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Temka [501]
2 years ago
6

Francine applies the commutative property to the product. (−8/9)⋅(−13)⋅(18) Which expression illustrates the commutative propert

y applied to the product? (−8/9)⋅(18)⋅(−13) [(−8/9)⋅(−13)]⋅(18) (−8/9)⋅[(−13)⋅(18)] (−8/9)⋅(−13)⋅(18)
Mathematics
2 answers:
oksian1 [2.3K]2 years ago
4 0

The commutative property implies that, the order of multiplication is not important.

(-\frac 89) \cdot (18) \cdot (-13) is true

Commutative property of multiplication states that:

If a \times b  = b \times a

The expression is given as:

(-\frac 89)\cdot (-13) \cdot (18)

To get the commutative expression, we simply change the position of each factor in the expression.

So, some possible equivalent expressions are:

(18) \cdot (-13) \cdot (-\frac 89)

(18)\cdot (-\frac 89) \cdot (-13)

(-13) \cdot (18) \cdot (-\frac 89)

There are several other equivalent expressions.

From the list of options;

(-\frac 89) \cdot (18) \cdot (-13) is true

Read more about commutative property at:

brainly.com/question/7037119

Firlakuza [10]2 years ago
4 0

Answer:(−8/9)⋅(18)⋅(−13)

Step-by-step explanation: I took the test ;)

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Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
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Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

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