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3 years ago

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Angle X is the larges angle in the triangle XYZ. Angle Y is the smallest angle. How does the sum of the measures of angles Y and

Z compare to the measure of angle X? Explain.

1 answer:

loris [4]3 years ago

3 0

Dear Dollster444, the sum of angles Y and Z is bigger than Y.

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Answer:

Second choice:

$x=2t$

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

Fifth choice:

$x=t+1$

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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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The answer choice isn't even up there. The answer is 15. Since Because hit 22 home runs; you would just subtract to find the number of Beverly's home runs since it says "7 more home runs than Beverly".

22 - 7= 15.

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The equation of nth term will be written as for n as will be ( $\rm a_n$ - a₁ + d) / d. Then the correct option is D.

The missing options are attached to the picture given below.

<h3>What is a sequence?</h3>

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The formula for the nth term of an arithmetic sequence can be found using the formula given below.

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Then arrange the equation for n, we have

$\begin{aligned} \rm a_n - a_1 & \rm = nd - d\\\\\rm a_n - a_1 + d & \rm =nd\\\\\rm n & \rm = \dfrac{a_n - a_1 + d}{d} \end{aligned}$

Then the correct option is D.

More about the sequence link is given below.

brainly.com/question/21961097

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1 year ago