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lina2011 [118]
3 years ago
12

Simplify the expression -3(x+3)-3+3x into standard form

Mathematics
1 answer:
timofeeve [1]3 years ago
6 0
That in standard form would be 12
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Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2, −5, 6), C(4, −2, −1), D(3, 4, −4
almond37 [142]

Answer:

Area = 71.3 sq unit

Step-by-step explanation:

a) We will use properties of parallelogram to verify the given vertices.

Property: Have a pair of parallel opposite sides

Hence, vectors AB AD BD BC CD AC. A pair should be parallel:

vectors

AB = A - B = (1, 1 , 3) - ( 2 , -5 , 6 ) = (-1 , 6 , -3)

AD = A - D = (1, 1 , 3) - (3, 4 , -4) = (-2 , -3 , 7)

BC = B - C = (2 , -5 , 6) - (4, -2 , -1) = (-2 ,-3 , 7)

CD = C - D = (4, -2 , -1) - (3, 4 , -4) = (1 , -6 , 3)

Hence we can see  that AB //CD and AD // BC as their unit vector co-efficents are identical/scalar multiple of each other.

b)

Equation of line AB = (1,1,3) + t*(-1 , 6 , -3 )

Point E = (1-t , 1+6t , 3 -3t) ... denotes an position of point E on line AB.

Choose a point on line CD, lets suppose C = ( 4 , -2 , -1 )

Vector EC = ( 1-t , 1+6t , 3-3t ) - (4 , -2 , -1 ) = (-3 -t , 3 +6t , 4 -3t)

For EC to be perpendicular to AB then dot product of AB . EC = 0

Hence,

EC . AB = -1 * (-3-t) -2*(3+6t) -3*(4-3t) = 0

3 + t -6 -12t -12+9t = 0

-2t-3 = 0

t = -3/2

Vector EC = (-3 -t , 3 +6t , 4 -3t) = (-1.5 , -6 , 8.5)

Area = magnitude (AB) * magnitude (EC)

Area = sqrt ((-1)^2 + 6^2 + (-3)^2) * sqrt ((-1.5)^2 + 6^2 + (8.5)^2)

Area = sqrt (46) * sqrt (442) / 2

Area = 71.3 unit^2

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3 years ago
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RideAnS [48]
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2 years ago
Mel wants to buy a pair of shoes that costs $120. She has saved $45 and has a job that pays her $10 per hour. The number of hour
maksim [4K]
<h2>Answer: 8</h2>

Step-by-step explanation:

10x+45 > 120\\10x+45-45 > 120-45\\10x > 75\\\frac{10x}{10} > \frac{75}{10} \\x > 7.5

Therefore, Mel has to work at least 7.5 hours or 8 total hours.

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1 year ago
Please help me with this question
Mrrafil [7]

Answers: Options A and D

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Polygon LMNO is similar to polygon QRST, and I and QR are
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Step-by-step explanation:

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