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max2010maxim [7]
2 years ago
5

It can be shown that every integer can be uniquelyrepresented in the form of

Mathematics
1 answer:
Alexeev081 [22]2 years ago
8 0

a. 5_{10}=1(-1)(-1)_{\mathrm{bal}3} because

5 = 9 - 3 - 1 = 3^2 - 3^1 - 3^0

b. 13_{10}=111_{\mathrm{bal}3} because

13 = 9 + 3 + 1 = 3^2 + 3^1 + 3^0

c. 37_{10}=1101_{\mathrm{bal}3} because

37 = 27 + 9 + 1 = 3^3 + 3^2 + 3^0

d. 79_{10}=100(-1)1_{\mathrm{bal}3} because

79 = 81 - 3 + 1 = 3^4 - 3^1 + 3^0

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Fill in the missing statement and reason in the proof of the Alternate Exterior Angles Theorem.
ludmilkaskok [199]

Answer:

∠EGB and ∠AGF are congruent;

Transitive Property of Equality

Step-by-step explanation:

The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other

Vertical angles are congruent i.e their measures are equal

Look at the attached graph

Given:

AB // CD

E , G , H , F are col-linear

The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD

∵ AB and EF intersected at point G

∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem

When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent (  vertical angle theorem)

∵ AB // CD and EF is a transversal

∴ m∠AGF = m∠CHF (corresponding angles theorem)

Transitive Property of Equality:  if one angle is equal to two other angles, then the two other angles are equal

 Therefore, If a = b and b = c, then a = c

∵ m∠EGB = m∠AGF

∵ m∠AGF = m∠CHF

∴ m∠EGB = m∠CHF (transitive property theorem)

 ∠EGB and ∠AGF are congruent; Transitive Property of Equality

4 0
3 years ago
Read 2 more answers
A manatee surfaced for air 3 times in 120 seconds.how many seconds went by before the manatee surfaced the first time if it held
Juliette [100K]

Answer:

40 seconds

Step-by-step explanation:

The ratio would be 3:120, indicating the amount of times it went up for air in 120 seconds. In order to find the answer, we'll find the unit rate. 120 divided by 3 is evenly 40. That means, the unit rate is 1:40. It also means that 40 seconds went by before the manatee surfaced the first time (if it held its breath for the same rate).

7 0
3 years ago
Write the equation in vertex form for the parabola with focus (7, –27/4) and directrix y= – 13/4
Nataliya [291]

Answer:

x2 +8x +4y +4 = 0

4y= -x2 -8x -4y = -.25*x^2 -2x -1

a = -.25b = -2c = -1

x position of vertex:

h = -b / 2a

h = 2 / 2*-.25h = 2 / -.5h = -4

y position of vertex:

k = ah^2 + bh + ck = -.25*-4^2 + -2*-4 + -1k = -4 +8 -1k = 3

VERTEX = (-4, 3)*

x value of focus =x value of vertex = -4

y value of focus =(1 (-b^2 -4ac)) / 4a

a = -.25 b = -2 c =-1

y value = (1 (-4 -4*-.25*-1)) / 4*-.25

y value = (1 (-4 -4*-.25*-1)) / -1

y value = (1 -4 +1) / -1y value = (-2 / -1)y value = 2

focus value = (-4, 2)

Answer is the last one.

7 0
2 years ago
Help me plsss the photo is down fast
kiruha [24]

Answer:

<h2><em><u>Option</u></em><em><u> </u></em><em><u>B</u></em><em><u>:</u></em></h2><h2>\frac{1}{5}</h2>

Step-by-step explanation:

<em><u>Given</u></em><em><u>,</u></em>

Number of numbers of each side of the cube

= 4, 5, 6, 7, 8 and 9

= 6 numbers

Number of sides of cube having the number 5

= 1

<em><u>Therefore</u></em><em><u>,</u></em><em><u> </u></em>

Probability of getting a side of the cube of no. 5 is

=  \frac{no. \: of \: favourable \: outcomes}{total \: no. \: of \: possible \: outcomes}

=  \frac{1}{6} (ans) \: (option \: B)

8 0
2 years ago
What is the ratio of a:b, knowing that a-b / a+b = 3/5
Marysya12 [62]

Answer

i am going to give you 2 answer

1. solving for A is:  A=3/5 -b

2. solving for B is:  B=3/5 -a

Step-by-step explanation:

correct me if I'm wrong

let me know if it's correct or not

5 0
2 years ago
Read 2 more answers
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