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2 years ago

Explain why the 25 is rational and the square root of 26 is irrational

Mathematics

1 answer:

torisob [31]2 years ago

6 0

Step-by-step explanation:

rational expression can be written as a ratio and all neutral numbers xan be written as a ratio

root of 26 is irrational because it can't be written as a ratio since its not a whole number.

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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

3 0

3 years ago

Read 2 more answers

11. The regression equation y=2x + 8 represents how many minutes a sound will last after applying x pounds of pressure to the sy

Sidana [21]

Then y=2(4)+8
=8+8
=16

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3 years ago

The radius r of a circle is increasing at a rate of 7 centimeters per minute. (a) find the rate of change of the area when r = 1

VikaD [51]

Dr /dt = 7

A = pi r^2

dA / dr = 2pir

dA/dt = dA/dr * dr/dt = 2pir * 7 = 14pir

when r = 12 rate of change of the area = 14*pi*12 = 168pi

= 527.79 cm^2 / minute to nearest hundredth

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2 years ago

Alexi’s restaurant bill is $58, and he wants to leave a 20 percent tip. Which expression represents the total amount that Alexi

IRISSAK [1]

Answer:

58 dollars (0.20) + 58 dollars

Step-by-step explanation:

58 dollars (0.20) + 58 dollars

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2 years ago

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-x+7-6x=19-7x<br>Determine whether this has one solution, no solution, or infinitely many solutions

rewona [7]

Reduces to ,7=19. no solutions

6 0

3 years ago