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3 years ago

Simplify: −z3+5k6−(−z3+10k6)

Mathematics

2 answers:

natta225 [31]3 years ago

7 0

Answer:

The answer to your question is -5k⁶

Step-by-step explanation:

Polynomial

- z³ + 5k⁶ - (-z³ + 10k⁶)

Use law of signs for the parenthesis

- z³ + 5k⁶ + z³ - 10k⁶

Use associative property for like terms

(-z³ + z³) + (5k⁶ - 10k⁶)

Simplify like terms

(0) + (-5k⁶)

Result

-5k⁶

Likurg_2 [28]3 years ago

4 0

Answer:

-5k ^6 is your answer! Hope this helps!

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Second choice:

$x=2t$

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Fifth choice:

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Step-by-step explanation:

Let's look at choice 1.

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$y=t^2+2t$

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.

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

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Let's look at choice 2.

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

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

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

Let's plug this into equation 2:

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

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

This is the desired result.

Choice 3:

$x=t-3$

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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:

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

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

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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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