Mathematics High School

Explain why f(x) = x^2-x-6/x^2-9 is continuous at x = 2.
a. f is defined at x = 3
b. f is not defined at x = 2
c. f is defined at x = -3
d. f is defined at x = 2

Explain Why F(x) = X^2-x-6/x^2-9 Is Continuous At X = 2. A. F Is Defined At X = 3 B. F Is Not Defined

Answers

Answer 1

The correct answer is option D. ([tex]f[/tex] is defined at [tex]x = 2[/tex])

The rational Function is continuous at a given value if its Denominator is not zero. In this exercise, we proceed to Factor the expression by check the value Denominator for each value of [tex]x[/tex].

[tex]f(x) = \frac{x^{2}-x-6}{x^{2}-9}[/tex]

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

As we can see, [tex]f[/tex] is not defined for [tex]x = -3[/tex] and [tex]x = 3[/tex]. Hence, we conclude that right answer is D.

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Related Questions

BRAINLY FOR CORRECT ANSWER

m∠1=?
m∠2=?
m∠3=?
m∠4=?
m∠5=?
m∠6=?

Answers

1 = 60
2 = 120
3 = 60
4 = 120
5 = 30
6 = 30

Solve by combining:

-x-y=6
5x-7y=66

Answers

Answer:

x = 2

y = 8

Step-by-step explanation:

-x - y = 6

5x - 7y = 66

-x - y = 6

x = -y - 6

5x - 7y = 66

5 ( -y - 6 ) - 7y = 66

-12y - 30 = 66

-12y = 96

y = -8

x = -y - 6

x = 8 - 6

x = 2

What is the equation of the line that passes through the point (-6, -2) and has a
slope of 1/6

Answers

Answer:

y=1/6x-1

Step-by-step explanation:

Recall that the equation of a line is y = mx + b.

m is the slopeb is the y-intercept

We know the line passes through (-6, -2), so we substitute x and y in the equation of a line. We also know the variable m (the slope) is 1/6. It would look something like this: -2=(1/6)(-6) + b.

From here, we can solve for b:

b + (1/6)(-6) = -2

b - 1 = -2

b = -1

The equation of the line that passes through the point (-6,-2) with a slope of 1/6  is  y=1/6x-1.

This is my first solution, let me know if I can improve on anything. Thanks, have a great day!

Original Shirts Cost: $55
Current Shirts Cost: $40
Find The Percent Of Decrease
?%
Round To Nearest Whole %
I really need to know??

Answers

Answer: 27% decrease

Step-by-step explanation:

50 Points if wrong u will get reported

Answers

Based on the fact that Mario increases by a scale factor of 2, the three points on the new Mario:

(7, 0)(0, 10.4)(4, 17.4)

What are the new points?

If Mario is increased by a scale factor of 2, then it means that all the points would be expanded by multiplying them by 2.

The first point would therefore be:

= 3.5 x 2 = 7

= 0 x 2 = 0

(7, 0)

The second point:
= 0 x 2 = 0

= 5.2 x 2 = 10.4

(0, 10.4)

The third point:
= 2 x 2 = 4

= 8.7 x 2 = 17.4

(4, 17.4)

The points on New Mario are:

(7, 0), (0, 10.4), and (4, 17.4)

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I’ll mark u as brainlist (all that apply)

Answers

Answer:

use some brain cells

Step-by-step explanation:


For every 3 girls in Mr Hegarty's class there are 5 boys. What is the ratio of boys to girls in the class?
Give your answer in its simplest form. HELP

Answers

Answer:
5:3

Explanation:
The question that tells us that for every 3 girls in Mr. Hegarty’s class, there are 5 boys. This means for every 5 boys, there are 3 girls. Therefore, the ratio of boys to girls in the class is 5:3.

I hope this helps!

pls help its timed!!​

Answers

I believe it’s A
Writing random things so it lets me send this

Given the point (2.6) is ok the graph of Y=f(x)
what are the coordinates of the point of the transformed graph: y=-2f(-(x+4))+3?​

Answers

y = -2fx (-x + 4) +3

y = 2fx -8f + 3

y = 2fx - 8f + 3

(HELP!! WILL GIVE 86 POINTS!!)

Use the elimination method to solvethe system of equations. Choose the
correct ordered pair.
-x+y= -2
2x- 3y = 4

Answers

Answer: 2(−x+y=−2)

2(−x+y=−2)

1(2x−3y=4)

Becomes:

−2x+2y=−4

2x−3y=4

Add these equations to eliminate x:

−y=0

Then solve−y=0for y:

−y=0

−y/-1 = 0/-1 (Divide both sides by -1)

y=0

Step-by-step explanation:

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

−x+y=−2

Substitute 0 for y in −x+y=−2:

−x+0=−2

−x=−2(Simplify both sides of the equation)

−x/-1 = -2/-2 (Divide both sides by -1)

x=2

Answer:

x=2 and y=0

Answer: x=y+2

Step-by-step explanation:

Step 1: Add -y to both sides.

