Which of the following is a multiple of 8?<br> A: 22<br> B: 48<br> C: 18<br> D: 30

The function Q(x)=2x^2-kx+18. For what value of k does Q(x) have one distinct real solution? (NEEDS TO BE DONE WITHIN 2 HOURS!)

Aliun [14]

Answer:

k = 12

Step-by-step explanation:

Given:

The equation $Q(x)=2x^2-kx+18$

To find:

Value of $k = ?$ for which the given equation has one distinct real solution.

Solution:

The given equation is a quadratic equation.

There are always two solutions of a quadratic equation.

For the equation: $ax^{2} +bx+c=0$ to have one distinct solution:

$b^2 - 4ac = 0$

Here,

a = 2,

b = -k and

c = 18

Putting the values, we get:

$(-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12$

The equation becomes:

$Q(x)=2x^2-12x+18$

And the one root is:

$2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3$

4 0

3 years ago

Can someone help me i keep getting different answer!!

spayn [35]

Answer:

The second option: 3 (6 - 5n)/20n

Step-by-step explanation:

Make sure all fractions have a common denominator:

Step 1. Find a common multiple between all three denominators

5, 4, and 10 all have a common multiple of 20. Proof: 5 × 4 = 20, 4 × 5 = 20, and 10 × 2 = 20

Step 2. Multiply the denominators to get to 20. Whatever you do to the bottom (denominator) must be done to the top (numerator).

1/5n × 4/4 = 4/20n

3/4 × 5n/5n = 15n/20n

7/10n × 2/2 = 14/20n

Your fractions now all have a common denominator of 20n.

Rewrite the equation using the new fractions:

4/20n - 15n/20n + 14/20n

Only focus on adding/subtracting the numerators; the denominators will stay the same: 20n.

(4 - 15n + 14)/20n

Combine like terms:

(18 - 15n)/20n

Factor out any numbers possible:

3(6 - 5n)/20n

Note* 3 go into both 18 and 15, which allows us to factor 3 out. 18 ÷ 3 = 6 and 15 ÷ 3 = 5, giving us our new numbers inside the parentheses.

6 0

3 years ago

Solve. 3(x+1)-2x=-6

RideAnS [48]

D.) x = - 9

C.) x = 0

Hope that helps, Good luck! (:

4 0

3 years ago

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with

NISA [10]

Answer:

a) 0.125

b) 7

c) 0.875 hr

d) 1 hr

e) 0.875

Step-by-step explanation:l

Given:

Arrival rate, λ = 7

Service rate, μ = 8

a) probability that no requests for assistance are in the system (system is idle).

Let's first find p.

a) ρ = λ/μ

$\frac{7}{8} = 0.875$

Probability that the system is idle =

1 - p

= 1 - 0.875

=0.125

probability that no requests for assistance are in the system is 0.125

b) average number of requests that will be waiting for service will be given as:

λ/(μ - λ)

$= \frac{7}{8 - 7}$

= 7

(c) Average time in minutes before service

= λ/[μ(μ - λ)]

$= \frac{7}{8(8 - 7)}$

= 0.875 hour

(d) average time at the reference desk in minutes.

Average time in the system js given as: 1/(μ - λ)

$= \frac{1}{(8 - 7)}$

= 1 hour

(e) Probability that a new arrival has to wait for service will be:

λ/μ =

${7}{8}$

= 0.875

5 0

3 years ago

Hellppp im so stuck

77julia77 [94]

35= 5,000

45=15,000

55=50,000

3 0

4 years ago

Which of the following is a multiple of 8? A: 22 B: 48 C: 18 D: 30