20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.

Answers

Answer 1

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

[tex]f(x)=\frac{x^2+9}{x-3}[/tex]

We have to find true statement about given function.

[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]

=[tex]\infty[/tex]

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.


Related Questions

A cylinder has a height of 16 cm and a radius of 5 cm.A cone has a height of 12 cm and a radius of 4 cm.if the cone is placed inside the cylinder as shown,what is the volume of the air space surrounding the cone inside the cylinder

Answers

Answer:

Step-by-step explanation:

Cylinder height= 16cm and radius =5cm

Formula for volume= π r squared times height

π x 5²(r)  x 16 (h) =  1256cm³

Formula for volume of a cone= π  x radius x height divided by 3

π x 4² x 12/3= 200.96cm³

Answer= 1256-200.96= 1055.04cm³

have a good day hope it helped

A girl who normally gets A's didn't do the first assignment given on the first day of school and now has 0%. How many 95% grades will she need to achieve an average of 90% overall? The points for each assignment are based on what she scores.

Answers

Answer:

19 of 95% grades

Step-by-step explanation:

90= (0+95(x-1))/x

90x=0+95(x-1)

90x=95(x-1)

90x=95x-95

90x-95x=-95

-5x=-95

x=-95/-5

x=19

find the volume of the figure​

Answers

Answer:

16 inches³

Step-by-step explanation:

Volume of prism = base area * height

Base is square, so area of base = side * side = 2 * 2 = 4 in²

Volume of prism = 4 * 4

Volume of prism = 16 in³

Find the volume of this cone.
Use 3 for T.
V =
71 r2h
3
V
V ~ [?]in3
110in
4in

Answers

Answer:

V = 40 in^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h  where r is the radius and h is the height

The diameter is 4 so the radius is 1/2 the diameter or 1/2(4) =2

The height is 10 and we are using 3 for pi

V = 1/3 (3)(2)^2 (10)

V = 40 in^3

Which is the graph of y = [x]-2?

PLEASE HELP TIMED PLEASE

Answers

Answer:

3rd graph

Step-by-step explanation:

Please help me solve this problem fast!!

Answers

Answer:

12.53

Step-by-step explanation:

√(11²+(10-4)²)

= √157

= 12.53 (rounded to two decimal places)

Answered by GAUTHMATH


[tex]( - 72) \div ( + 9) + (16) \div ( - 4)[/tex]
could you help.....​

Answers

Answer:

-12

Step-by-step explanation:

Use PEMDAS,

doing the division first, then addition to simplify the terms

(-72)/(+9) + 16/(-4)

(-72/9) + (16/-4)

-8+(-4) = -12

Answer:

-12

Step-by-step explanation:

((-72)÷(9))+((16):(4))

= (-8)+(-4)

= -12

Given the mean of a random variable, X, is 10 and P(X < 11) = 0.67. Find the standard deviation.

Answers

Answer:

Step-by-step explanation:

This is the problem we need to solve:

[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.

If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:

P(z < .43) = .66640 and P(z < .44) = .67003

We'll use z = .44

[tex].44=\frac{11-10}{\sigma}[/tex] and

[tex].44=\frac{1}{\sigma}[/tex] and

[tex]\sigma=\frac{1}{.44}[/tex] so

σ = 2.27 (check it; it works!)

GIVING BRAINLY TO CORRECT ANSWER!!

Answers

Answer:

7/0

Step-by-step explanation:

7/0 = 7

A rational number is written in the form of p/q, where q is not equal to zero. Therefore it is not a rational number.

I hope this answer helps you out! Brainliest would be appreciated :)

Answer:

7/0

Step-by-step explanation:

a irrational can not be written as a fraction

please help me guys its important ​

Answers

Answer:

1441.08in^3

Step-by-step explanation:

whats does it me study the exercises in which both addends are negative.what do you notice about the sum

Answers

Answer:

Jsjiaghajqkkooo898iiwiqiooopwpppwopfokejejieieieieiie

For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?

Answers

Answer:

(2 + 1)^2 + 2 = 10 - 6  

Falso

Step-by-step explanation:

The left side  

11

does not equal to the right side  

4

, which means that the given statement is false.

False

Please answer ASAP!!! A ski store has 60 different boots available, 30 different pairs of skis, and 40 different hats.

If a customer were to only buy ONE item, how many different ways can a customer purchase an item from the store?

