show that the problem of determining the satis ability of boolean formula in disjun tive normal form is polynomial-time solvable.

Given:

[tex]\Delta MAT\cong \Delta MHT[/tex] and [tex]m\angle 2=82^\circ[/tex].

To find:

Whether [tex]m\angle 1=47^\circ[/tex] is possible or not.

Solution:

We have,

[tex]\Delta MAT\cong \Delta MHT[/tex]

[tex]\angle AMT\cong \angle HMT[/tex]                      (CPCTC)

[tex]m\angle 3=m\angle 8[/tex]              ...(i)

And,

[tex]m\angle 1=m\angle 8[/tex]              ...(ii)        (Vertically opposite angles)

From (i) and (ii), we get

[tex]m\angle 1=m\angle 3[/tex]              ...(iii)

Now,

[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ[/tex]          (Linear pair)

[tex]m\angle 1+82^\circ+m\angle 1=180^\circ[/tex]             (Using (iii))

[tex]2m\angle 1=180^\circ-82^\circ[/tex]

[tex]2m\angle 1=98^\circ[/tex]

Divide both sides by 2.

[tex]m\angle 1=\dfrac{98^\circ}{2}[/tex]

[tex]m\angle 1=49^\circ[/tex]

The measure of angle 1 is 49 degrees so it cannot be equal to 47 degrees.

Therefore, the required answer is "no", the given statement [tex]m\angle 1=47^\circ[/tex] is not possible.

Answer:

5-1(b+2) = 5-b-2=3-b

3+4(3m+2n) =3 +12m +8n

Answer:

1/8

Step-by-step explanation:

The question is incomplete, here is the complete question

Michael split 3/4

pounds of candy among 8 people.

What is the unit rate in pounds per person?

Write your answer in simplest form

SOLUTION:

Micheal splits 3/4 candy among 8 people

Therefore the unit rate per pounds per person can be calculated as follows

= 3/4 ÷ 8

= 3/4 × 1/8

= 3/24

= 1/8

Hence the unit per pound per person is 1/8

Answer:

P and Q add up to 90°.

Step-by-step explanation:

Answer:

These are both 20 so that means that this is proportional, yes.

Step-by-step explanation:

Hi.

To figure this out we can do something called cross multiplying to find a cross product. If we do this and our two answers are equal then it is indeed a proportion.

Here is how we do this.

[tex]\frac{4}{2}[/tex]    [tex]\frac{10}{5}[/tex]

So basically what we are doing is multiplying across in a diagonal direction.

Diagonal meaning like a slash / .

So in this case we would multiply the 4 and the 5 , since they're diagonal from each other.

Do the same for the 2 and the 10.

So we have to multiply :

4 x 5

2 x 10

=

20

These are both 20 so that means that this is proportional, yes.

Hope this helps.

If you have any questions or concerns feel free to message me.

Yes the ratios 4/2 and 10/5 form a proportion.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

To figure this out we can do something called cross multiplying to find a cross product. If we do this and our two answers are equal then it is indeed a proportion.

4/2, 10/5

So basically what we are doing is multiplying across in a diagonal direction.

Diagonal meaning like a slash.

So in this case we would multiply the 4 and the 5 , since they're diagonal from each other.

Do the same for the 2 and the 10.

So we have to multiply :

4 x 5

2 x 10

=20

Hence these are both 20 so that means that this is proportional, yes.

To learn more about Ratios click:

https://brainly.com/question/26974513

#SPJ2

Answer:

24 units²

Step-by-step explanation:

4(12)/2=24

Answer:

C.                          m∠1 +m∠2 = 90

Step-by-step explanation:

Answer:

y = 1x + 4

OR

y = x + 4

Step-by-step explanation:

Answer:

Add all the outer lines and they may add up to be the perimeter, if you need the area multiply 4 times 8 and add that to 5.6*4/2 +4.5*4/2 plus four times eight

Step-by-step explanation:

Answer:

I remember these form when I was like 10 but ok.

Step-by-step explanation:

pretty sure you multiply the base times the height. But first you have to take out all triangwkes which leaves you with two of them.

so 8x4 for the top one and then 14x4.5 for the bottom one.

then for the triangles the one on the left is 5.6x4

the right one is 4.5x14

then divide both triangles answers into two. That should be the triangle areas. Then add the two triangles pieces together.

once don’t add the squares areas with the triangles and that’s THE AREAAAA

im sry I’m a lil rusty so if it’s wrong pwease forgive me :/

Answer: 2 2/3 miles

Step-by-step explanation:

From the question, we are informed that three runners in a relay race share the 8-mile distance equally.

