how to write a fraction in interval notation

Answer:

x > 4; r–1(x) = 4 + StartRoot StartFraction 11 Over x EndFraction EndRoot

Step-by-step explanation:

We are given that

[tex]r(x)=\frac{11}{(x-4)^2}[/tex]

We have to find the domain of restriction on r(x) and corresponding inverse function.

Let

[tex]y=r(x)=\frac{11}{(x-4)^2}[/tex]

[tex](x-4)^2=\frac{11}{y}[/tex]

[tex]x-4=\sqrt{\frac{11}{y}}[/tex]

[tex]x=\sqrt{\frac{11}{y}}+4[/tex]

[tex]r^{-1}(y)=\sqrt{\frac{11}{y}}+4[/tex]

Now, replace x by y and y by x then, we get

[tex]r^{-1}(x)=\sqrt{\frac{11}{x}}+4[/tex]

The function is not defined at x=4

But,

The inverse function defines for all positive real values.

Therefore, domain of r(x)=x>4 and inverse function

[tex]r^{-1}(x)=\sqrt{\frac{11}{x}}+4[/tex]

Option:

x > 4; r–1(x) = 4 + StartRoot StartFraction 11 Over x EndFraction EndRoot

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

b

Answer:

h=-3

Step-by-step explanation:

-4h-2=-6h-8

+6h     +6h

2h-2=-8

   +2  +2

2h=-6

h=-3

Answer: 24

Step-by-step explanation:

Because if you do 4.80 times 5 you’ll get 24 because each orange cost $4.80

Answer:

the cost of 5 oranges would be $2.00

Step-by-step explanation:

To solve this we need to find the unit rate and when we do this we can solve this problem.  To find that we need to divide 4.80 by 12 once we do that we just have to multiply that number by 5 to get our answer, when you divide you'll get 0.4 and then multiply that by 5 and you'll get $2.00.

Answer:

#1. 3/8 and #2. 27/35

Step-by-step explanation:

3/4 - 3/8 change to 6/8 - 3/8 = 3/8 can not reduce

2/7 + 2/5 change to 10/35 + 17/35 = 27/35 can not reduce

Answer:

3/8

Step-by-step explanation:

3/4 - 3/8

= 3*2/4*2 - 3/8

= 6/8 - 3/8

= 6-3/8

= 3/8

Answer:

24/35

Step-by-step explanation:

2/7 + 2/5

= 2*5/7*5 + 2*7/5*7

= 10/35 + 14/35

= 10+14/35

=24/35

Answer:

D

Step-by-step explanation:

Answer:the nswer is    

Step-by-step explanation:

Answer:

C. Point D

Step-by-step explanation:

Distance between two points

Given two points A(x,y) and B(w,z), the distance between them is:

[tex]d=\sqrt{(z-y)^2+(w-x)^2}[/tex]

If both points have the same y-coordinate (y=z), then

[tex]d = |w - x|[/tex]

Point A has coordinates (-2,3). Point D has coordinates (-3,3). The distance between them is

[tex]d = | -2 - (-3) |[/tex]

Thus the correct choice is

C. Point D

Answer:6

Step-by-step explanation:

The total number of blocks is 42 and the number of rows is 7. So the equation would be 42 ÷ 7. So, 42 ÷ 7 = 6. There are 6 blocks in each row

Answer:

Infinitely many solutions (the lines are identical)

Step-by-step explanation:

Let's start by getting each equation into slope intercept form (y=mx+b)

-14x-14y=28

-14x-28=14y

-x-2=y

and

7x+7y= -14

7x+14= -7y

-x-2=y

We can see that these two lines are identical which means that there are an infinite amount of answers

Answer:

1/2

Step-by-step explanation:

Answer:

The expression for the total cost of the visit to dentist is T = 50 + 100n .

Step-by-step explanation:

As given

The price of a visit to the dentist is $50.

If the dentist fills any cavities, an additional charge of $100 per cavity gets added to the bill.

If the dentist n cavities .

Let us assume that the total cost of the visit to dentist be T.

Than the expression becomes

T = 50 + 100n

Therefore the expression for the total cost of the visit to dentist is T = 50 + 100n .

Answer:

wow bkrioavpoimpmqe

Step-by-step explanation:

Answer:

Area of the shaded region = 1.92 cm²

Step-by-step explanation:

Area of the shaded region = Area of sector OMN - Area of isosceles triangle OMN

Drop a perpendicular OP from vertex O to opposite side MN.

Perpendicular OP will bisect angle MON.

m∠MOP = 25°

By cosine ratio in triangle OPN,

cos(25°) = [tex]\frac{OP}{ON}[/tex]

OP = ON.cos(25°)  

OP = 6cos(25°)

OP = 5.438 cm

By sine ratio of angle PON,

sin(25) = [tex]\frac{PN}{ON}[/tex]

PN = ON.sin(25)

     = 6sin(25°)

     = 2.536 cm

Since, MN = 2(PN)

MN = 5.071 cm

Area of ΔOMN = [tex]\frac{1}{2}(OP)(MN)[/tex]

                         = [tex]\frac{1}{2}(5.438)(5.071)[/tex]

                         = 13.788 cm²

Area of sector OMN = [tex]\frac{\theta}{360}(\pi r^{2})[/tex]

Here 'θ' is the angle subtended by the arc MN at the center.

