Mathematics High School

If possible, choose k so that the following function is continuous on any interval:

f(x)= (5x^4-20x^3)/(x-4) , x≠4
f(x)= K , x=4

k=?,

Answers

Answer 1
We need to cancel out the discontinuity in x = 4

In order to do that, factorize the numerator:
5x⁴ - 20x³ = 5x³(x-4)

This way, your function will be:
f(x) = 5x³(x-4) / (x-4)

and the two parentheses cancel out, leaving
f(x) = 5x³ 

which at x = 4 gives:
f(4) = 5·4³ = 5 · 64 = 320

Therefore K = 320.

Answer 2

Using continuity concepts, it is found that K = 320 makes the function continuous.

------------------

A function f(x) is said to be continuous at x = a if:

[tex]\lim_{x \rightarrow a^{-}} = \lim_{x \rightarrow a^{+}} = f(a)[/tex]

------------------

The piece-wise function given is:

[tex]f(x) = \frac{5x^4 - 20x^3}{x-4}, x \neq 4[/tex]

[tex]f(x) = K, x = 4[/tex]

------------------

The definition for x different of 4 can be simplified, as follows:

[tex]f(x) = \frac{5x^4 - 20x^3}{x-4} = \frac{5x^3(x - 4)}{x - 4} = 5x^3[/tex]

Thus, the simplified definition is:

[tex]f(x) = 5x^3, x \neq 4[/tex]

[tex]f(x) = K, x = 4[/tex]

------------------

For the lateral limits, x is close to but not exactly 4, so the first definition is used.

[tex]\lim_{x \rightarrow 4^-} = \lim_{x \rightarrow 4} 5x^3 = 5(4)^3 = 5 \times 64 = 320[/tex]

[tex]\lim_{x \rightarrow 4^+} = \lim_{x \rightarrow 4} 5x^3 = 5(4)^3 = 5 \times 64 = 320[/tex]

------------------

For continuity, it is needed that:

[tex]f(4) = 320[/tex]

Thus:

[tex]K = 320[/tex] makes the function continuous.

A similar problem is given at https://brainly.com/question/14755764

Related Questions

Compounds with high melting points have _____. (1 point)
covalent bonds
metallic bonds
ionic bonds
no chemical bonds

Answers

Melting points are determined by how much the molecules in the compound interact with the other molecules in the compound. Those that have many interactions with the other molecules have higher melting points.  
Of those listed, Ionic bonds have the most rigid interactions with other molecules so have the higher melting points.

Answer:

Melting points are determined by how much the molecules in the compound interact with the other molecules in the compound. Those that have many interactions with the other molecules have higher melting points.  

Of those listed, Ionic bonds have the most rigid interactions with other molecules so have the higher melting points.

Andrew and Ryan spend a total of $44 at a state fair. There is an entrance fee of x dollars per person, and each ride costs $3.50. If they went on the same number of rides, which equation correctly represents this relationship, where n is the number of rides? Choose all that apply.

A. x + 7n = 44

B. 2(x + n) = 44

C. 2(x + 3.5n) = 44

D. x + 3.50n = 44

E. 2x + 7n = 44

F. 2x + 3.50n = 44

Answers

n represent the number of rides each of them took

entrance fee for both of them = 2x
Total cost of rides = 2n x 3.50 = 7n

The total cost is 44
2x + 7n = 44 (Answer E)

2x + 7n = 44
2(x + 3.5n) = 44 (Answer C)


Answer:

C. 2(x + 3.5n) = 44

E. 2x + 7n = 44

Step-by-step explanation:

Hi, to answer this question we have to write an equation that represents the situation:

So, the total money spent by the 2 friends is $44. That cost is equal to the price of the entrance fee (x) multiplied by 2 (since they are 2), plus the cost of each ride (3.50) multiplied by the number of rides (n) and also by 2 (since they are 2)

Mathematically speaking:

2(x + 3.5n) = 44

So, the correct options are  

C. 2(x + 3.5n) = 44

E. 2x + 7n = 44 (is equivalent, obtained if we apply distributive property to option C.)

Chord AC intersects chord BD at point P in circle Z.

