My homework is hard<br>

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.

3 0

4 years ago

Read 2 more answers

Holly has $125 she spends $35 on gas for her car which model represents how much money holly has left idk if the answer is right

inn [45]

Answer:

The second one would be the answer.

Step-by-step explanation:

If you look at the model, it shows it on 125 going down to 90.

If she has $125 and she spends $35 on gas, you would subtract that from how much money she has.

125 - 35 = 90.

Feel free to let me know if you need more help. :)

5 0

3 years ago

Emmett bought 10 packages of cat food and 3 packages of dog food. Each package of cat food contained 10 cans, and each package o

xz_007 [3.2K]

Answer: Emmet bought 94 more cans of cat food than dog food.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the initial value of y= 8x+7

allochka39001 [22]

Answer:

7

Step-by-step explanation:

The initial value is another name for the y-intercept. This equation is written in point slope form (y=mx+b). And before you think y-intercept means y, right? No that is incorrect, I got that wrong in the beginning too ;)

y=mx+b

y=8x+7

b in the point slope form equation is always the initial value or y-intercept or whatever people call it. So what substitutes b out here? 7. So 7 is the initial value!

:) Hope you understand now! Have a good day!

8 0

3 years ago

A bag contains 12 beads 2 blue 1 green 3 purple the rest red

Anestetic [448]

Answer : 6 red beads

explanation: 2+1+3 = 6

12-6 = 6

hope this helps :)

3 0

3 years ago

My homework is hard​

My homework is hard