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3 years ago

In triangle JKL, angle K is a right angle. Write the sine of angle J as a ratio of side lengths

Mathematics

1 answer:

Evgen [1.6K]3 years ago

5 0

Answer:

$Sin J =\frac{|KL|}{|JL|}$

Step-by-step explanation:

In Right Triangle JKL, with Right angle at K

$sin \theta =\frac{Opposite}{Hypotenuse} \\$

Opposite =|KL|

Hypotenuse=|JL|

Therefore, sin J as a ratio of side lengths is:

$Sin J =\frac{|KL|}{|JL|}$

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Help!! 50 points and brainliest!

Viktor [21]

Answer:

Second choice:

$x=2t$

$y=4t^2+4t-3$

Fifth choice:

$x=t+1$

$y=t^2+4t$

Step-by-step explanation:

Let's look at choice 1.

$x=t+1$

$y=t^2+2t$

I'm going to subtract 1 on both sides for the first equation giving me $x-1=t$ . I will replace the $t$ in the second equation with this substitution from equation 1.

$y=(x-1)^2+2(x-1)$

Expand using the distributive property and the identity $(u+v)^2=u^2+2uv+v^2$ :

$y=(x^2-2x+1)+(2x-2)$

$y=x^2+(-2x+2x)+(1-2)$

$y=x^2+0+-1$

$y=x^2$

So this not the desired result.

Let's look at choice 2.

$x=2t$

$y=4t^2+4t-3$

Solve the first equation for $t$ by dividing both sides by 2:

$t=\frac{x}{2}$ .

Let's plug this into equation 2:

$y=4(\frac{x}{2})^2+4(\frac{x}{2})-3$

$y=4(\frac{x^2}{4})+2x-3$

$y=x^2+2x-3$

This is the desired result.

Choice 3:

$x=t-3$

$y=t^2+2t$

Solve the first equation for $t$ by adding 3 on both sides:

$x+3=t$ .

Plug into second equation:

$y=(x+3)^2+2(x+3)$

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

$y=(x^2+6x+9)+(2x+6)$

$y=(x^2)+(6x+2x)+(9+6)$

$y=x^2+8x+15$

Not the desired result.

Choice 4:

$x=t^2$

$y=2t-3$

I'm going to solve the bottom equation for $t$ since I don't want to deal with square roots.

Add 3 on both sides:

$y+3=2t$

Divide both sides by 2:

$\frac{y+3}{2}=t$

Plug into equation 1:

$x=(\frac{y+3}{2})^2$

This is not the desired result because the $y$ variable will be squared now instead of the $x$ variable.

Choice 5:

$x=t+1$

$y=t^2+4t$

Solve the first equation for $t$ by subtracting 1 on both sides:

$x-1=t$ .

Plug into equation 2:

$y=(x-1)^2+4(x-1)$

Distribute and use the binomial square identity used earlier:

$y=(x^2-2x+1)+(4x-4)$

$y=(x^2)+(-2x+4x)+(1-4)$

$y=x^2+2x+-3$

$y=x^2+2x-3$ .

This is the desired result.

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4 years ago

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What role does gravity and inertia play in our Solar System?

Varvara68 [4.7K]

It keeps the planets in orbit.

Inertia is what keeps an object moving (in the same direction). Gravity is the pull of an object to another.

The planets have reached the perfect medium to where inertia keeps the planets moving (instead of remaining completely still in space), and gravity pulls them toward the sun so that they move around it instead of moving straight past it or straight into it.

This is also true about the Earth and the moon.

This is also true with satellites in orbit.

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3 years ago

What is the measure of ZB, in degrees?

shusha [124]

Angle B is 32 degrees

This triangle is an isosceles triangle so two sides are equal, angle A and angle C are equal so 74+74=148 and then a triangle equals 180 degrees so you subtract the angles of A and C to find B. 180-148=32

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3 years ago

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snow_tiger [21]

Answer:

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Step-by-step explanation:

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