AP=3.5 in.
DP=4 in.
PC=6 in.



What is BP?

Enter your answer as a decimal in the box.

Answers

1. To solve this exercise, you must use the "Intersecting chords theorem".

2. You have that:

AP=3.5 in
PC=6 in
DP=4 in

3. Then, by applying the "Intersecting chord theorem", you have:

(AP)(PC)=(BP)(DP)

4. When you substitute the values into (AP)(PC)=(BP)(DP), you obtain:

(3.5 in)(6 in)/BP(4 in)

5. Now, you must clear BP. Then:

(3.5 in)(6 in)/4 in=BP
21 in^2/4 in=BP

6. Therefore, the value of BP is:

BP=5.25 in

PLEASE HELP ME ON THIS N TRY TO EXPLAIN!!!!!!!!

IF 2 PPL ANSWER I WILL GIVE BRAINLIEST IF ITS CORRECT

Answers

So first you have x, number of hot dogs, and y, the number of hamburgers. You need to add x to y to find 230, which is the total amount of hot dogs and hamburgers sold. Then you add 0.50x to 0.75y, which equals $138.50

Your answer is x + y = 230 and 0.50x + 075y = 138.50.

What is the value of y?

A. Cannot be determined
B. 120
C. 60
D. 65

Answers

60, since adding all 3 up equals 180
when talking about a trianlge it has to have 3 sides adding up to 180 degress so just take 60 + 60 = 120 then 180 - 120 = 60 degrees. hope this helps! :)

Solve each multiplication problem, use the cancellation method if possible, and reduce your answers.

a. 39⁄64 × 8⁄13
b. × 1⁄5 × 4⁄7
c. 3⁄5 × 10⁄12 × 1⁄2
d. 4⁄9 × 54
e. 20 × 3 1⁄5
f. 11 × 2 7⁄11
g. 5 1⁄3 × 5 1⁄8
h2⁄3. 10 2⁄3 × 1 3⁄8

Answers

You should google the worksheet that this is from, easier results.

a. 3/8
b. 8/105
c. 1/4
d. 24
e. 64
f. 29
g. 27 1/3
h. 14 2/3

Jeremy is going to roll a fair 6-sided die 180 times. What is the best prediction for the number of times that Jeremy will roll a number greater than 4?

Answers

around 66 times i belive its right you might have to round up a little 

Answer:

Step-by-step explanation:Close to 60 times but probably not exactly 60 times

A rectangle is 999 meters long and 444 meters wide. what is its area?

Answers

the area is 443,556. you multiply 999 by 444

Answer:

36

Remember, This is if you actually typed 9 and 4 but copy and pasted.

The equation for area is Width x height.

now replace the Values, which is 9 x 4, and that equals 32.

**The other option

443556

Remember, This is if you actually typed 999 and 444.

The equation for area is Width x height.

Now replace Values, which is 999 x 444, and that equals 443556.

I hope it helped!! <3

Solve the radical equation. square root 6n-11= n – 3 Which solution is extraneous? A.)2
B.)There are no extraneous solutions to the equation.
C.)7
D.)10

Answers

d 10 right????????????:
ANSWER


D) 10

EXPLANATION

We want to solve the radical equation,

[tex] \sqrt{6n - 11} = n - 3[/tex]

Square both sides,



[tex]6n - 11 = (n - 3) ^{2} [/tex]

Expand brackets on right hand side,

[tex]6n - 11 = {n}^{2} - 6n + 9[/tex]

Rewrite in general quadratic equation form,

[tex] {n}^{2} - 12n + 20 = 0[/tex]

Factor to obtain,

[tex](n - 2)(n - 10) = 0[/tex]

Apply the zero product principle to get,

[tex]n = 2 \: or \: n = 10[/tex]


We put n=2 into the equation to get,

[tex] \sqrt{6(2) - 11} = 2 - 3[/tex]


[tex] 1 = - 1[/tex]


This statement is false, hence 2 is an extraneous solution


We put n=10, to get

[tex] \sqrt{6(10) - 11} = 10 - 3[/tex]


[tex] \sqrt{49} = 7[/tex]


[tex]7 = 7[/tex]


This is true, hence the only solution is
[tex]n = 10[/tex]

The key idea of the transformation called a rotation is moving a plane a specified -------- about a fixed ------.

