I need help with this

Z^5=-7776i

Sloan [31]

Answer:

Z=+6

Step-by-step explanation:

Z^5=-7776i

Let's note that i I mathematics means negative one i.e

i = -1

So the equation is equal to

Z^5=-*-(7776)

Z^5 = 7776

Z= 5√7776

Since it's a divisible by 6

It's giving us a clue that 6 it's the answer.

Ok let's check the 5th root of 7776 in our calculator.

Z=+6

+6 is the solution to the equation

Z^5=-7776i

7 0

4 years ago

A triangle has angles that measure 46° and 61°. What is the measure of the third angle? A. 15° B. 73° C. 107° D. 134°

Nastasia [14]

The interior angles of a triangle need to be equal to 180°, so to solve this you need to figure out how many degrees you need to get 180°.

46 + 61 = 107

180 - 107 = 73

The measure of the third angle is B. 73°.

5 0

3 years ago

Which is the difference of 21 1/4 - 18 2/4? A:2 1/4. B:2 2/4. C:2 3/4. D:3 1/4.

seropon [69]

Answer:

2 3/4 C

Step-by-step explanation:

$(21+\frac{1}{4})-(18+\frac{2}{4})\\=21-18+\frac{1}{4} -\frac{2}{4} \\=3-\frac{1}{4} \\=\frac{12-1}{4} \\=\frac{11}{4} \\=2\frac{3}{4} \\or\\21\frac{1}{4} -18\frac{2}{4} \\=\frac{85}{4} -\frac{74}{4} \\=\frac{85-74}{4} \\=\frac{11}{4} \\=2\frac{3}{4}$

3 0

4 years ago

Graph the image of this figure after a dilation with a scale factor of 13 centered at the point (4, −2) .

Sonja [21]

Answer:

From the given triangle figure;

Labelled the triangle as A , B and C.

The coordinates of this triangle ABC are;

A = (1, 10) ,

B = (-2, 4)

C = (7, 4).

Given : Scale factor(k) = $\frac{1}{3}$ and centered at point (4, -2).

The rule of dilation with $k= \frac{1}{3}$ and center at point (4,-2) is:

$(x, y) \rightarrow (\frac{1}{3}(x-4)+4 , \frac{1}{3}(y+2)-2)$

$(x, y) \rightarrow (\frac{1}{3}x-\frac{4}{3}+4 , \frac{1}{3}y+\frac{2}{3}-2)$

or

$(x, y) \rightarrow (\frac{1}{3}x+\frac{8}{3} , \frac{1}{3}y-\frac{4}{3})$

then, the dilation of the given figure are;

$A(1, 10) \rightarrow (\frac{1}{3}\cdot 1+\frac{8}{3} , \frac{1}{3} \cdot 10-\frac{4}{3})$ = $(\frac{1}{3}+\frac{8}{3} , \frac{10}{3}-\frac{4}{3})$ = $(\frac{9}{3} , \frac{6}{3})$ = A'(3 , 2)

$B(-2, 4) \rightarrow (\frac{1}{3}\cdot -2+\frac{8}{3} , \frac{1}{3} \cdot 4-\frac{4}{3})$ = $(-\frac{2}{3}+\frac{8}{3} , \frac{4}{3}-\frac{4}{3})$ = $(\frac{6}{3} , \frac{0}{3})$ =B'(2 , 0)

$C(7, 4) \rightarrow (\frac{1}{3}\cdot 7+\frac{8}{3} , \frac{1}{3} \cdot 4-\frac{4}{3})$ = $(\frac{7}{3}+\frac{8}{3} , \frac{4}{3}-\frac{4}{3})$ = $(\frac{15}{3} , \frac{0}{3})$ = C'(5 , 0)