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3 years ago

Create an inequality with the solution set-3

1 answer:

6 0

Answer: Using the digits 0 to 9 at most one time each, fill in the boxes to create an inequality whose solution set is x < -1/2.

Step-by-step explanation:

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blondinia [14]

The trick is to exploit the difference of squares formula,

$a^2-b^2=(a-b)(a+b)$

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

$(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2$

Whatever you do to the denominator, you have to do to the numerator too. So

$\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2$

Expand the numerator:

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}$

So we have

$\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2$

But √12 = √(3•4) = 2√3, so

$\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}$

7 0

2 years ago

Help please!!!!!!!!!!!!

Sedbober [7]

Step-by-step explanation:

$\frac{8}{6} = \frac{x}{3} \\ x = \frac{3 \times 8}{6} = 4$

7 0

2 years ago

Plz help.will give brainliest

Oksi-84 [34.3K]

Answer:

x+2 x+2 x+2

Step-by-step explanation:

8 0

3 years ago

On the first day, you deposit $.01 in the bank. The second day you deposit $.02. The third day,

sergiy2304 [10]

$1.2

Step-by-step explanation:

5 0

3 years ago

A woman received 5 per cent interest on a loan of $300 for 1 year. How much interest did she receive? $5 $15 $30 $150 none of th

choli [55]

Answer:

15$

Step-by-step explanation:

this is because if you use our formula of I= prt

we can substitute our varibles for our equation

I= 300 x 0.05 x 1

we turn 5 in 0.05 to represent out rate, due to this our rate would have to be Simplified into a percent then a decimal

after this if we now proceed through our equation we will get

I = 300 x 0.05 x 1

I = 15

6 0

2 years ago