The number of miles that each runner travel will be the total miles divided by number of runners. This will be:

= 8/3

= 2 2/3 miles

Answer:

w=1.4

Step-by-step explanation:

11w+5w-1=65w-36

16w-1=65w-36

16w-65w= -36+1

-49w= -35

w= -35/-49

w= 1.4

Answer:

6/27

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

5/27+1/27=6/27

reduced to lowest denominator

(divide top & bottom by 3)

2/9

Answer:

3 mph

Step-by-step explanation:

UPSTREAM:

distance = 36 miles ;

Speed = 15-c mph ;

TIME, t = distance / speed = 36/(15-c)

Downstream :

distance = 36 miles ;

speed = 15+c mph ;

time, t = 36/(15+c)

upstream time + downstream time = 5 hrs

36/(15-c) + 36/(15+c) = 5

36(15+c) + 36(15-c) = 5(15-c)(15+c)

1080 = 5(225 - c²)

1080 / 5 = 225 - c²

216 = 225 - c^2

216 - 225 = c²

-9 = c²

c = 3

Answer:

65 cm²

Step-by-step explanation:

follow for more on my id

Answer:

65 cm I just took the test

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expanded Exponential Form:

1,492.034 =

1 × 10^3

+ 4 × 10^2

+ 9 × 10^1

+ 2 × 10^0

+ 0 × 10^-1

+ 3 × 10^-2

+ 4 × 10^-3

Expanded Exponential Form:

1,200.36 =

1 × 10^3

+ 2 × 10^2

+ 0 × 10^1

+ 0 × 10^0

+ 3 × 10^-1

+ 6 × 10^-2

Answer:

75

Step-by-step explanation:

5(2.5)(6)

5*2.5*6

=75

Answer:

75

Step-by-step explanation:

5*(6x2.5)

6x2.5=15

15x5=75.

Answer:

y = .5x+30

Step-by-step explanation:

[tex]m= \frac{y2-y1}{x2-x1}[/tex]

hope this helps, good luck :)

Answer:

100000 × 1.04 × 1.04

Step-by-step explanation:

108160

Answer:

This one

1

_

3

1

-_

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

r=4 :)

Step-by-step explanation:

Answer:

Esteban

Step-by-step explanation:

Divide 30 by 85%

30/0.85 = 35.29411765

Answer:

35 5/17 or 35.29411765

Step-by-step explanation:

30 times 100 divided by 85

Answer:

y=8

Step-by-step explanation:

add 36 to 12. then divide 48 (the result) by 6 to get 8

Answer:

Y=8

Step-by-step explanation:

12 = 6 x y - 36

12=6 x 8 - 36

12 = (6x8) - 36

12 = 48 - 36

Y= 8

Hope this helps

Mark brainliest if it helps.

Answer:

a) The acceleration between 20 and 40 seconds is equal to the slope in that range.

Remember that for aline that passes through the points (a, b) and (c, d) the slope is:

slope = (d - b)/(c - a)

In this case we can see the points:

(20s, 2m/s) and (40s, 4m/s)

Then the slope (and thus the acceleration) is:

slope = (4m/s - 2m/s)/(40s - 20s) = (2m/s/20s) = 0.1 m/s^2

The acceleration between 20 seconds and 40 seconds is 0.1 m/s^2

b) The total distance travelled is equal to the area under the curve.

So we could just count the number of squares, this is the easy way.

We can see that each square measures 10 seconds by 1 m/s, then the "area" of each square represents:

a = (10s)*(1m/s) = 10m

This means that each square represents a distance of 10 meters.

We can count that:

between 0s and 10s we have 1 whole square.

between 10s and 20s we have 2 whole squares.

between 20s and 30s we have 2 and half squares.

between 30s and 40s we have 3 and half squares.

Then the total number of squares under the curve is:

1 + 2 + 2.5 + 3.5 = 3 + 2.5 + 3.5 = 3 + 6 = 9

So we have 9 whole squares under the curve, and each square represents a distance of 10 meters, so the total distance traveled is:

Distance = 9*10m = 90m

c) We have an isosceles triangle where we know that one side measures 8.2 cm and another side measures 9.4cm

An isosceles triangle has two equal sides and one different.

So if we want to have the maximum perimeter, the two equal sides must have the longest side length (9.4 cm)

Then the (largest) perimeter of the triangle (the sum of the lengths of all 3 sides) is:

8.2cm + 9.4cm + 9.4cm = 27cm

Answer:

sorry no se la respuesta

Step-by-step explanation:

[tex] \frac{5}{8} \times \frac{3}{2} \div \frac{15}{16} \\ \frac{15}{16} \times \frac{16}{15} \\ = 1[/tex]

Answer:

1

Step-by-step explanation:

5/8 x 1 1/2 / 15/16 = 1                        (5/8 / 15/16 = 2/3,   2/3 x 1 1/2 =1 )