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saveliy_v [14]
3 years ago
14

What is the graph of g?

Mathematics
1 answer:
Umnica [9.8K]3 years ago
5 0

Answer:

function gis defined as g (6) = - f (-4) graph

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What does i^739 equal? explain how you found your answer.
Sophie [7]
<h3>Answer:   -i</h3>

========================================================

Explanation:

i = sqrt(-1)

Lets list out the first few powers of i

  • i^0 = 1
  • i^1 = i
  • i^2 = -1
  • i^3 = i*i^2 = i*(-1) = -i
  • i^4 = (i^2)^2 = (-1)^2 = 1

By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.

For example, i^5 = i^1 because 5/4 leads to a remainder 1.

Another example: i^6 = i^2 since 6/4 = 1 remainder 2

Again, we only care about the remainder to find out which bin we land on.

-------------

Turning to the question your teacher gave you, we have,

739/4 = 184 remainder 3

So i^739 = i^3 = -i

<h3>-i is the final answer</h3>

--------------

Side notes:

  • if i^a = i^b, then a-b is a multiple of 4
  • Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.
4 0
3 years ago
A motorboat can maintain a constant speed of 15 miles per hour relative to the water. The boat makes trip upstream to a certain
Ira Lisetskai [31]

Answer:

The speed of the current is 2 miles per hours

Step-by-step explanation:

Given as :

The speed of motorboat = x = 15 miles per hour

The time taken by motorboat trip upstream = 51 minutes

The time taken by motorboat trip downstream = 39 minutes

Let The speed of the current = y miles per hour

Let The total distance cover = A miles

So ,

Speed = \dfrac{\textrm Distance}{\textrm Time}

So, x - y = \dfrac{A}{51}

I.e  15 - y =  \dfrac{A}{51}

And x + y = \dfrac{A}{39}

I.e  15 + y = \dfrac{A}{39}

\dfrac{x-y}{x+y} = \dfrac{39}{51}

I.e \dfrac{x-y}{x+y} = \dfrac{13}{17}

Or, 17 × (x - y) = 13 × (x + y)

Or, 17 x - 17 y = 13 x + 13 y

Or, 17 x - 13 x = 13 y + 17 y

Or, 4 x = 30 y

Now, ∵ x = 15 miles per hour

So, 4 × 15 = 30 y

Or, y =  \dfrac{60}{30}

∴   y = 2 miles per hour

Hence The speed of the current is 2 miles per hours   Answer

8 0
3 years ago
The weight of a car is modeled with the polynomial x2 + 10x + 200. The weight of a x3 + x + 100. Which polynomial represents the
Zolol [24]
<h3>The combined weight of a car and truck is given as the polynomial   P(W) = x³ + x² + 11 x + 300</h3>

Step-by-step explanation:

The weight of the car is given as:

P(C)  =  x² + 10 x  + 200

The weight of the truck is given as:

P(T)  =  x³ +  x  + 100

Now, the combined weight of both vehicles is given as

= Weight of Car P(C)   + Weight of Truck P(T)

P(W)  = x² + 10 x  + 200 +  x³ +  x  + 100

         =  x³ + x² + (10 x +  x)+ (200 + 100)

         = x³ + x² + 11 x + 300

⇒ The combined weight of a car and truck is given as the polynomial P(W) = x³ + x² + 11 x + 300

3 0
3 years ago
What is the slope and how f the linear 4x + 2y=24
lorasvet [3.4K]
Answer: y=-2x+12

Step by Step explanation:

4x+2y=24
-4x -4x
-------------------
2y=-4x+24
---- ----- -----
2 2 2

y=-2x+12
7 0
4 years ago
Read 2 more answers
The graphs below have the same shape. what is the equation o the red graph?
maw [93]

So the equation of the red graph is already given to us: f(x) = x^2. I assume you meant the blue graph?

We can use the vertex form: y = a(x - h)^2+ k, where (h,k) is the vertex. (We can ignore a because a is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).

The vertex for g(x) is at (-4, -2) on the coordinate plane. (4 left, 2 down)

Plug into the vertex form:

y = (x - (-4))^2 -2

The double negative becomes a positive, and then you're done:

y = (x + 4)^2-2

5 0
3 years ago
Read 2 more answers
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