HELPPPP Solve the inequality. 9 - 12 13 O q>1 O 9-1 o 925 09>

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

3 years ago

Read 2 more answers

Simplify the following expressions. All answers should be in standard form.

Ratling [72]

Answer:

The given expression in simplified form is: $15x^2+10x$

Step-by-step explanation:

Simplifying the expression involve reducing the number of terms to minimum and making the expressions in standard form.

This may involve addition, subtraction and multiplication of variables.

Given expression is:

$5x(3x+2)$

Distributing 5x will give us:

$= 5.3.x.x + 5.2.x\\=15x^2+10x$

Hence,

The given expression in simplified form is: $15x^2+10x$

6 0

3 years ago

Bethany has a garden box that is 4. feet long, 8 feet wide, and foot deep . How many cubic feet of dirt does she need to fill th

Firdavs [7]

You need to work out the area so

Area of a rectangle is l x b

So

A= l x b
A= 8 x 4
A= 32

Therefor 32 cubic feet of dirt is needed

6 0

2 years ago

PLEASE HELP!!!!!!!!!!!!

liq [111]

9514 1404 393

Answer:

a Plane FGI

Step-by-step explanation:

A plane is named either by its designator (Q) or by three non-collinear points in the plane. Here, the point I must be used, as the other designated points in the plane are all on the same line. The appropriate choice is ...

Plane FGI

4 0

2 years ago

A family has a combined monthly income of $2580. Their food budget is $310/month. What percentage of their monthly income is bud

stellarik [79]

So you have 318/2580 (since the top is the amount of money they use for food and the bottom is the total). You will want to divide it into 2 so 318/2 and 2580/2. Then you will get 159/1290. The divide 159/1290 with 3. So you will get 52/430. It may seem that you will need to divide 430 with 52 now. Once you get that, you will get the decimal 0.123255814. (I used a calculator). Then Move the decimal twice to the right to make that whole percentage. You will get 12 as you whole number (Ignoring the fact you have 3255814 as your remaining.). So the answer for that is….

12%!!

6 0

3 years ago

HELPPPP Solve the inequality. 9 - 12 13 O q>1 O 9-1 o 925 09> - 25