answer: x = 8

MN = 52

LK is congruent to LM

LN is congruent to NL

ΔKLN and ΔMLN have:

LN ≅ LN

∠K = ∠M = 90°

∠KLN = ∠MLN

=> ΔKLN ≅ ΔMLN

=> KN = MN

=> 7x -4 = 5x + 12

⇔ 2x = 16

⇔ x = 8

=> KN = MN = 7.8 - 4 = 52

Step-by-step explanation:

Ksju [112]2 years ago

5 0

Answer:

x=8

KN=24

LK is congruent to LM

LN is congruent to NL

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A sector with an area of 26pie cm^2 has a radius of 6 cm. What is the central angle measure of the sector in radians?

Zolol [24]

Answer:

The central angle measure of the sector in radians is $\theta=\frac{13}{9}$ .

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.

The area of a sector when the central angle is in radians is given by

$A=(\frac{\theta}{2})\cdot r^2$

where

r = radius

θ = central angle in radians

We know that the area of the sector is $26 \:cm^2$ and the radius is 6 cm. Applying the above formula and solving for the central angle ( $\theta$ ) we get that

$26=(\frac{\theta}{2})\cdot (6)^2\\\\\left(\frac{\theta}{2}\right)\left(6\right)^2=26\\\\\frac{\frac{\theta}{2}\cdot \:6^2}{36}=\frac{26}{36}\\\\\frac{\theta}{2}=\frac{13}{18}\\\\\theta=\frac{13}{9}$