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Ray Of Light [21]
3 years ago
9

How many acute/obtuse/right angles does a pentagon have

Mathematics
1 answer:
KengaRu [80]3 years ago
4 0
5 obtuse no acute and no right
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One number is 2 less than a second number. Twice the second number is 5 less than 3 times the first. Find the two numbers.
Evgen [1.6K]

Answer:

9 and 11  

Step-by-step explanation:

First number = x -2

Second number = x

  and   2x = 3(x-2)  - 5

            2x = 3x - 6 - 5

             x = 11

              first number = 11-2 = 9

8 0
2 years ago
Suppose that a family wants to increase the size of the garden which is currently 16 feet long and 8 feet wide without changing
Cloud [144]

Answer:

See below

Step-by-step explanation:

<u>Sides of the garden</u>

  • 16 feet and 8 feet

<u>New dimensions of the garden</u>

  • 16 + 2x and 8 + x

<u>1. The area of the new garden</u>

  • (16 + 2x)(8 + x) =
  • 2x^2 + 32x + 128

<u>2. The difference in area </u>

  • 2x^2 + 32x + 128 - 16*8 =
  • 2x^2 + 32x

<u>3. x= 2 effect on the area</u>

  • 2*2^2 + 32*2 =
  • 8 + 64 =
  • 72 ft²

<u>4. Area difference = 160</u>

  • 2x^2 + 32x = 160
  • x^2 + 16x - 80 = 0
  • Solving we get positive root of 4 ft

<u>5. Area difference = 4 times</u>

  • 2x^2 + 32x = 128*3
  • 2x^2 + 32x - 384 = 0
  • x^2 + 16x - 192= 0
  • Solving we get positive root of 8 ft

3 0
3 years ago
Y-6=-4(x+4) show steps.
Flauer [41]

Answer:

y = -4x - 10

Step-by-step explanation:

y-6=-4(x+4)

1: distributive property

y-6= -4x - 16

2: add 6 both sides

y = -4x - 10

8 0
2 years ago
What percent of 200 is 16?,,,,
Zina [86]

Answer:

8%

Step-by-step explanation:

To find the percent, divide 16 by 200, then multiply it by 100.

(16 / 200) x 100

0.08 x 100

= 8

So, 16 is 8% of 200

8 0
3 years ago
Read 2 more answers
Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible cho
yaroslaw [1]

Answer:

a) attached below

b)  ( T,T )

c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )

Step-by-step explanation:

A) write down the game in matrix form

let: E = exit at the industry immediately

     T = exit at the end of the quarter

     N = exit at the end of the next quarter

matrix is attached below

B) weakly dominated strategies is ( T,T )

C) Find the pure-strategy Nash equilibria

The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

D ) Find the unique mixed-strategy Nash equilibrium

The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE

Assume that P is the probability of firm 1 exiting immediately ( E )

and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.

hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .

The expected utilities of E and N to firm 2 =

0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3

4 0
2 years ago
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