Find the domain for the rational function f of x equals quantity x minus 1 end quantity divided by quantity x plus 3 end quantity.

(−∞, 1) (1, ∞)
(−∞, −1) (−1, ∞)
(−∞, 3) (3, ∞)
(−∞, −3) (−3, ∞)

Answers

Answer 1

Answer:

[tex]\mathrm{Domain\:of\:}\:\frac{x-1}{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:x>-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, the 4th option i.e. (−∞, −3) (−3, ∞) is the correct answer.

Step-by-step explanation:

Given the expression

[tex]f\left(x\right)=\frac{x-1}{x+3}[/tex]

We know that the domain is the set of all the input or argument values for which is the function is real and defined.

From the given expression, we need to make sure the denominator of a rational function can be anything but 0, because 0 would make the function undefined.

Thus, we need to find undefined points such as:

x+3 = 0

x = -3

Therefore, the function domain must be:

x < -3 or x > -3

In other words,

[tex]\mathrm{Domain\:of\:}\:\frac{x-1}{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:x>-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, the 4th option i.e. (−∞, −3) (−3, ∞) is the correct answer.


Related Questions

Find X in this picture. ​

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Answer:

x is in the top left of the triangle :)

Step-by-step explanation:

Answer:

its there....

Step-by-step explanation:

Find the value of x.
12
2x
x=

Answers

Answer:

24x

Step-by-step explanation:

i hope this is correct! c:

Write sin (4theta) in terms of sin (2theta) and cos (2theta).

Answers

Answer:

2 sin 2 theta cos 2 theta

Step-by-step explanation:

Mathematically;

sin (4theta) = sin (2theta + 2theta)

Using the sine addition rule

That would be;

sin 2 theta cos 2 theta + sin 2 theta cos 2 theta

= 2 sin 2 theta cos 2 theta

PLEASEE HELP ASAP IM BEGGIMG YOUUUUUU
I WILL GIVE BRAINLIEST ASAP

Answers

Answer:

Below

Step-by-step explanation:

Problem 1

Blank 1 = 6

Blank 2 = 17

(5*3)+2

Blank 3 = 4

(4*1)

Problem 2

Blank 1= (-5)^3=-5*-5*-5=-125

Blank 2= 18

(6*3)

Blank 3= 12

(4*3)

expand and simplify (x-3)(2x+1)(3x-2)

Answers

Answer:

6x³ - 19x² + x + 6

General Formulas and Concepts:

Algebra I

Terms/CoefficientsExpand by FOIL (First Outside Inside Last)

Step-by-step explanation:

Step 1: Define

(x - 3)(2x + 1)(3x - 2)

Step 2: Expand

Expand [FOIL]:                     (2x² + x - 6x - 3)(3x - 2)Combine like terms:            (2x² - 5x - 3)(3x - 2)Expand:                                6x³ - 15x² - 9x - 4x² + 10x + 6Combine like terms:            6x³ - 19x² + x + 6
Ya what they said above, I need em points

Please help I don’t get it I will mark brainleist

Answers

Answer:

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism with equilateral bases, and square sides.

Step-by-step explanation:

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~Uh- ~ Hey ~ can ~ someone ~ help ~ me ~ out ~ once ~ again...?~
A circle has a radius of 6 meters. What is the circumference of the circle?

Answers

Answer:

The answer is option A

A) Circumference= 12[tex]\pi[/tex] m

Step-by-step explanation:

To find the circumference of a circle the formula you would use is C=2[tex]\pi[/tex]r

if the radius is 6 meters, C is

C = 2*6 [tex]\pi[/tex]r

C= 12[tex]\pi[/tex] m

the answer is a) 12 .......

Which two operations are needed to wrte the expression that represents Fournes heerence of a number and three? mult cation and subtraction Komision and subtraction Cmu tip cation and addition division and addition​

Answers

Answer:

CMU+the curcumin of three is Fournes

Step-by-step explanation:

What is the slope of a line perpendicular to the line whose equation is x−2y=12.

Answers

Answer:

-2/x

Step-by-step explanation:

simplified is y = -x/2 - 6

Perpendicular slopes are just reciprocals of the original slope, so just flipp the original slope around to be the complete opposite.

Example if slope= -2, the reciprocal= -1/2

Just flip the numerator with the denominator for perpendicular slope

find the angle p (add a explanation too)​

Answers

Step 1: Find the sum of the interior angles

Use this formula: 180 x (n - 2)

n is the number of sides of the polygon

Work:

180 x (4 - 2)

180 x 2

360

Step 2: Find the angle right above the 94 degree angle

The entire angle (a circle) is equal to 360 degrees. To find the part we're looking for (inside of the polygon), we need to subtract the angle we already know from 360.

Work:

360 - 94

266

Step 3: Set up an equation to find the missing angle p

We now know every angle except p! And we know the sum of the interior angles. Knowing this information makes it really easy to set up an equation.

360 = 12 + 75 + 266 + p

360 = 353 + p

p = 7 degrees

Does this answer make sense?

