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OLga [1]
4 years ago
8

In the graph, the vector terminating at A represents the complex number z. The vector terminating at B represents the product of

z and -2. Which graph correctly represents the product?

Mathematics
2 answers:
marin [14]4 years ago
6 0

Answer:


Step-by-step explanation:

A = z

B = -2z


Since  z is in the second quadrant ( x is negative and y is positive)

when we multiply by -2,   B is   (-*-  = +,  + * - = -)

B is in the 4th quadrant ( x is positive, y is negative)


This is the only graph that meets that requirement.

Oksi-84 [34.3K]4 years ago
6 0

Answer:

The answer is the second graph

Step-by-step explanation:

1. A complex number is coumposed by a real coordinate (in the x axis) and a imaginary coordinate (in the Y axis). If we see the vector A, we can note its direction is <-1,3>  .

2. When we multiply a number by a vector, we multiply the number by each component of the vector, as follows:

       -2  *   <-1,3>  =  <2,-6>

We can note the new direction <2,-6> is represented by the second graph.

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Determine the inverse of the function f(x) = log3(4x + 5) − 6.
beks73 [17]

Answer:

f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4

Step-by-step explanation:

The function f(x)=\log_3 (4x+5)-6 can be thought of as a series of steps, one operation at a time:

Start with x

Multiply by 4

Add 5

Take the \log_3

Subtract 6

That gives you a function value f(x).

To get the inverse function, read that list from the bottom up (in reverse order, using inverse operations at each step).

Start with x  (a bit confusing, because this  x  represents the function value you get at the end of the above list).

Add 6   (add is the inverse operation of subtract)

Raise 3 to the ...    3^{\text{result of previous step}

Subtract 5

Divide by 4

f^{-1}(x) = \frac{3^{x+6}-5}{4}

Let's test this out.  Find f(1).

f(1)=\log_3(4 \cdot 1 + 5)-6 =\log_3(9)-6=2-6=-4

Now put -4 into the inverse function.

f^{-1}(-4)=\frac{3^{-4+6}-5}{4}=\frac{3^2-5}{4}=\frac{9-5}{4}=\frac{4}{4} =1

The final result is the number we started with when we put 1 into <em>f</em>(<em>x</em>).

Finding an inverse is reversing the action of the function  <em>f</em>  by doing inverse operations in "backwards" order.

A lot of authors have you do this by switching  x  and  y  in the formula for a function, then solving for  <em>x</em>.

y = \log_3(4x+5)-6\text{  switch x and y}\\\\x = \log_3(4y+5)-6\\\\x+6 = \log_3(4y+5)\\\\3^{x+6}=4y+5\\\\3^{x+6}-5=4y\\\\\frac{3^{x+6}-5}{4}=y

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How did Clay and Webster fight against Jackson’s dislike for the bank?
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Answer:

Jackson's opponents planned to use the bank to defeat him in the 1832 presidential campaign. Senators Henry Clay and Daniel Webster were friends of Biddle. ... They thought that if Jackson tried to veto, or reject, the renewal of the charter, he would lose support.

Step-by-step explanation:

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Bethania's garden is in the shape of a right triangle. She has built walls on two sides
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Answer:

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Step-by-step explanation:

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4 years ago
How many cuts do you need to cut a stick into:<br><br> 6 parts?<br> 11 parts?<br> x parts?
yKpoI14uk [10]

Answer:

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Step-by-step explanation:

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7 0
3 years ago
Read 2 more answers
Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation
Kryger [21]

Answer:

y + x - 6 = 0

Step-by-step explanation:

Given

M(0,6) \ and \ N(6,0)

Required

Find the equation of the line

First, the slope of the line has to be calculated using the following formula;

m = \frac{y_2 - y_1}{x_2 - x_1}

where\  (x_1,y_1) = (0,6) \ and \ (x_2,y_2) = (6,0)

So, the equation becomes

m = \frac{0 - 6}{6 - 0}

m = \frac{-6}{6}

m = -1

The equation of the line can then be calculated using

m = \frac{y - y_1}{x - x_1} \ or \ m = \frac{y - y_2}{x - x_2}

Using \ m = \frac{y - y_1}{x - x_1}

-1 = \frac{y - 6}{x -0}

-1 = \frac{y - 6}{x}

Multiply both sides by x

-1 * x = \frac{y - 6}{x} * x

-x = y - 6

Add x to both sides

x -x = y - 6 + x

0 = y - 6 + x

Reorder

y + x- 6 = 0

Using \ m = \frac{y - y_2}{x - x_2}

-1 = \frac{y - 0}{x - 6}

-1 = \frac{y}{x - 6}

Multiply both sides by x - 6

-1 * (x-6) = \frac{y}{x - 6} * (x-6)

-1 * (x-6) = y

-x+6 = y

Add x - 6 to both sided

x - 6 -x+6 = y +x - 6

0 = y + x - 6

y + x - 6 = 0

Hence, the equation of the line is y + x - 6 = 0

3 0
3 years ago
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