1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kondaur [170]
3 years ago
7

Find the value of the constant k that makes the function continuous. ​g(x)equals=startset start 2 by 2 matrix 1st row 1st column

startfraction 2 x squared minus 4 x minus 16 over x minus 4 endfraction 2nd column if x not equals 4 2nd row 1st column kx minus 16 2nd column if x equals 4 endmatrix 2x2−4x−16 x−4 if x≠4 kx−16 if x=4
Mathematics
2 answers:
jolli1 [7]3 years ago
8 0

Answer:

The value of k is 7.

Step-by-step explanation:

Given function,

f(x)=\left\{\begin{matrix}\frac{2x^2-4x-16}{x-4} & x\neq 4\\ kx-16 & x=4\end{matrix}\right.

The function f(x) would be continuous, if,

\lim_{x\rightarrow 4} \frac{2x^2-4x-16}{x-4}=f(4)

\lim_{x\rightarrow 4} 2(\frac{x^2-2x-8}{x-4})=4k-16

\lim_{x\rightarrow 4} 2(\frac{x^2-4x+2x-16}{x-4})=4k-16

\lim_{x\rightarrow 4} 2(\frac{x(x-4)+2(x-4)}{x-4})=4k-16

\lim_{x\rightarrow 4} 2(\frac{(x+2)(x-4)}{x-4})=4k-16

\lim_{x\rightarrow 4} 2(x+2)=4k-16

2(4+2) = 4k-16

2(6)=4k-16

12+16 = 4k

\implies 4k=28\implies k=7

Hence, the value of k would be 7.

tiny-mole [99]3 years ago
7 0
You seem to have
.. g(x) = {(2x^2 -4x -16)/(x -4) . . . x ≠ 4
.. .. .. .. ..{ kx -16 . . . . . . . . . . . . . . x=4

The first expression can be simplified to
.. (2x^2 -4x -16)/(x -4) = 2(x +2)(x -4)/(x -4) = 2(x +2) . . . . x ≠ 4
At x=4, this simplified version has the value
.. 2(4 +2) = 12

To make the alternate definition of g(x) have that same value at x=4, we must have
.. k*4 -16 = 12
.. 4k = 28
,, k = 7

The constant k must be 7 for the function to be continuous at x=4.
You might be interested in
3. Sophie and Jackie each have a collection of baseball cards, Jackie has 5 more cards than
IRISSAK [1]

Answer:

Sophie has 12.5 cards

Step-by-step explanation:

Let

x -----> number of cards Sophie has

y -----> number of cards Jackie has

we know that

x+y=30 -----> equation A  

y=x+5 -----> equation B

Solve by substitution

Substitute equation B in equation A and solve for x

x+(x+5)=30

2x=30-5

x=12.5 cards

Note I assume the problem was invented without taking into account the result, because the amount of cards should be a whole number

5 0
3 years ago
If ln(a)=2, ln(b)=3, and ln(c)=5, evaluate the following:<br><br> ln(a^-4/b^1 c^1)
Mila [183]
Ln ( a^(-4) / b^1  c^1 ) =
= ln a ^(-4) - ( ln b + ln c ) =
= - 4 ln a - ln b - ln c =
= - 4 * 2 - 3 - 5 =
= - 8 - 3 - 5 = - 16
4 0
3 years ago
Complete the square to transform the quadratic equation into the form (x – p)2 = q. x2 - 12x - 5 = 7 A) (x - 36)2 = 9 B) (x - 6)
iren2701 [21]

x2 - 12x - 12 = 0

(x - 6)2 - 48 = 0

(x - 6)2 = 48

Hence, the answer is (B).

6 0
3 years ago
Read 2 more answers
Will mark brainliest
Varvara68 [4.7K]

Answer: I don’t think u gave enough info

Step-by-step explanation:

3 0
3 years ago
100,000 equals 10 to the what power?
Likurg_2 [28]
100,000 equals 10 to the power of 5, hope helps.
4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the surface area of the prism 2ft 1ft 3ft and 2.2ft
    12·1 answer
  • Tina has been dieting for a total of 13 weeks. She lost 3 pounds on the first week of her diet, but gained back a pound on the s
    8·1 answer
  • Carla had $40 to spend at the mall. she spent 20% of her money on lunch and 3/4 of her remaining money on a necklace. what fract
    12·1 answer
  • Which expression is equivalent to the following complex fraction?
    5·1 answer
  • Help please anyone help please
    12·2 answers
  • Find the number which when added to 10 times itself gives 264
    5·1 answer
  • A company rents out 11 food booths and 24 game booths at the county fair. The fee for a food booth is $175 plus $5 per day. The
    5·1 answer
  • Can someone please help me with this math question please. Please
    8·1 answer
  • TheUnlisted????????????
    13·1 answer
  • p+3w=-79-5p+w=-5Solve the system using the elimination method if there is no solution put no solution if there is infinite solut
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!