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3 years ago

What is the determinant of the coefficient matrix of the system {4x+3y+2z=0 -3x+y+5z=0 -x-4y+3z=0

Mathematics

1 answer:

slava [35]3 years ago

7 0

Answer:

130

Step-by-step explanation:

You want the determinant of the matrix ...

$\left[\begin{array}{ccc}4&3&2\\-3&1&5\\-1&-4&3\end{array}\right]$

One way to figure it is as the difference between the sum of products of the down-diagonals and the sum of products of the up-diagonals:

D = (4)(1)(3) +(3)(5)(-1) +(2)(-3)(-4) -(-1)(1)(2) -(-4)(5)(4) -(3)(-3)(3)

= 12 -15 +24 +2 +80 +27

D = 130

The determinant of the coefficient matrix is 130.

_____

Many scientific and graphing calculators and web sites can perform this calculation for you.

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A pair of congruent angles are described as follows: The degree measure of one angle is three more than twice a number, and the

Fiesta28 [93]

Answer:

The measure of the angles in degree is 57.5 degrees

Step-by-step explanation:

If two angles are congruent, they are equal in value

Let the number be x

2x + 3 = 3x-54.5

Thus;

3x-2x = 54.5 + 3

x = 57.5

6 0

3 years ago

Which description best compares the graphs given by the equations:

nexus9112 [7]

x - 5y = -5, -5x - 25y = 25

First, you'll need to get the x variable by itself.

x - 5y = -5
 +5 +5
 x = 0
So x is plotted on the 0.

For the second part of the first equation, you'll be looking for what the y variable represents.

x - 5y = -5
-x -x
 -5y = -5
 5 5
 y = 1
So y is plotted on the 1 on the vertical line above the 0.

For the first part of the second equation, you'll do the same thing as in the first equation.

-5x - 25y = 25
 +25 +25
 -5x = 50
 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.

For the second part of the second equation, you will do the same thing as in the first equation.

-5x - 25y = 25
+5 +5
 -25y = 30
 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.

<h2>Answer: B) Perpendicular</h2>

Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.

Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.

Intersecting means the lines may or may not be of equal length but will touch each other.

6 0

2 years ago

Planes S and R both intersect plane T Which statements are true based on the diagram? Select three options OPlane S contains poi

jeka94

Answer:

Options (2), (4) and (5)

Step-by-step explanation:

Option (1).

Planes S contains points B and F.

False.

(Point B lies on plane S and point F lies on plane R)

Option (2).

The line containing points A and B lie on the plane T.

True.

(points A and B lie on plane T)

Option (3).

Line v intersects lines x and y at the same plane.

False.

Option (4).

Line z intersects plane S at point C.

True.

Option (5).

Planes R and T intersect at line y.

True.

5 0

4 years ago

A circle has an equation (x+2)2+(y−5)2=64. What is 34 of its area.

skad [1K]

Answer:

3/4 of the area of the circle is of $48\pi$ squared units.

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In which the center is $(x_0,y_0)$ and r is the radius.

Area of a circle:

The area of a circle of radius r is given by:

$A = \pi r^2$

Circle (x+2)² + (y-5)² = 64

Comparing with the standard equation, we have that:

$r^2 = 64$

Area of the circle:

$A = \pi r^2 = 64\pi$

What is 3/4 of its area?

$\frac{3A}{4} = \frac{3*64\pi}{4} = 3*16\pi = 48\pi$

3/4 of the area of the circle is of $48\pi$ squared units.

8 0

3 years ago

Match each equation with a diagram:

denis23 [38]

Answers:
Equation 1: B
Equation 2: D
Equation 3: A
Equation 4: C

*I am pretty sure are right

3 0

3 years ago

Read 2 more answers