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Rashid [163]
3 years ago
11

Find the rational number halfway between 5/16 and 7/8

Mathematics
1 answer:
saveliy_v [14]3 years ago
8 0
\left(\frac{5}{16}+\frac{7}{8}\right):2=\left(\frac{5}{16}+\frac{14}{16}\right):\frac{2}{1}=\frac{5+14}{16}\cdot\frac{1}{2}=\frac{19}{16}\cdot\frac{1}{2}=\frac{19}{32}
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Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, −1), B(4, −3, 0), C(1
zavuch27 [327]

Answer:

Angle at vertex  A : 59.2° B: 61.7° C : 59.1°

Step-by-step explanation:

1. First find the length of the vectors  

AB = B-A = (4-1, 3-0, 0-1) = (3, 3, -1)

AC = C-A = (1-1, 4-0, 3-1) = (0, 4, 2)

BC = C-B = (1-4, 4-3, 3-0) = (-3, 1, 3)

2. Find magnitude of the vectors

|AB| = √(3^2+3^2+〖(-1)〗^2 )=√19  

|AC| = √(0^2+4^2+2^2 )=2√5

|BC| = √(〖(-3)〗^2+1^2+3^2 )=√19

3. Find the angles between them

cos θ = (a.b)/(|a||b|) -----> θ = arc cos ((a.b)/(|a||b|))

AB, AC : θ =arc cos (AB.AC)/(|AB||AC|) = arc cos ( (3.0+3.4+ -1.2)/(√19  x 2√5)=  10/(2√95) ) =59.136, which is approximately 59.14°

AB, BC : θ =arc cos (AB.BC)/(|AB||BC|) = arc cos( (3.-3+3.1+ -1.3)/(√19  x √19)=  (-9)/19 ) = 118.27°

Because of the direction of BC is pointing relative to AB this is the angle outside the triangle, and we should find the supplementary angle.

180-118.27 = 61.73°

If we used –(BC) = CB in the formula (just negate the numerator) we would have gotten the correct angle on first try.

The 3rd angle should be what’s left after subtracting from 180°;

180-61.73-59.14 = 59.13 °

You can confirm using the formula again :

AC, BC : θ =arc cos (AC.BC)/(|AC||BC|) = arc cos( (0.-3+4.1+ 2.3)/(√19  x 2√5)=  10/(2√95) = 59.13°

Rounding everything up so they add up to 180 degrees we have Angle at vertex  A : 59.2° B: 61.7° C : 59.1°

7 0
3 years ago
HELP!! Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are add
vekshin1
1/4*x -  1/6*y= 5    |*18    
4/5 *x + 3/8*y = 10 | *8

18/4*x                  -3*y= 90
32/5*x                + 3y   = 80
-------------------------
18/4*x+32/5*x   /       = 170

The answer is a





4 0
3 years ago
Is there a dilation that maps shape I onto shape II? If so, what is the scale factor, and is it an enlargement or a reduction?
katrin2010 [14]

Answer:

Enlargement.

Scale Factor: 3

Step-by-step explanation:

Use points to find the enlargement. Typically, you will use all the points.

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B(2 , 1) ⇒ B'(6 , 3)

C(1 , 2) ⇒ C'(3 , 6)

D(2 , 2) ⇒ D'(6 , 6)

To find the scale factor, simply divide the Point' with the original Point. Use any number.

A'(3 , 3)/(A(1 , 1)) = 3

B'(6 , 3)/(B(2 , 1)) = 3

C'(3 , 6)/(C(1 , 2)) = 3

D'(6 , 6)/(D(2 , 2)) = 3

Your scale factor is 3.

~

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