Yes! Although the drawing may not be to scale, it is very possible that angle p could be 7 degrees because of how 12 degrees looks on this graph.

Hope this helps!! :)

Maddie can not decide which of two Ski sets to buy. The original price of each is $850. The first ski set is marked 50% off. The second was marked down by 30% then a few days later an additional 20% off. 1. Find the sale price of the first ski set... 50% off. Show your work. 2. Find the Sale Price of the Second Ski Set Marked 30% then 20%. Show your work. 3. Which one is a better deal for Maddie and why?

Answers

Answer:

$425i. $595             ii. $476First ski

Step-by-step explanation:

1. The first ski was valued at $850 but was then given a 50% discount. The sales price will therefore be:

= 850 * ( 1 - 50%)

= 850 * 50%

= $425

2. The first one was first discounted by 30% so the sales price was:

= 850 * ( 1 - 30%)

= 850 * 70%

= $595

It was then marked down by a further 20%:

= 595 * ( 1 + 20%)

= $476

3. The first ski is a better option because the discount makes it cheaper than the second ski even after the second ski had been discounted twice.

The triangle shown is an equilateral triangle. An equilateral triangle has sides lengths a. What is the area of the equilateral triangle with the length of each side equal to a? One-half a sine (60 degrees) 3 a sine (60 degrees) One-half a squared sine (60 degrees) a squared sine (60 degrees)

Answers

Answer: its C

Step-by-step explanation:

The area of an equilateral triangle can be written as a squared sine (60 degrees) thus Option D is correct.

What is an equilateral triangle?

The triangle in which all three sides are of the same length. In this the all angles are the same 60°.

The area of a triangle can be calculated by,

A = 1/2 x b x h..................1

Where,A - Area of triangle

b - base

h - height

From, Pythagoras Theorem

a² = h² + (a/2)²

h² = a² - (a/2)²

Put the value of “h” in equation 1

A = 1/2 x b x h

A = 1/2 x √[a² - (a/2)²] x h

A =  √3/4 a²

Since √3/4 = sin 60°.

So, the area of an equilateral triangle as a squared sine (60 degrees).

Learn more about the equilateral triangle;

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12 ÷ 4 x ___ = 12

im so confused on this question can you guys help

Answers

Answer:

Step-by-step explanation:

12/4 = 3

3 x 4 = 12

4 is the answer

what is the square root of 5 divided by 5 square root of 3?

Answers

Should be 0.77459666924.

Just the first 3 numbers

A building is 200 feet high. One end of a wire is attached to the top of the building.
The other end is attached to the group 150 feet away from the base of the building. How
long is the wire?

Answers

Answer:

250 feet

Step-by-step explanation:

If you draw out this situation, you would get a right triangle with a height of 200 (feet) and a base of 150 (feet). The wire is the missing length, or the 'hypotenuse' of this right triangle. You use the pythagoras thingie, and the formula is a^2 + b^2 = c^2.

a= 200

b= 150

c= ?

40,000 + 22,500 = c^2

62,500 = c^2

c = √62,500

∴ c = 250

Please help!! Show your work!! Will mark brainliest!!

Answers

Answer:

17 degrees because 180-163=17

Step-by-step explanation:

let the picture be named as above picture:

angle D +163=180 (linear pair)

D=180-163

D=17⁰

Sum of exterior angle of polygon is 360⁰.

148+50+17+90+angleC=360

198+107+angleC=360

305+angleC=360

angleC=360-305

angleC=55⁰

Solve 24≤−6t.

the solution is __

Answers

Answer:

t ≤ − 4

Step-by-step explanation:

Answer: t ≤ -4

Step-by-step explanation:

rearrange the problem 24-(-6*t)≤0  Pull out like factors :24 + 6t  =   6 • (t + 4)

Divide both sides by 6    Subtract  4  from both sides t ≤ -4

         

-5x + y = 1
- 10x + 2y = -2
plz answer right this is the last math problem i have to do!

Answers

Answer:

-1 -y/5

Step-by-step explanation:

-5x + y = 1

Subtract yy from both sides.

-5x=1-y

−5x=1−y

2 Divide both sides by -5−5.

x=-\frac{1-y}{5}

x=−

5

1−y

-10x+2y=-2

Factor out the common term 22.

2(5x+y)=-2

2(5x+y)=−2

2 Divide both sides by 22.

5x+y=-1

5x+y=−1

3 Subtract yy from both sides.

5x=-1-y

5x=−1−y

4 Divide both sides by 55.

x=\frac{-1-y}{5}

x=

5

−1−y

Evaluate the power.

0.4 2=____

Answers

Answer:

0.2

Step-by-step explanation:

Answer:

0.16

Step-by-step explanation:

James is solving a number puzzle that involves three integers, a, b, and c, where c
is a positive integer. The product of A and B is 6. The product of a and c is – 4.
The product of b and c is -6.



Please help!!!

