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3 years ago

What is the decimal form of 45/120

Mathematics

1 answer:

lapo4ka [179]3 years ago

8 0

Answer: 37.5 or 0.375

Step-by-step explanation:

to write 45/120 as a decimal you have to divide the numerator by the denominator of the fraction. we divide now 45 by 120 what we write down as 45/120 and get 0.375

Hope this helped!

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Help please i don’t know the answer

son4ous [18]

Answer:

$6A=8B=6\left[\begin{array}{ccc}-4&-1&-9\\-9&6&9\\-1&-1&3\end{array}\right]$ $-8\left[\begin{array}{ccc}-10&-2&-5\\9&-7&-1\\9&-4&2\end{array}\right]$

$=\left[\begin{array}{ccc}-24&-6&-54\\-54&36&54\\-6&-6&18\end{array}\right]$ $-\left[\begin{array}{ccc}-80&-56&-40\\72&-56&-8\\72&-32&16\end{array}\right]$

$=\left[\begin{array}{ccc}56&50&-14\\-120&92&62\\-78&26&2\end{array}\right]$

$So,~ A ~is ~your~ answer~$

<u>---------------------------</u>

<u>hope it helps..</u>

<u>have a great day!!</u>

7 0

2 years ago

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

Find the exact value of tan22.5 using the half angle formula.

mote1985 [20]

Tan(a/2) = sin a / (1 + cos a)
tan(45/2) = sin(45) / (1 + cos(45)) = (1/√2) / (1 + 1/√2) = (1/√2) / (√2 + 1)/√2 = 1/(√2 + 1) = (√2 - 1)

7 0

3 years ago

Read 2 more answers

What is the sum of all values of m that satisfy 2m (squared) -16m+8=0?

vodomira [7]

<h2>Steps:</h2>

So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:

$2m^2-16m=-8$

Next, divide both sides by 2:

$m^2-8m=-4$

Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:

-8 ÷ 2 = -4, (-4)² = 16

Add 16 to both sides of the equation:

$m^2-8m+16=12$

Next, factor the left side:

$(m-4)^2=12$

Next, square root both sides of the equation:

$m-4=\pm \sqrt{12}$

Next, add 4 to both sides of the equation:

$m=4\pm \sqrt{12}$

Now, while this is your answer, you can further simplify the radical using the product rule of radicals:

Product rule of radicals: √ab = √a × √b

√12 = √4 × √3 = 2√3.

$m=4\pm 2\sqrt{3}$

<h2>Answer:</h2>

In exact form, your answer is $m=4\pm \sqrt{12}\ \textsf{OR}\ m=4\pm 2\sqrt{3}$

In approximate form, your answers are (rounded to the hundreths) $m=7.46, 0.54$

6 0

3 years ago

Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books

slavikrds [6]

Answer:

2/3

Step-by-step explanation:

Let x be the number of books that Millicent has. So the number of books that Harold has is x/2. And the number of book that Harold is bringing to the new home is (x/2)/3 = x/6.

The home has enough room for another half of Millicent's books, which is x/2. So the total books capacity of the new home is

$\frac{x}{6} + \frac{x}{2} = \frac{x}{6} + \frac{3x}{6} = \frac{4x}{6} = \frac{2x}{3}$

Since x is also the number of books in Millicent's old library capacity, we can conclude that the fraction of Millicent's old library capacity to the new home's library capacity is 2/3, or 2 thirds

3 0

3 years ago