4. What do you call a set that contains no element?

-8<2x-4<4 solve the inequality

il63 [147K]

Answer:

Step-by-step explanation:

The inequality will be split into two

It is know that, if a<b<c

Then a<b and b<c

-8<2x-4<4

Apply that to this

Then,

-8<2x-4. Equation 1

Also,

2x-4<4 equation 2

Solving equation 1

-8<2x-4

Add 4 to both side of the equation

-8+4<2x-4+4

-4<2x

Divide both sides by 2

-4/2<2x/2

-2<x

Note, if a is less than b, then, b is greater than a, e.g. 4 is less than 10, this implies 10 is greater than 4

Therefore,

-2<x

Then, x greater than -2

Equation 2

2x-4<4

Add 4 to both side of the inequalities

2x-4+4<4+4

2x<8

Divide both side by 2

Then,

2x/2<8/2

x<4

Therefore x is between -2 and +4.

Check attachment for graphical solution

7 0

3 years ago

*Asymptotes*<br> g(x) =2x+1/x-3 <br><br> Give the domain and x and y intercepts

Nataly [62]

Answer: Assuming the function is $g(x)=\frac{2x+1}{x-3}$ :

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The horizontal asymptote is $y=2$ .

The vertical asymptote is $x=3$ .

Step-by-step explanation:

I'm going to assume the function is: $g(x)=\frac{2x+1}{x-3}$ and not $g(x)=2x+\frac{1}{x}-3$ .

So we are looking at $g(x)=\frac{2x+1}{x-3}$ .

The x-intercept is when y is 0 (when g(x) is 0).

Replace g(x) with 0.

$0=\frac{2x+1}{x-3}$

A fraction is only 0 when it's numerator is 0. You are really just solving:

$0=2x+1$

Subtract 1 on both sides:

$-1=2x$

Divide both sides by 2:

$\frac{-1}{2}=x$

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is when x is 0.

Replace x with 0.

$g(0)=\frac{2(0)+1}{0-3}$

$y=\frac{2(0)+1}{0-3}$

$y=\frac{0+1}{-3}$

$y=\frac{1}{-3}$

$y=-\frac{1}{3}$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The vertical asymptote is when the denominator is 0 without making the top 0 also.

So the deliminator is 0 when x-3=0.

Solve x-3=0.

Add 3 on both sides:

x=3

Plugging 3 into the top gives 2(3)+1=6+1=7.

So we have a vertical asymptote at x=3.

Now let's look at the horizontal asymptote.

I could tell you if the degrees match that the horizontal asymptote is just the leading coefficient of the top over the leading coefficient of the bottom which means are horizontal asymptote is $y=\frac{2}{1}$ . After simplifying you could just say the horizontal asymptote is $y=2$ .

Or!

I could do some division to make it more clear. The way I'm going to do this certain division is rewriting the top in terms of (x-3).

$y=\frac{2x+1}{x-3}=\frac{2(x-3)+7}{x-3}=\frac{2(x-3)}{x-3}+\frac{7}{x-3}$

$y=2+\frac{7}{x-3}$

So you can think it like this what value will y never be here.

7/(x-3) will never be 0 because 7 will never be 0.

So y will never be 2+0=2.

The horizontal asymptote is y=2.

(Disclaimer: There are some functions that will cross over their horizontal asymptote early on.)

6 0

3 years ago

A store buys purses for $24.50 and then marks them up 25%. The store then discounts any purses that do not sell in the first mon

Sergeu [11.5K]

Answer:$27,57

1)find out how much wallets cost in the first month:

24,50 -100%

х - 125%

х= 24,50*125/100 ≈ 30,63

2)we will find out how much the wallets cost after the price is reduced by 10%:

30,63 - 100%

х -90%

х=30,63*90/100 ≈ 27,57

Step-by-step explanation:

3 0

3 years ago

Violet used 4 scoops of sugar to make 26cups of lemonade.How many scoops of sugar would violate need to use if she made 234 cups

alisha [4.7K]

Answer:

Violet used 4 scoops of sugar and mixed it with 26 cups of lemonade and if it makes 234 cups of lemonade then there is 208. 26 scoops of sugar would violate the cups of lemonade.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Could someone please answer these two

exis [7]

Answer:

SEE BELOW

Step-by-step explanation:

1. find value of m

a^2 + b^2 = c^2

7.5^2+10^2=c^2

15+100=c^2

115=c^2

square it

=10.7 (not answer)

a^2+b^2=c^2

10.7^2+30^2=c^2

114.49+900=c^2

1014.49=c^2

square it

m=31.9

2.20^2 + 21^2 = 841

29^2=841

yes the triangle is right angled !!!

hope this helps :)

6 0

3 years ago