Answers

Answer:

a = -2, b = -3, c = 2

Step-by-step explanation:

We have the following three equations.

ab = 6

ac = -4

bc = -6

Multiply equation 2 and 3, we get

abc^2=24

Dividing it by the first equation, we get

c^2=4

c=2 or -2 (rejected since c is a positive integer)

We can then substitute c=2 into the equations, and find out that a = -2 and b = -3.

A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns​ shown, making the​ one-day sale price of the ski set ​$323. Find the original selling price of the ski set.

Answers

Answer:
The original selling price is $520.632
Explanation:
Consider the initial selling price be $x
After marking down 10%,
Final Selling price = Selling price(1-10%)
Selling price = x – 10% of x = x – 0.1x = 0.9x
After marking 30%
Final Selling price = Selling price(1-10%)
Selling price = 0.9x – 0.3*0.9x = 0.9x – 0.27x = 0.63x
According to the question,
0.63x = 328

Therefore, the original selling price is $520.632

Answer:

The original selling price is $520.632

Explanation:

Consider the initial selling price be $x

After marking down 10%,

Final Selling price  = Selling price(1-10%)

Selling price = x – 10% of x = x – 0.1x = 0.9x

After marking 30%

Final Selling price  = Selling price(1-10%)

Selling price = 0.9x – 0.3*0.9x = 0.9x – 0.27x = 0.63x

According to the question,

0.63x = 328

Therefore, the original selling price is $520.632

Hope It helps!!❤

An aircraft flies at a speed of 480 miles per hour. It takes the aircraft t hours to reach its destination.
Which of the following equations can be used to find the number of hours it takes the aircraft to reach a destination that is 1200
miles away?
A 1200t=480
B480+1200=t
C480t=1200
D 480+t=1200

Answers

Answer:

A

Step-by-step explanation:

The equation 480t = 1200 can be used to find the number of hours an aircraft takes to reach a destination that is 1200 miles away.

The correct answer is option (C) 480t = 1200.

What is equation?

"An equation is a mathematical statement that is made up of two expressions connected by an equal sign."

Formula to calculate speed:

speed = distance / time

For given question,

An aircraft flies at a speed of 480 miles per hour and takes t hours to reach its destination.

Let d represents the distance(in miles) traveled by an aircraft in t hours with a speed of 480 miles per hour.

By using the formula of speed,

⇒ 480 = d/t

When destination is 1200 miles away.

This means d = 1200 miles.

⇒ 480 = 1200/t

480t = 1200                      .....................(Multiplying both the sides by t)

This equation can be used to find the number of hours it takes the aircraft to reach a destination that is 1200 miles away.

Therefore, option (C) is the correct answer.

Learn more about equation here:

https://brainly.com/question/13170101

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What is the measure of

PLEASE HELP HURRY

Answers

Answer:

112.5°

in pretty sure that's the answer

112.5° is the answer because 8x=180 which then means x=22.5

What would the temperature be on a hot day?
A.35°C
B.32
C.10°C
D.0°F

Answers

Answer:

A. 35°C.

Step-by-step explanation:

35 C (Celsius), converted to F (Fahrenheit), would be 95. Which would make it a hot day.

So, you answer is 35°c.

Mary has a \large 16\frac{1}{2} ounce bag of chocolate chips. She will only use \large \frac{1}{4} of the bag for decorating a cake. How many ounces will she use for decorating

Answers

Answer:

4 1/8 ounces

Step-by-step explanation:

Total bag of chocolate chips Mary has = 16 1/2 ounces

She will only use 1/4 of the bag for decorating a cake.

How many ounces will she use for decorating

Ounces used in decoration = 1/4 of 16 1/2

= 1/4 × 33/2

= (1*33)/(4*2)

= 33/8

= 4 1/8 ounces of chocolate chips

She will use 4 1/8 ounces of chocolate chips for decorating a cake

HELP WHAT EQUATION MATCHES THE GRAPH? PLEASE HELP ME​

Answers

Step-by-step explanation:

I think no. c is correct

if it helps you then plzz mark me brainliest

HELP PLA I NEED HELP

Answers

x=20

x=5 root under 3

x=4 root under 2

Very confused. Will give 40pts.

Answers

Answer:

Y = 10.25 or 10.247

Step-by-step explanation:

Alright So use the Formula A^2 + B^2 = C^2

You have one leg and the hypotenuse so first you are going to find 19 ^2 = 361.

Next, you need to find 16^2 = 256.

Last but not least, you subtract the leg from the hypotenuse, which equals 361-256=105

Finally, you take 105 and find its square root.

And depending on how far you round it down, your answer would be 10.25(that is in tenths), or 10.247(which is rounded to hundredths)

Hope this helps!

6 x 2/3 x 2 1/2 = what plss help

Answers

Answer:

10

Step-by-step explanation:

Answer

10

Step-by-step explanation:

Plz help!! Meera is researching cruising speeds of different planes. Which airplanes has a greater cruising speed?

Answers

Answer:

The one on the graph

Step-by-step explanation:

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