Answers

1)Angle 
2)fixed

hope this helped

The key idea of the transformation called a rotation is moving a plane a specified Distance about a fixed Point

mafaaaaaaaaaaaaaaaaaaaaaaaa

Answers

Subtract 2 from the inequality. Then it becomes obvious that the 3rd selection is appropriate.

_____
-3 ≤ n ≤ 4
Hey there! 

Add [tex]2[/tex] to your sides 

Like: [tex]-1 + -2 \leq n +2 + -2 \leq 6 + -2 \\ Answer: -3 \leq n \leq 4 (C) [/tex]

Good luck on your assignment and enjoy your day! 

~[tex]LoveYourselfFirst:)[/tex]

need help ASAP

Noah has 3 3/4 quarts of motor oil. He puts 1/2 that amount into a riding lawn mower.



How much oil does Noah put into the riding lawn mower?
Express your answer in simplest form.

Answers

He used 15/2 or 7 1/2 quarts of oil

Why is it advantages to take market trends into consideration when planning a career path?

Answers

It is very important. In the future, things change. Some jobs won't be needed anymore. Jobs like travel agents won't be needed because of technology.

Answer:

Its important because history repeats its self. some jobs won't be available in 5-10 years due to advance in technology, or a job that is fruitful/ profitable in one year may be completely dead and dry in the next.

Step-by-step explanation:

William had $45 dollars to spend on vegetables. After buying 6 watermelons, he had $25.50 left. How much did each watermelon cost?

Answers

45-25.50 = 19.50 spent
19.5 / 6 = 3.25 per watermelon

Let us suppose cost of 1 watermelon be x.

Cost of 6 watermelons = 6x.

It is given after buying 6 watermelons, he had $25.50 left.Total amount William spends on vegetable is $45.

We can form an equation with above information's

6x+25.50=45

To solve for x we isolate the x term .25.50 is added to the x term .

Opposite of addition is subtraction .Subtracting 25.50 both sides we have:

6x=45-25.50

6x=19.50

Dividing both sides by 6

x=3.25.

Cost of each watermelon is $3.25.


Please, help me. I'm not sure what to do.
Factor completely: 8x5 + 28x4 + 12x3
A) 2x3(2x + 6)(x + 1)
B) 2x3(2x - 6)(x - 1)
C) 4x3(2x + 1)(x + 3)
D) 4x3(2x - 1)(x - 3)

Answers

answer is d, its simple....

A car travels from town a to town b at an average speed of 40 miles per hour, and returns immediately along the same route at an average speed of 50 miles per hour. what is the average speed in miles per hour for the round trip?

Answers

The total distance from town a to town b is the same as town b to town a.

Average speed per hour = (40 + 50) ÷ 2 

Average speed per hour = 45

-----------------------------------------------------------------------------
Answer: The average speed is 45 miles/hour.
-----------------------------------------------------------------------------

For which polygon is the sum of the interior angles equal to 720 degrees?
A. Quadrilateral
B. Hexagon
C. Octagon

Answers

The answer to this is Hexagon.

There are 48 colas and 24 lemon-lime sodas in the cooler. What is the ratio of colas to lemon-lime sodas?

A. 1 to 4

B. 4 to 1

C. 1 to 2

D. 2 to 1

Answers

c, if you divide by 24, it would be 1:2 because 24 goes into 48 twice
for my answer I got D.) 2 to 1
hope this helped!
let me know if I was wrong.

Which properties justify the steps taken to solve the system?

4x+3y=25
2x+−5y=19

Drag the answers into the boxes to match each step.