−x+y+−y=−2+−y

−x=−y−2

Step 2: Divide both sides by -1.

-x/-1 = -y - 2/-1

asnwer: x=y+2

Answer: x = 3/2y + 2

2x−3y=4

Step 1: Add 3y to both sides.

2x−3y+3y=4+3y

2x=3y+4

Step 2: Divide both sides by 2.

2x/2 = 3y + 4/2

answer: x = 3/2y + 2

2x1+(1+7)+(7x2) write this expression as the product of two products

Answers

2x1+(1+7)+(7x2)➡️ 3+(8)+(14)➡️25


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Something that occurs continuously, or something that doesn't change!

Step-by-step explanation:

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The clock below shows what time mason mom drops him off for practice . what time did mason mom drop him off

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Answer:

where is the clock?

Step-by-step explanation:

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Answers

DHJBDVSFIUGWEIUWEIURG F4GIUFGICUSIVGERG834Y83REDSNCJHHBBHN

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Answers

Answer:

-50+9x

Step-by-step explanation:

multiply the numbers                              -49+9x -1

calculate the difference(-49-1                   -50 + 9x

Use synthetic division to evaluate f(x)=x^3-2x^2+4x+3 for x=2 . f(2)=
Need help asap

Answers

Step-by-step explanation:

Your problem is equivalent to

(x3 - 3x2  + x - 4)/(x-2)

The coefficients of the numerator    are 1, -3, 1, -4.

The solution is as follows:

2 | 1  -3   1  -4    Set up the coefficients in decreasing power of x, and 2 is the divisor.

            2  -2  -2

  ------------------

    1  -1  -1  -6

Here are the steps:

(a) Bring down the leading coefficient of 1.

(b) 2*1=2. Add -3 and 2 to obtain -1.

(c) 2*-1=-2. Add 1 and -2 to obtain -1.

(d) -1*2=-2. Add -2 and -4 to obtain -6

The quotient has the coefficients 1,-1,-1 so it is x2 - x  - 1. The remainder is -6.

Answer :

The result is x2  - x - 1  - 6/(x-2).

You can verify that the answer is correct, because

(x-2)*(x2 - x - 1) - 6 = x3 - 3x2  + x - 4

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Answer:

1st option...............

How do I do this? Please help

Answers

Answer:

Step-by-step explanation:

SEE ATTACHMENT

Create a table of values, and plot them.

graph the points of the equations onto the graph

What is the slope of a line parallel to the line whose equation is 6x + 3y = -54

Answers

The slope of the line parallel to the line is -2

What are linear equations?

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to determine the slope of the line parallel to the line?

The line equation is given as

6x + 3y = -54

Subtract 6x from both sides

3y = -6x - 54

Divide through the equation by 3

So, we have

y = -2x - 17

A linear equation is represented as

y = mx + c

Where m represents the slope

This means that

m = -2

Parallel lines have the same slope

This means that the slope of the line parallel to the line is -2

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Solve for r.

23 = r + 11

r=


Please help me and tell me quickly and explain how you solve for r PLEASE

Answers

subtract 11 from both sides
r=12

Answer:

r = 12

Step-by-step explanation:

23 = r + 11

23 - 11 = r

r = 12

Zane puts $1,000.00 into an account to use for school expenses. The account earns 11% interest, compounded annually. How much will be in the account after 4 years? Use the formula A= P (1+/), where A is the balance(final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Answers

Answer:

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Step-by-step explanation:

A = 1000(1 + 0.11)^4

Find an equivalent ratio in simplest terms: 30:18

Answers

Answer:

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Step-by-step explanation:

To simplify the ratio, we have to divide both terms by the greatest common factor (GCF). The GCF is the highest number that can divide evenly into two or more numbers. The GCF of 30 and 18 is 6.

30/6 = 5

18/6 = 3

30:18 = 5:3

5:3 LOL because it’s in simplest form

Lauren, Shannon, and Maddie all work at a restaurant. Lauren earned $11.00 less than 3 times the amount Maddie earned. ShWhich equation below correctly represents the situation above?annon earned $9.00 more than 2 times the amount Maddie earned. If Lauren and Shannon both earned the same amount of money, how much money, m, did Maddie earn?

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Music us enter a memento ---L'ordinateur

Select the function that represents the simple interest formula.

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Answer:

C

Step-by-step explanation:

A P E X

Xina has $289 and spends $55 at the grocery
store, and $32 on gas. How much does she
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200 dollars like the answer please

Name a point on this line.
y - 8 = -7(x + 1)

(-1,8)
(1, -8)
(8,-1)
(-8,1)

Answers

Answer:

A

Step-by-step explanation:

You should approach this problem by plugging the answer choices into the equation, since there are only four that you need to do. A works because 8-8 = -7(-1+1) which are both equal to 0

Pls, Help Math!!!!!!

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Question 1 is yes question 2 is x-3

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A = -6 , that is the answer
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