Answers

In this question, the client will buy one item, which is composed by a boot, a pair of skis and a hat. Since the items are independent, the fundamental counting principle can be used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

60 boots, 30 pairs of skis, 40 hats. So

60*30*40 = 72,000

The customer can purchase an item in 72,000 ways from the store.

For another example of the fundamental counting principle, you can check https://brainly.com/question/24067651

solve for w.
-9/7=-2/3w-1/2

Answers

Answer: [tex]w=\frac{33}{28}[/tex]

Step-by-step explanation:

To solve for w, we want to isolate w.

[tex]-\frac{9}{7}=-\frac{2}{3}w-\frac{1}{2}[/tex]            [add both sides by 1/2]

[tex]-\frac{11}{14}=-\frac{2}{3}w[/tex]                 [multiply both sides by -3/2]

[tex]w=\frac{33}{28}[/tex]

Now we know that [tex]w=\frac{33}{28}[/tex].

Answer:

[tex]\sf w=\dfrac{33}{28} \\[/tex]

Step-by-step explanation:

[tex]\sf -\dfrac{9}{7} =-\dfrac{2w}{3} -\dfrac{1}{2}[/tex]

First, take -2w/3 to the left side.

[tex]\sf -\dfrac{9}{7}+\dfrac{2w}{3} = -\dfrac{1}{2}[/tex]

Then, add 9/7 to both sides.

[tex]\sf \dfrac{2w}{3} = -\dfrac{1}{2}+\dfrac{9}{7}[/tex]

Make the denominators the same and add the fractions.

[tex]\sf \dfrac{2w}{3} = -\dfrac{1*7}{2*7}+\dfrac{9*2}{7*2}\\\\\sf \dfrac{2w}{3} = -\dfrac{7}{14}+\dfrac{18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{-7+18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{11}{14}[/tex]

Use cross multiplication.

[tex]\sf 2w*14=11*3\\\\28w=33[/tex]

Divide both sides by 28.

[tex]\sf w=\dfrac{33}{28} \\[/tex]

An angle measures 73.6° more than the measure of its complementary angle. What is the measure of each angle?

PLEASE help, I'm struggling a lot!

Answers

Answer:

Let ABC = 73.6

Complement = ABD = 16.4

ABx = unknown angle

ABx + (ABx + 73.6) = 90

ABx = 16.4 / 2 = 8.2

The angles are 8.2 and (8.2 + 73.6) = 90

A recipe requires 500 mL of milk. You will make the recipe once a month for the next 4 months. You do not use milk other than for cooking. Which container of milk should you buy? (1L=1000 mL) *

Answers

Answer: 1 month = 500ml

4 month = 500ml × 4 = 2000ml = 2L

you should use the 2L container

Step-by-step explanation:

Once again, move points C, D, and E on the circle, and complete the table below. This time, you’ll consider what happens to the lengths of the sides of quadrilateral BCDE. Notice that m∠B is predetermined, so set that angle measure first.

Answers

Answer:

Also to help some of you out here’s the answer to question 6 !!

Question 6 : No apparent relationship exist between the side lengths of quadrilateral BCDE inscribed in circle A

Step-by-step explanation:

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME THE STEP BY STEP EXPLANATION!!
The data value that occurs most often in a data set is the ____________.
A. mode
B. median
C. mean
D. range

Answers

mode is the data that occurs most often in a data

What is the image of the point (3, 2) after a rotation of 90° counterclockwise about the origin?​

Answers

(-2,3). When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).

if A ={1,2,3,4} and B={3,4,5,6} find A-B.​

Answers

Answer: {1,2} is the answer.

Step-by-step explanation:

A-B

{1,2,3,4}-{3,4,5,6)

= {1,2}

What is the value of y?
A. 55°
B. 850
C. 10°
D. 110°

Answers

I may not know I am sorry ma’am for your math problem is to hard

Am I suppose to substitute the variables with random numbers in order to answer these questions???

Translation A maps (x, y) to (x + n, y + 1). Translation B maps (x, y) to (x +s, y + m).
1. Translate a point using Translation A, followed by Translation B. Write an algebraic rule for the final image of the point after this composition.
2. Translate a point using Translation B, followed by Translation A. Write an algebraic rule for the final image of the point after this composition.
3. Compare the rules you wrote for parts (a) and (b). Does it matter which translation you do first? Explain your reasoning.

Answers

9514 1404 393

Answer:

(x, y) ⇒ (x +n +s, y +1 +m)(x, y) ⇒ (x +s +n, y +m +1)they are identical in effect; order does not matter

Step-by-step explanation:

Substitute the expressions.