Answers

step 1
Multiplication property of equality
Multiplying the second equation by -2
Step 2
Additional property of equality 
We add the two equations generated in step 1
Step 3
The division property of equality
We divide both sides of equation obtained in step 2 by 13
Step 4
Substitution property of equality
We substitute the value obtained in step 3 for y in the first equation.
Step 5
Simplify

Step 6 
Additional property of equality
We add +3 on both sides of the equation in order to have an equation with a variable x.
Step 7
Division property of equality
We divide both sides of the equation obtained to get the value of x

Answer:

hope this helps :)

jason built a rectangular tool shed that is 8 meters wide and has an area of 96 square meters what is the length of Jason's tool shed? meters

Answers

Area = length x width
96 = length x 8
Length =96/8
Length = 12 metres

Will fan and medal. How is this correct?

3. A family is building a circular fountain in the backyard. The yard is rectangular and measures 7x by 6x and the fountain is going to be circular with a radius of 2x. Once the fountain is build, what will be the area of the remaining yard?
A. 38x^2
B. [x] 2x^2 (21 – 2pi)
C. 42x^2 – 2pix^2
D. 38pix^2,

Answers

The yard is rectangular with a measurement of 7x by 6x. 
The fountain is circular with a radius of 2x.
Since we are looking for the remaining area, we need to know the area of the rectangular backyard and the circular fountain.

The formula for a rectangle is 
A=lw
where:
 l=length
 w=width 

So, 
A=(7x)(6x)
  =42x^2

Now for the area of the circular fountain, 
A=

Step [tex]1[/tex]

Find the area of the rectangular yard

the area of the rectangular yard is equal to

[tex]A=L*W[/tex]

where

L is the length side of the rectangle

W is width side of the rectangle

in this problem we have

[tex]L=7x\ units\\W=6x\ units[/tex]

[tex]A=L*W[/tex]

[tex]A=7x*6x[/tex]

[tex]A=42x^{2}\ units^{2}[/tex]

Step [tex]2[/tex]

Find the area of a circular fountain

we know that

the area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

where

r is the radius of the circle

in this problem we have

[tex]r=2x\ units[/tex]

substitute

[tex]A=\pi (2x)^{2}[/tex]

[tex]A=4\pi x^{2}\ units^{2}[/tex]

Step [tex]3[/tex]

Find area of the remaining yard

Subtract the area of a circular fountain from the area of the rectangular yard

[tex]42x^{2}\ units^{2}-4 \pi x^{2}\ units^{2}=2x^{2}[21-2\pi][/tex]

therefore

the answer is the option B

[tex]2x^{2}[21-2\pi]\ units^{2}[/tex]

f(x) = cot x PRE CALC HELP PLS?!

Answers

check the picture below.

is it even?  well, even functions use the y-axis as a mirror, so a pre-image on the right-side, will be a mirror of the image on the left-side, but in this case it isn't so, if you put a mirror right on the y-axis, the left-side will look a bit different.

does it have a zero at x = 0?  well, just look at the graph, is the line touching the x-axis at 0? nope.

does it have an asymptote at 0?  well, surely you can see it right there.

Generate the first 5 terms of this sequence:

f(1) = 0 and f(2) = 1, f(n) = f(n - 1) + f(n - 2), for n > 2.

A. 0, -1, 1, 0, 2

B. 0, 1, 1, 2, 3

C. 0, 1, 2, 2, 3

D. 0, 1, 1, 2, 2

Please helppp! Thanks! <3,

Answers

We are given f(1) = 0 and f(2) = 1. Going forward, the term is the sum of the two previous terms. f(3) = f(2) + f(1) = 0 + 1 = 1. f(4) = f(3) + f(2) = 1 + 1 = 2 f(5) = f(4) + f(3) = 2 + 1 = 3 This matches answer B.

what is the solution of the following system?
4x-y=15
3x+2y=-8

(-1,-19)
(2,-7) <--- is this the right answer?
(4,-5)
(5,5),

Answers

4x-y = 15 3x+2y = -8 Multiplying the first equation by two makes for an easy elimination of the y variable. 8x - 2y = 30 3x + 2y = -8 Add vertically. 11x = 22. Divide by 11 on both sides and get x = 2. Plug into an equation. 4(2) - y = 15 8 - y = 15 8 = 15 + y 8 - 15 = y -7 = y. Thus the solution is indeed (2, -7).

