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3 years ago

The two chords shown in the circle intercept the given arcs. What is the measure of MPN?

Mathematics

1 answer:

lutik1710 [3]3 years ago

6 0

Answer:

Option (2)

Step-by-step explanation:

If two chords intersect inside the circle, measure of angle between them is half of the sum of intercepted arcs.

From the picture attached,

m∠MPN = $\frac{1}{2}[m(\text{arc MN}) + m(\text{arc OL})]$

= $\frac{1}{2}(40+110)$

= 75°

Therefore, Option (2) will be the answer.

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What’s the solution to 12x + 2 > 14

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Answer:

x>1

Step-by-step explanation:

12x+2>14

12x>12

x>1

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3 years ago

Find the orthogonal complement W⊥ of W and give a basis for W⊥. W = x y z : x = 1 2 t, y = − 1 2 t, z = 6t.

igor_vitrenko [27]

Answer:

W⊥= (a, b, c)

a = v - (1/2)w

b = v

c = w

Basis for W⊥ = <(1,1,0),(-1/2,0,1)>

Step-by-step explanation:

The orthogonal complement of W is the set of vectors (a,b,c) that satisfy:

(x,y,z)·(a,b,c) = 0

ax + by + cz = 0

So, taking into account that x=12t, y=-12t and z=6t, the equation above is equal to:

12ta + -12tb + 6tc = 0

12a - 12b + 6c = 0

Then, if we made b=v and c=w and solve for a, we get:

12a - 12v + 6w = 0

a = (12v - 6w)/12

a = v - (1/2)w

Therefore, the orthogonal complement W⊥ of W has the form:

W⊥ = (a,b,c) = (v - (1/2)w, v, w)

On the other hand, we can write W⊥ as:

W⊥ = (v - (1/2)w, v, w)

W⊥ = (v,v,0) + ((-1/2)w,0,w)

W⊥ = v(1,1,0) + w(-1/2,0,1)

That means that we can write any vector of W⊥ as a linear combinations of the vectors (1,1,0) and (-1/2,0,1), so they are a basis for W⊥

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3 years ago

James has a piece of construction paper with an area of 50 1/4 inches. It is 4 3/16 inches long. What is the width of the piece

Flura [38]

Answer:

The width of the piece of construction paper is 12 inches.

Step-by-step explanation:

The length of the construction paper= 4 3/16 in log

$4\frac{3}{16} = 4 + \frac{3}{16} = 4 + 0.1875 = 4.1875$

⇒Length of the paper = 4.1875 inches

Let the width of the paper = w inches

The area of the paper = 50 1/4 sq. inches.

$50\frac{1}{4} = 50 + \frac{1}{4} = 50 + 0.25 = 50.25$

⇒Area of the paper = 50.25 sq. inches

Now, Area of the paper = LENGTH x WIDTH

or, 50.25 sq. inches = 4.1875 inches x w

⇒ w = 50.25 / 4.1875 = 12 in

or, w = 12 in

Hence, the width of the piece of construction paper is 12 inches.

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4 years ago

Are the rational numbers (-1/2) and (1/-2) equivalent?

spayn [35]

Answer:

Yes

Step-by-step explanation:

The negative sign was simply moved to either the numerator or denominator. Either way the number is still a negative one half.

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