A then B

After the first translation, the value of x is (x+n). Put that as the value of x in the second translation.

  x ⇒ x +s . . . . . . . . . the definition of the second translation

  (x+n) ⇒ (x+n) +s . . . the result after both translations

The same thing goes for y. After the first translation, its new value is (y+1).

  y ⇒ y +m . . . . . . . . the definition of the second translation

  (y+1) ⇒ (y+1) +m . . . the result of both translations

Then the composition of A followed by B is (x, y) ⇒ (x +n +s, y +1 +m).

__

B then A

The same reasoning applies. After the B translation, the x-coordinate is (x+s) and the y-coordinate is (y+m). Then the A translation changes these to ...

  x ⇒ x +n . . . . . . . . . . definition of translation A

  (x+s) ⇒ (x+s) +n . . . . translation A operating on point translated by B

  y ⇒ y +1 . . . . . . . . . . . definition of translation A

  (y+m) ⇒ (y+m) +1 . . . . translation A operating on point translated by B

The composition of B followed by A is (x, y) ⇒ (x + s + n, y + m + 1).

__

You should recognize that the sums (x+n+s) and (x+s+n) are identical. The commutative and associative properties of addition let us rearrange the order of the terms with no effect on the outcome.

The two translations give the same result in either order.

Suppose you roll a die. Find the probability of the given event. Simplify your answer. P(a number less than 7)​

Answers

Answer:

1/6

Step-by-step explanation:

There are 6 faces on a die, and you can only roll one face only. So, the denominator will be 6 because there are 6 faces, and 1 as the numerator because that's the equal proportion for each face (unless you use two dice)

help please ITS OF TRIGONOMETRY
PROVE ​

Answers

Answer:

The equation is true.

Step-by-step explanation:

In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation.  Please note that each side is named with respect to the angle is it across from.

Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

One is given the following equation,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

As per the attached reference image, one can state the following, using the right angle trigonometric ratios,

[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]

Substitute these values into the given equation. Then simplify the equation to prove the idenity,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]

[tex]1+(-1)=0[/tex]

[tex]1-1=0[/tex]

[tex]0=0[/tex]

Just need to know if I answered this correctly please!

Answers

Answer:

yes, your answers are correct

(-4)-(+2)= PLS HELPPP MEEEEEEE

Answers

[tex]\sf( - 4) - ( + 2) \\ = \sf - 4 - 2 \\ \sf \: = - 4 + - 2 \\ = \underline{\bf - 2}[/tex]

[tex]( - 4) - ( + 2)[/tex]

[tex] = - 4 - 2[/tex]

[tex] = - 4 + ( - 2)[/tex]

[tex] \boxed{ = - 2}[/tex]

I need the answer ASAP
1. Add Area (Split the shape up to two or more known
shapes first)
12.5 ft
11.6 ft
19.2 ft
16.7 ft

Answers

Answer:

Step-by-step explanation:

The shape cam be split into a triangle and a trapezoid

✔️Area of the trapezoid = ½(a + b)h

Where,

a = 12.5 ft

b = 16.7 ft

h = 11.6 ft

Plug in the values

Area of the trapezoid = ½(12.5 + 16.7)*11.6

Area of trapezoid = 169.36 ft²

✔️Area of the triangle = ½*b*h

b = 16.7 ft

h = 19.2 - 11.6 = 7.6 ft

Area of the triangle = ½*16.7*7.6

= 63.46 ft²

✔️Area of the shape = 169.36 + 63.46

= 232.82 ft²

0.9 x 100=
13.79 x 100=
29.894 x 100=

Answers

Answer:

multiplying by 100 "shifts" decimal point to the right by 2

90  

1379  

2989.4

Step-by-step explanation:

Answer:

0.9 x 100=90

13.79 x 100=1379

29.894 x 100=2989.4

Step-by-step explanation:

SEE QUESTION IN IMAGE

Answers

Answer:

B. 48°

Step-by-step explanation:

∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)

m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)

m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)

Correct choice is B

(3×sqrt(3)-2×sqrt(2))÷(sqrt(3)-sqrt(2))

Answers

Answer:

5+√6

Step-by-step explanation:

(3√3 -2√2) ÷ (√3-√2 )

= (3√3 -2√2) (√3+√2) ÷ (√3 -2√2) (√3+√2)

= (9+3√3√2-2√2√3-4) ÷ ((√3)^2 -(√2)^2)

=(9+3√6-2√6-4) ÷ (3-2)

= (5+√6)

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