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3 years ago

Select the correct answer. What is the solution set of 4x = y and 2x2 − y = 0? {(0.5, -0.5), (2, -8)} {(0, 0), (2, 8)} {(1.5, 2)

, (8, 2)} {(-1.5, -2), (2, 8)}

Mathematics

1 answer:

Vesna [10]3 years ago

8 0

$\left\{\begin{array}{ccc}4x=y&(1)\\2x^2-y=0&(2)\end{array}\right\\\\/\text{substitute (1) to (2)/}\\\\2x^2-4x=0\\2x(x-2)=0\iff 2x=0\ \vee x-2=0\\\\x=0\ \vee\ x=2\\\\for\ x=0\to y=4\cdot0=0\\for\ x=2\to y=4\cdot2=8\\\\(0;\ 0);\ (2;\ 8)\\\\Answer:\ \{(0;\ 0);\ (2;\ 8)\}$

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Solve log4 (y – 9) + log4 3 = log4 81.

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3 years ago

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ohaa [14]

Answer:

Step-by-step explanation:

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Q(x)=x^3+ax^2+2b is divided by (x-3) and has a remainder of 4. Find the values of "a" and "b"

Sati [7]

Answer:

Let p(x) = x3 + ax2 + bx +6

(x-2) is a factor of the polynomial x3 + ax2 + b x +6

p(2) = 0

p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0

7 +2 a +b = 0

b = - 7 -2a -(i)

x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.

p(3) = 3

p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3

11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)

Equating the value of b from (ii) and (i) , we have

(- 7 -2a) = (-10 - 3a)

a = -3

Substituting a = -3 in (i), we get

b = - 7 -2(-3) = -7 + 6 = -1

Thus the values of a and b are -3 and -1 respectively.

Step-by-step explanation:

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3 years ago

At a concession stand five hotdogs and two hamburgers cost 8.00 two hotdogs and five hamburgers cost 9.50 find the cost of one h

Svetach [21]

Think of this situation as a system of equations.

let y be the price of hotdogs
let x be the price of hamburgers

5y + 2x = 8
2y + 5x = 9.50

now use your solution method of choice
substitution, elimination, matrices, etc

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3 years ago

A college student with a bachelors degree in nursing from an accredited institution has an 86.74% chance of getting hired full t

Vladimir79 [104]

Answer:

86.74% probability of a Madonna University nursing student getting hired within 6 months of graduation given that they complete their degree here.

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Compute the probability of a Madonna University nursing student getting hired within 6 months of graduation given that they complete their degree here.

In this problem, we have that:

Event A: Completing their degree there.

There is a 34.72% chance of a student interested in a nursing degree not making it through the program.

So 100 - 34.72% = 65.28% = 0.6528 probability of completing their degree. So P(A) = 0.6528.

Event B: Getting hired

86.74% chance of getting hired full time in a hospital setting within 6 months of graduation.

Completing their degree and getting hired:

$P(A \cap B) = 0.6528*0.8674$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.6528*0.8674}{0.6528} = 0.8674$

86.74% probability of a Madonna University nursing student getting hired within 6 months of graduation given that they complete their degree here.

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3 years ago