1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mandarinka [93]
3 years ago
15

Help!! 50 points and brainliest!

Mathematics
2 answers:
algol [13]3 years ago
5 0

Answer:

Option 2; Option 5

Step-by-step explanation:

x² + 2x - 3 = 0

x = 2t

y = (2t)² +2(2t) - 3 = 4t² + 4t - 3

x = t+1

y = (t+1)² + 2(t+1) - 3

y = t² + 2t + 1 + 2t + 2 - 3 = t² + 4t

Viktor [21]3 years ago
3 0

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.

You might be interested in
You withdraw $29.79 from your bank account. Now your balance
Vika [28.1K]

Answer:

<h2>you had $9.28 prior to making the withdrawal</h2>

<h2>-$20.51= × - $29.79</h2><h2>× =$9.28</h2>

Step-by-step explanation:

<h2>i hope this help you</h2>
3 0
2 years ago
What is the answer to the math problem 18 minus 4x = negative 2?
pentagon [3]
The answer to this equation is 5.
3 0
3 years ago
18 POINTS MATH HELP PLEASE
lyudmila [28]

Answer:

yes it is safe

Step-by-step explanation:

so if you d base times hight you will get 27 witch is the degrees of witch the triangle it creates

7 0
2 years ago
What is the unit value of the 6 in 216?
eduard
The 6 is in the ones place the 1 is in the tens place and the 2 is in the hundreds place.
8 0
3 years ago
100 lbs divided by 2.2 equals what
Keith_Richards [23]
The answer is 45.4545454545
3 0
3 years ago
Read 2 more answers
Other questions:
  • Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most $75000 and use at least 320 wo
    15·1 answer
  • Freshman: 3 applications
    13·1 answer
  • Triangle ABC was translated 2 units to the right and 3 units down. Which rule describes the translation that was applied to tria
    15·1 answer
  • In a circle, I 90° sector has an area of 36 pi inches squared what is the radius of the circle
    13·2 answers
  • Explain how to multiply decimals by powers of 10. Use 8.653 x 10 3 as an example, to show how the multiplication is done.
    8·2 answers
  • John, Sally, and Natalie would all like to save some money. John decides that it
    8·1 answer
  • You have 143 toy farm animals.<br><br> Round that number to the nearest ten.
    8·1 answer
  • Kira looked though online census information to determine the average number of people living in the homes in her city
    5·1 answer
  • The sum of two numbers is 35. One number is 7 less than the other. Find the numbers.
    10·1 answer
  • THis is wierd math g g g g g
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!