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3 years ago

4/16 in simplest form

Mathematics

2 answers:

vova2212 [387]3 years ago

6 0

4 goes into 4 once, and then into 16 4 times. Making the final answer 1/4

ozzi3 years ago

5 0

1/4 is 4/16 in simpliest form

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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.

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

6 0

3 years ago

Can someone write down the answers pls!!!!!!!!!!

snow_lady [41]

Step-by-step explanation:

6b x>=1

6c y>7

7a x>3

7b -2<=2x<6

-1<=x<3

answer:-1,0,1,2,3

7 0

3 years ago

What is 8.25 as a fraction in simplest form?

vekshin1

8 is a whole number, so this will be the whole number part of our mixed number.

0.25 is a decimal, where 25 is in the HUNDREDths place, so we write 25 as a fraction over 100.

$\sf\dfrac{25}{100}$

Simplify by dividing 25 to the numerator and denominator.

$\sf25\div25=1$
$\sf100\div25=4$

So our fraction is $\sf8\dfrac{1}{4}$

0.55 is a decimal, where 55 is in the HUNDREDths place, so we write 55 as a fraction over 100.

$\sf\dfrac{55}{100}$

Simplify by dividing 5 to the numerator and denominator.

$\sf55\div5=11$
$\sf100\div5=20$

So our fraction is $\sf\dfrac{11}{20}$

$\sf\dfrac{5}{8}$

To convert this to a decimal, just divide 5 / 8

$\sf5\div8=0.625$