Heeellllppp!!!! Please

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

Anita took 1/6 of a cake and Barry took 60% of what remained. What fraction of original cake is left. Explain full method.

Sedaia [141]

The cake = 1
1-1/6=5/6
60% as a fraction =3/5
5/6-3/5
25/30-18/30
7/30
There are 7/30 of the original cake left.

Hope this helps :)

8 0

3 years ago

Read 2 more answers

A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s.

Alex777 [14]

Answer:

$Sequence = 120$

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

$Sequence = \frac{6!}{3!}$

$Sequence = \frac{6 * 5 * 4* 3!}{3!}$

$Sequence = 6 * 5 * 4$

$Sequence = 120$

Hence, there are 120 possible sequence.

7 0

3 years ago

Thirty three different video games showing violence were observed. The duration times of violence (in seconds) were recorded. W

AlladinOne [14]

Answer:

The "df" stands for "degrees of freedom", and represents the number of independent observations in a set of data.

Its value in this case is df=32.

Step-by-step explanation:

The sample is of size n=33.

As we do not know the population's standard deviation, we use as estimate the sample's standard deviation. Because of this, we use the t-statistic in place of the z-value.

The "df" stands for "degrees of freedom", and represents the number of independent observations in a set of data (the data in this case is the sample of 33 video games).

In one-sample tests, the degrees of freedom are calculated as:

$df=N-1=33-1=32$

6 0

4 years ago

Hi guys can you help me evaluating expressions <br><br> Please

EastWind [94]

26.) 3(2)² - 8(-3)²

= 3*4 - 8 + 9

= 12 - 8 + 9 = 13

27.) I 7 - 4(2) I

7 - 8 = -1, but since this is absolute value, which is a number's distance from zero, your answer for 27 would be a positive one.

28.) (-2)² + 2(-3 * 1)

= 4 + 2(-3)

= 4 + (-6) = 4 - 6 = -2

29.) 7(-4)² + 5 / 4(1) - (-5)

=7 * 16 + 5 / 4 + 5

= 112 + 5 / 9 = 117/9 = 13

30.) Product: the result of a multiplication problem

Increased by: multiplied by

3(n * 7)

31.) 2n - 1

5 0

3 years ago