23. Drug Testing Job Applicants Find the probability of selecting someone who uses drugs.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

34kurt

Answer:

Infinitely many solutions

Step-by-step explanation:

First, let's organize the equations of the lines into slope-intercept form.

x + 4y = 1
=> 4y = -x + 1
=> y = -x/4 + 1/4

And,

2x + 8y = 2
=> 8y = -2x + 2
=> y = -2x/8 + 2/8
=> y = -x/4 + 1/4

Since both the graphs are the same, the two equations have infinitely many solutions.

5 0

1 year ago

A number cube is rolled and a coin is tossed. What is the probability of rolling a number less than 1 and heads?

Fittoniya [83]

I believe it is zero, because there is no number less than 1.

3 0

3 years ago

Solve: x2 − x − 6/x2 = x − 6/2x + 2x + 12/x After multiplying each side of the equation by the LCD and simplifying, the resultin

Vesna [10]

The resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

According to the given question.

We have an equation

$\frac{x^{2}-x-6 }{x^{2} } = \frac{x-6}{2x} +\frac{2x+12}{x}$

So, to find the resulting equation of the above equation we need to simplify.

First we will take LCD

$\frac{x^{2} -x - 6 }{x^{2} } = \frac{x -6+2(2x + 12)}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } =\frac{x-6+4x+24}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } = \frac{5x +18}{2x}$

Multiply both the sides by x.

$\frac{x^{2}-x-6 }{x} = \frac{5x+18}{2}$

Again multiply both the sides by x

$2x^{2} -2x-12 = 5x^{2} +18x$

$\implies 5x^{2} -2x^{2} +18x +2x +12 = 0$

$\implies 3x^{2} + 18x+2x + 12 = 0$

Factorize the above equation

⇒3x(x+6)+2(x+6) = 0

⇒(3x + 2)(x+6) = 0

⇒ x = -2/3 or x = -6

Hence, the resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

Find out more information about equation here:

brainly.com/question/2976807

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7 0

1 year ago

3(x + 4) = 3x + 12 solve for x

iris [78.8K]

Answer:

all real numbers.

Step-by-step explanation:

First, distribute 3 to all terms within the parenthesis:

3(x + 4) = 3(x) + 3(4) = 3x + 12

3x + 12 = 3x + 12

Because both sides are the same, your answer for x is "all real numbers".

~

8 0

2 years ago

Suppose that the trace of a 2×2 matrix a is tr(a)=15 and the determinant is det(a)=50. find the eigenvalues of

IrinaK [193]

Recall that the characteristic polynomial of a 2x2 matrix $\mathbf A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is

$\det(\mathbf A-\lambda\mathbf I)=\begin{vmatrix}a-\lambda&b\\c&d-\lambda\end{vmatrix}=(a-\lambda)(d-\lambda)-bc=\lambda^2-(a+d)\lambda+(ad-bc)$

but $\det(\mathbf A)=ad-bc$ and $\mathrm{tr}(\mathbf A)=a+d$ , so the characteristic polynomial for $\mathbf A$ is

$\lambda^2-\mathrm{tr}(\mathbf A)\lambda+\det(\mathbf A)$

We're given that the trace is 15 and determinant is 50, so the characteristic polynomial for the matrix in question is

$\lambda^2-15\lambda+50$

and the eigenvalues are those $\lambda$ for which the characteristic polynomial evaluates to 0.

$\lambda^2-15\lambda+50=(\lambda-5)(\lambda-10)=0\implies\lambda=5,\lambda=10$

5 0

2 years ago