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2 years ago

What is the determinant of this matrix:

Mathematics

2 answers:

melisa1 [442]2 years ago

7 0

$\\ \rm\Rrightarrow \left|\begin{array}{ccc}0 &8 \\ 7& 0\end{array}\right|$

$\\ \rm\Rrightarrow 0-8(7)$

$\\ \rm\Rrightarrow 0-56$

$\\ \rm\Rrightarrow -56$

vodka [1.7K]2 years ago

6 0

Answer:

-56

Step-by-step explanation:

Formula to get determinant is::

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc$

0(0)-8(7)

0 - 56

-56

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Is EFGH below a rectangle

poizon [28]

Answer:

D. No, because EFGH is a parallelogram but it’s diagonals are not congruent

Step-by-step explanation:

The differences between the end points of the diagonals are ...

F -H = (1, 1) -(2, -5) = (1 -2, 1 -(-5)) = (-1, 6)

G -E = (4, -2) -(-1, -2) = (4 -(-1), -2 -(-2)) = (5, 0)

The length of FH is more than 6, the length of GE is exactly 5. The diagonals are different length, so the figure cannot be a rectangle.

The midpoints of the diagonals will be in the same place if the sum of their end points is the same. (Dividing each sum by 2 gives the midpoint of that segment.)

F+H = (1, 1) +(2, -5) = (3, -4)

G+E = (4, -2) +(-1, -2) = (3, -4)

The diagonals bisect each other (have the same midpoint), so the figure is a parallelogram.

EFGH is a parallelogram, but not a rectangle: its diagonals are not congruent.

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Nostrana [21]

Check out the image attachment for one way to draw this problem out. Notice how angles AEC and DEB are vertical angles, so that means they are congruent angles

(measure of angle AEC) = (measure of angle DEB)
6x + 20 = 10x
6x + 20-6x = 10x-6x ... subtract 6x from both sides
20 = 4x
4x = 20
4x/4 = 20/4 ... divide both sides by 4
x = 5

The value of x is 5.

Let's check the answer
6x + 20 = 10x
6*5 + 20 = 10*5 ... replace every x with 5
30+20 = 50
50 = 50
We have confirmed the answer.

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Step-by-step explanation:

3x + y = 15

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