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3 years ago

Explain why multiplying two irrational numbers could result in either an irrational number or a rational number.

1 answer:

7 0

Because if you multiply 2 different irrational numbers (like the following)
$\sqrt{3} \times \sqrt{17}$
You will get an irrational answer.

BUT
if you multiply the same square root (which are both irrational, you get a rational number)

$\sqrt{3} \times \sqrt{3} = 3$

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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

Pls help I really need to pass this if like for 4th quarter where I m pls help me

Tom [10]

Answer:

✨Both will be the same✨

✨Step-by-step explanation:✨

there is 1 in each section 61 and 38

HOPE THAT HELPS

3 0

2 years ago

How to find the area of a polygon

ipn [44]

The rectangle is 7 x 4 so the area is 28 sq cm
The triangle has a base of 4 and a height of 3.
The formula is A = 1/2 * b*h
You have 2 triangles so:
2(1/2)*4*3= 12 sq cm
Add together:
28 + 12= 40 sq cm

6 0

3 years ago

Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of

Aleks [24]

Cone Volume = (π • r² • h) ÷ 3

Cone Volume = (3.14 * 1.5^2 * 4.5) / 3

Cone Volume = 10.5975 
answer is B

5 0

2 years ago

Read 2 more answers

2 divided by one third

Jobisdone [24]

2 / 1/3
= 2* 3/1
= 2*3
= 6

4 0

2 years ago

Read 2 more answers