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
MrRa [10]
2 years ago
7

Find the Value of k that will make the function f(x) continuous everywhere.​

Mathematics
1 answer:
cricket20 [7]2 years ago
6 0

well, if that function f(x) were to be continuos on all subfunctions, that means that whatever value 7x + k has when x = 2, meets or matches the value that kx² - 6 has when x = 2 as well, so then 7x + k = kx² - 6 when f(2)

f(x)= \begin{cases} 7x+k,&x\leqslant 2\\ kx^2-6&x > 2 \end{cases}\qquad \qquad f(2)= \begin{cases} 7(2)+k,&x\leqslant 2\\ k(2)^2-6&x > 2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 7(2)+k~~ = ~~k(2)^2-6\implies 14+k~~ = ~~4k-6 \\\\\\ 14~~ = ~~3k-6\implies 20~~ = ~~3k\implies \cfrac{20}{3}=k

You might be interested in
What is 12 3/20 in simplest form?
Levart [38]

Answer:

12 3/20 is the simplest form

4 0
3 years ago
A cheetah can run 70 miles per hour. what is this speed in feet per hour? explain work,
MArishka [77]
So 70 miles per hour is 70 mile/1hour
1 mile=5280 feet
70 tmes 5280=feet=36,960

so 36,960 feet per hour
8 0
3 years ago
Need the answer thank you!
ohaa [14]

Answer:

256.

Step-by-step explanation:

1 × 4 = 4

4 × 4 = 16

16 × 4 = 64

64 × 4 = 256

4 0
3 years ago
Read 2 more answers
A submarine 625 feet below sea level ascends (rises up) 575 feet before descending (submerging down) another 455 feet. Describe
blagie [28]

Answer:

505ft below the surface

Step-by-step explanation:

subtract 575 from 625 and then add 455 to get your final answer.

4 0
3 years ago
A migraine sufferer took Two 400mg doses of naproxen. The half-life for
12345 [234]

Answer:

If y(t) is the mass (in mg) remaining after t years, then y(t) = y(0) (0.5)^{t/T} = 400 (0.5)^{t /4}, where T is the half-life period and y(0) is the amount at t = 0 years (initial).

Then at t = 20:

y(20) = 400 (0.5)^{20 /4} = \text{12.5 mg}

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • What is the data set
    5·1 answer
  • What value of q make the equation true 20/q 7/9
    6·1 answer
  • Find the number of real number solutions for the equation. x2 – 3x + 8 = 0<br><br><br> 1<br><br> 0
    9·1 answer
  • What does 2/4 + 5/10 equal
    13·1 answer
  • Pls help me^^
    14·2 answers
  • Which undefined term is used to define an angle ?
    8·2 answers
  • A 2013 study by pediatrician investigates whether it in better to give children the diphtheria, tetanus and pertussis (DTaP) vac
    11·2 answers
  • What makes 3+7+2 = +2
    14·1 answer
  • In the following diagram,what do the red arrows on the line mean?
    8·1 answer
  • The square of the product of 4 and a number.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!