Graph-2x+y=8 I need to know the answer

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

A large sphere has the radius of 6 centimeters. A small sphere is inside the sphere. After the volume of the small sphere is sub

neonofarm [45]

Answer:

3 in

Step-by-step explanation:

The volume of the large sphere is ...

V = (4/3)πr³ = 288π . . . cubic inches

The volume of the smaller sphere is ...

288π -252π = 36π . . . cubic inches

The ratio of volumes of the smaller sphere to the larger is the cube of the ratio of radii. The radius of the smaller sphere will be ...

(6 in)∛(36π/(288π)) = (6 in)∛(1/8) = 3 in . . . . small sphere radius

7 0

3 years ago

I need help with this please.

Alex

Hope this helps and hope u can see it

3 0

3 years ago

A

UkoKoshka [18]

The dilation of the rectangle stretches it with regards to the distances from the central point

The option that gives the coordinates of the point D is the option;

D (0, 5)

Reason:

The known parameter;

Coordinates of the center of dilation is M(-3, -4)

Scale factor of dilation = 3

The coordinates of the vertex of the rectangle ABCD are;

A(-2, 2), B(3, 2), C(3, -1), and D(-2, -1)

Length MD = $\sqrt{(-3 - (-2))^2 + (-4 - (-1))^2} = \sqrt{10}$

Therefore, length of MD' = 3·√10

Slope of MD, is given as follows;

$Slope, \ m = \dfrac{-1 - (-4)}{-2 - (-3)} = \dfrac{3}{1} = 3$

Therefore, y = 3·x

x² + y² = (3·√10)²

x² + (3·x)² = (3·√10)²

10·x² = 90

x = 3

y = 9

We note that the value of x, and y, are calculated as distance from the central point, M, therefore;

The coordinates of the point D' is (-3 + x, -4 + y)

∴ Coordinates of D' = (-3 + 3, -4 + 9) = (0, 5)

Coordinates of D' = (0, 5)

Learn more about dilation of a figure from a point here:

brainly.com/question/13625798

4 0

3 years ago

Andy,Taylor and Ben share their team payment in a ratio of 1:3:4. What % dies Andy receive

matrenka [14]

Andy receives 1 share out of 8 total.

$\frac{1}{8} *100=12.5 \text{ percent}$

7 0

4 years ago

Read 2 more answers