Question

question:17
the owner of a cellphone store wants to make a profit for her brand-new, reasonable, and also in-demand cellphone. she chooses a linear relationship to determine values for the probable phones market price. the linear function is ( -36x^2 - 324x - 6480 = 0 ). to solve for ( x ), the owner first factors 360 out of the polynomial expression (and then factors out the negative). which of the following is one of those factors?
a ( x + 12 )
b ( x - 2 )
c ( x + 24 )
d ( x - 14 )
question:18
find the inverse.
7 10
question:19
which of the following is equivalent to ( \frac{\frac{2}{x - 1} + \frac{3x + 4}{x^2 + x + 1}}{\frac{4x^2}{4x^2 - 2x + 4} - \frac{4x^2 - 8x + 4}{4x^2 - 8x + 4}} )?
a ( \frac{1}{x - 1} )
b ( \frac{2x - 1}{x + 1} )
c ( \frac{(x - 1)(x - 2)}{(x + 1)(x - 2)} )
d ( \frac{(x + 1)(x - 2)}{(x - 1)(x + 2)} )
e ( \frac{(x + 1)(x + 2)}{(x - 1)(x - 2)} )
question:20
turn is not printable

Explanation:

Step1: Identify the matrix

The given matrix is \(

$$\begin{bmatrix}7&1\\1&10\end{bmatrix}$$

\). Let's denote this matrix as \(A=

$$\begin{bmatrix}a&b\\c&d\end{bmatrix}$$

\), where \(a = 7\), \(b = 1\), \(c = 1\), \(d = 10\).

Step2: Calculate the determinant

The determinant of a \(2\times2\) matrix \(A=

$$\begin{bmatrix}a&b\\c&d\end{bmatrix}$$

\) is given by \(\det(A)=ad - bc\).
Substituting the values, we get \(\det(A)=(7\times10)-(1\times1)=70 - 1 = 69\).

Step3: Find the inverse formula

The inverse of a \(2\times2\) matrix \(A\) is \(\frac{1}{\det(A)}

$$\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$$

\) (when \(\det(A)
eq0\)).

Step4: Substitute values to find the inverse

Since \(\det(A) = 69\), \(a = 7\), \(b = 1\), \(c = 1\), \(d = 10\), the inverse \(A^{-1}\) is:

$$ \frac{1}{69}
LATEXBLOCK4
=
LATEXBLOCK5
$$

Answer:

The inverse of the matrix \(

$$\begin{bmatrix}7&1\\1&10\end{bmatrix}$$

\) is \(

$$\begin{bmatrix}\frac{10}{69}&-\frac{1}{69}\\-\frac{1}{69}&\frac{7}{69}\end{bmatrix}$$

\)