Which of the following sets of ordered pairs represents a function?

The bacteria in an old piece of cheese is growing at a rate that can be modeled by y = 280 • 2x. Determine which number represen

Sav [38]

2 is the growth rate

3 0

3 years ago

Match the features of the graph of the rational function.

Sunny_sXe [5.5K]

After applying algebraic analysis we find the right choices for each case, all of which cannot be presented herein due to length restrictions. Please read explanation below.

<h3>How to analyze rational functions</h3>

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the rational function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a vertical asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - Horizontal asymptote exists and represents the end behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

$y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}$

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

How many holes? 2
One horizontal asymptote along the line where y always equals what number: 0
This function has x-intercepts? True
One vertical asymptote along the line where x always equals what number: 1
There is a hole where the y-intercept should be? False

To learn more on rational functions: brainly.com/question/27914791

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5 0

2 years ago

Use a matrix equation to solve the system of linear equations. left brace Start 2 By 1 Matrix 1st Row 1st Column 2nd Row 1st Col

natali 33 [55]

Answer:

$\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]$

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

$\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]$

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

$A^{-1}$ = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = $\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]$

$A^{-1}$ = $\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]$ = $\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]$

4 0

2 years ago

Sarah and Eva are swimming use the ratio table to determine who is the faster swimmer

pentagon [3]

Sarahtime (min)    {3 } 5 12 17
distance (meters) {75} 125   300 425

Eva time (min)     {2}    7 10    20
distance (meters)    {52} 182   260 520

Sarah:meters over min =75 over 3 = 25 over 1
25 meters per min

Eva :meters over min= 52 over 2 =26 over 1
26 meters per min

eva is the faster swimming because 26 meters per min is faster then 25 meters per min .

i hope this help

6 0

2 years ago

Write the expression in simplest form. (-11/2x + 3) -2 (-11/4x - 5/2) = ?

mina [271]

(- $\frac{11}{2}$ x + 3) - 2(- $\frac{11}{4}$ x - $\frac{5}{2}$ ) = ?

in simplest form-

(-5 $\frac{1}{2}$ x + 3) -2( 2 $\frac{3}{4}$ x -2 $\frac{1}{2}$ )

6 0

2 years ago