The assessed value of property in Enterprise County is $196,000,000. The county supervisors feel the county needs $9,525,000 in revenue.
What is the tax rate (to 0.1 of a percent)?
5.1
4.9
4.7,

Answers

tax rate = ( $9,525,000 / $196,000,000 ) * 100% = 4.9%

Answer:

B. 4.9%.

Step-by-step explanation:

We have been given that the assessed value of property in Enterprise County is $196,000,000. The county supervisors feel the county needs $9,525,000 in revenue.

To find the tax rate we need to find $9,525,000 is what percent of $196,000,000.

[tex]\text{Tax rate}=\frac{\$9,525,000}{\$196,000,000}\times 100[/tex]

[tex]\text{Tax rate}=0.0485969387755102\times 100[/tex]

[tex]\text{Tax rate}=4.85969387755102\%[/tex]

Upon rounding our answer to nearest tenth of percent we will get,

[tex]\text{Tax rate}\approx 4.9\%[/tex]

Therefore, the tax rate is 4.9% and option B is the correct choice.

What is the quotient?
3x^2 – 11 + 60/x+5
3x – 11 + 60/x+5
3x^2 – 11 – 50/x+5
3x – 11 – 50/x+5

Answers

correct answer 3x – 11 + 60/x+5

Answer:

correct answer 3x – 11 + 60/x+5

Step-by-step explanation:

Which of the following points lie in the solution set to the following system of inequalities?

y ≤ x − 5
y ≤ −x − 4
(1, 10)
(−1, 10)
(10, 1)
(1, −10)

Answers

Only the point (1, -10) lies in the solution set.
Hi,
The answer is (1,-10)

The concession stand at the local high school sells pretzels and lemonade. The total cost of two pretzels and a lemonade is $5.75. The total cost of two lemonades is $0.25 more than the cost of a pretzel. What is the cost of a pretzel? $1.25 $2.00 $2.25 $2.75

Answers

The pretzel would be $2.25

Cost of a pretzel is equals to $2.25.

What is system of equations?

" A system of equations is a finite set of equations for which we find the common solution."

According to the question,

'x' represents the cost of  pretzel

'y' represents the cost of lemonade

As per situation given system of equation are,

Situation1: The total cost of two pretzels and a lemonade is $5.75, which can be represented by equation:

[tex]2x + y = \$5.75[/tex]                              ____(1)

Situation2: The total cost of two lemonades is $0.25 more than the cost of a pretzel, which can be represented by equation:

[tex]2y = 0.25 +x[/tex]                                _____(2)

Multiply equation (1) by 2 we get,

[tex]4x + 2y = \$11.5[/tex]                              ______(3)

Substitute the value of 2y from (2) in (3) to get the cost of pretzel,

[tex]4x + 0.25 +x = \$11.5[/tex]

⇒ [tex]5x = 11.5 - 0.25[/tex]

⇒ [tex]5x = 11.25[/tex]

⇒ [tex]x =\frac{11.25}{5}[/tex]

⇒[tex]x=\$2.25[/tex]

Hence, cost of a pretzel is equals to $2.25.

Learn more about system of equation here

https://brainly.com/question/13997560

#SPJ2

Helpp The Line Segment AB has endpoints at A(5,-3) and B(-2,0)

Answers

check the picture below, notice the red reflected image over the x-axis.

Calculate the sum or difference. Enter the answer as a fraction in lowest terms, using the slash ( / ) as the fraction bar.

3/4 + 4/5
Math~

Answers

the answer for this question 3/4 + 4/5 = 1 11/20 
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