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3 years ago

The Hamilton Brush Company issued 2500 shares of common stock worth 100,000,000 total.What is the par value of each share

Mathematics

1 answer:

Marrrta [24]3 years ago

7 0

The par value of each share is
100,000,000÷2,500
=40,000 per share

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The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

4 years ago

Fran has a poster that measures 3/4 square yard in area the length of the poster is 1/3 yard what is the width of the poster

Harrizon [31]

Answer:

9/4 yards

Step-by-step explanation:

A poster is a rectangle.

Area of rectangle = Length × Width

Given:

Area = 3/4 yd

Length = 1/3 yd

Substitute the given values to the equation.

3/4 = 1/3 × w

3/4 = 1/3w

3/4 ÷ 1/3 = w

3/4 × 3/1 = w

9/4 = w

6 0

3 years ago

a law firm charges $100 per hour plus a $300 origination fee for its services find a function notation

Kisachek [45]

F(t)= $100 x h + 300 A reasonable domain is (1,2,3) and the range is ($400,$500,$600)

5 0

3 years ago

Write in point-slope form an equation of the line that passes through the

QveST [7]

Answer:

$y+6 = - 5(x-4)$

Step-by-step explanation:

With the given information, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line. Substitute values for the $m$ , $x_1$ , and $y_1$ to find the answer.

$m$ represents the slope, so substitute -5 in its place. The $x_1$ and $y_1$ represent the x and y values of one point the line intersects, so substitute 4 for $x_1$ and -6 for $y_1$ . This gives the following equation:

$y+6 = - 5(x-4)$

3 0

3 years ago

a patient is receiving 1 liter of IV fluids every 8 hours at that rate how much will he recieve in 3 hrs

ASHA 777 [7]

Answer:

Step-by-step explanation:

1litres=8

x=3

x=0.375 litres

3 0

3 years ago