Area of sector OMN = [tex]\frac{50}{360}(\pi )(6^{2})[/tex]

                                  = 15.708 cm²

Area of the shaded region = 15.708 - 13.788

                                             = 1.92

                                             ≈ 1.92 cm²

Answer:

Area of the shaded region = Area of sector OMN - Area of isosceles triangle OMN

Drop a perpendicular OP from vertex O to opposite side MN.

Perpendicular OP will bisect angle MON.

m∠MOP = 25°

By cosine ratio in triangle OPN,

cos(25°) = \frac{OP}{ON}ONOP

OP = ON.cos(25°)  

OP = 6cos(25°)

OP = 5.438 cm

By sine ratio of angle PON,

sin(25) = \frac{PN}{ON}ONPN

PN = ON.sin(25)

     = 6sin(25°)

     = 2.536 cm

Since, MN = 2(PN)

MN = 5.071 cm

Area of ΔOMN = \frac{1}{2}(OP)(MN)21(OP)(MN)

                         = \frac{1}{2}(5.438)(5.071)21(5.438)(5.071)

                         = 13.788 cm²

Area of sector OMN = \frac{\theta}{360}(\pi r^{2})360θ(πr2)

Here 'θ' is the angle subtended by the arc MN at the center.

Area of sector OMN = \frac{50}{360}(\pi )(6^{2})36050(π)(62)

                                  = 15.708 cm²

Area of the shaded region = 15.708 - 13.788

                                             = 1.92

                                             ≈ 1.92 cm²

Answer:

≈ 33°

Step-by-step explanation:

So, first, you can draw a visual. Refer to the image attached below:

Using this info, you can use trigonometric ratios. Recall that:

tangent = opposite side/adjacent side

sine = opposite side/ hypotenuse

cosine = adjacent side/hypotenuse

You can clearly see that you have an opposite side and a given hypotenuse. This means we'll be using sine.

So:

[tex]sinX = \frac{150}{275}[/tex]

However, we're not trying to find sinX, we're trying to find X.

So we would have to use inverse sine, which would then be:

[tex]X = sin-1 (\frac{150}{275} )[/tex]

Put this into your calculator, and:

X ≈ 33.05573115...

Answer:

Step-by-step explanation:

If Susana runs 2 3/4 miles per 1/4 hour

in one hour

2 3/4=11/4

1h=11/4 *4=11 miles

11 miles/hour

Answer: Yes Y=x+2 is a linear function.

Answer:r

enor

Step-bay-step explanation:

Answer:

See the conversion from decimal to fraction:

13.

14.

15.

Answer:

la respuesta es (11.615)

Answer:

Lots of "ifs" here.

A=bh/2 is the formula for the area of a triangle.

A=bh is the formula for the area of a rectangle or a parallelogram.

If the 6 & 4 area the base & height of a rectangle, then (6)(4) = 24 in^2

If the 6 & 10 are the base and height of a triangle, then 1/2(6)(10) = 30 in^2

Step-by-step explanation:

Answer:

Geometric

Step-by-step explanation:

The given sequence is; 39, 156, 468, and 936 Geometric sequence.

Three parameters differentiate between which geometric sequence we're talking about. The first parameter is the initial value of the sequence. The second parameter is the quantity by which we multiply the previous term to get the next term. And the third parameter is the length of the sequence. It can be finite or infinite.

Consider that the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r.

Thus, the nth term of such sequence would be;  [tex]T_n = ar^{n-1}[/tex]

We have been given that the sequence is; 39, 156, 468, 936

Hence, the given sequence is; 39, 156, 468, and 936 Geometric sequence.

Learn more about geometric sequence here:

https://brainly.com/question/2735005

#SPJ2

Answer:

The answer is 80.5!

Step-by-step explanation:

The reason to the answer is because volume of a cuboid is l×B×H

(Substitute the values)  L = 2 , B = 3.5 , H = 11.5

2 × 3.5 × 11.5

Therefore, when we multiply these numbers we get, the answer 80.5!

I hope this answer helps!

Answer.

Step-by-step explanation:

Given = sum of two exterior angle of a triangle is 272 .

rule of triangle is that each and every angle which are outside a triangle is 360.

so, 272 + x = 360

x = 360 - 272

x = 88

Answer:

x = 1 or -5/2

Step-by-step explanation:

-2x^2 - 3x + 5 = 0

multiply all through by -1

2x^2 + 3x - 5 = 0

....... 2x^2 × 5 = 10x^2 = +5x × -2x

(2x^2 + 5x)-(2x - 5) = 0

x(2x + 5) - 1(2x + 5) = 0

x - 1 = 0 or 2x + 5 = 0

x = 1 or 2x = - 5

x = 1 or -5/2

Answer:

B.there is a horizontal shift 6 spaces to the right

Answer:

are you talking about y=mx+b? M would be the slope, and B would be the y intercept, so if we wanted to do, lets say 4,5, we would say y=4x+5, i think,

Step-by-step explanation:

An equation in slope-intercept form looks like this: y = mx+b

In the equation, m is equal to the growth rate of the line on the graph and b represents the y-intercept (where the line meets with the y-axis).

For the line shown in the picture below, the equation is y = 1x + 2 (not exactly but based on estimates). Also, you can ignore the writing on the picture. (0-0')

y = 1x + 2

In this equation. 1 represents the growth rate and 2 represents the y-intercept.

So, when writing an equation, look for these two things:

y-intercept: where the line of a graph meets with the y-axis

growth rate: how much is the line increasing by on the y-axis for every unit on the x-axis?

:3))

Answer:

y=3[tex](x-4)^{2}[/tex]-47.5

Step-by-step explanation:

I did it in my notebook.