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3 years ago

What is the square root of -1?

Mathematics

2 answers:

Natali [406]3 years ago

6 0

If you work with real numbers then the square root of - 1 CANNOT be defined.

If you work with complex numbers then the square root of - 1 is equal to the imaginary unit(which is symbolized as i)

vladimir2022 [97]3 years ago

3 0

Answer:

square root of -1 = i

Step-by-step explanation:

the imaginary Unit number is a solution to the quadratic equation x^{2}+1=0. basically any number times itself is a positive number or zero so you can't ever get to a negative number by squaring. Since square roots undo squaring, negative numbers can't have square roots.

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Let f(x)=7x-13. Find f^-1(x).

vitfil [10]

Ok but allow my humble self to use $y$ instead of $f(x)$ .

We have,

$y=7x-13$

If you wanna know what the inverse is swap the values of x and y,

$x=7y-13$

And now solve for y,

$x+13=7y\implies\boxed{y=f^{-1}(x)=\frac{x+13}{7}}$ .

Hope this helps.

5 0

3 years ago

Read 2 more answers

Round the decimal 0.575 to the nearest hundredth

soldier1979 [14.2K]

Answer:

0.58

Step-by-step explanation:

hundredths place is 2 after the decimal

any number 5 or higher will round up

so the 7 rounds up to a 8

Hope this helps!

7 0

3 years ago

Read 2 more answers

Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?

densk [106]

Answer:

$A.\ y = x^2 - 6x + 13$ is the correct answer.

Step-by-step explanation:

We know that vertex equation of a parabola is given as:

$y = a(x-h)^2+k$

where $(h,k)$ is the vertex of the parabola and

$(x,y)$ are the coordinate of points on parabola.

As per the question statement:

The parabola opens upwards that means coefficient of $x^{2}$ is positive.

Let $a = +1$

Minimum of parabola is at x = 3.

The vertex is at the minimum point of a parabola that opens upwards.

$\therefore$ $h = 3$

Putting value of a and h in the equation:

$y = 1(x-3)^2+k\\\Rightarrow y = (x-3)^2+k\\\Rightarrow y = x^2-6x+9+k$

Formula used: $(a-b)^2=a^{2} +b^{2} -2\times a \times b$

Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.

Comparing $y = x^2 - 6x + 13$ and $y = x^2-6x+9+k$

13 = 9+k

k = 4

Please refer to the graph attached.

Hence, correct option is $A.\ y = x^2 - 6x + 13$

3 0

3 years ago

Read 2 more answers

Show that |3+10|=|3|+ |10|?

Viefleur [7K]

|3+10|=|3|+|10|
|13|=|13|
13=13

8 0

3 years ago

Select the correct answer from each drop-down menu.

finlep [7]

Answer:

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)

Step-by-step explanation:

1) Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____

Let the coordinates of B be $(x_2,y_2)$

Coordinates of A = $(x_1,y_1)=(-6,5)$

Coordinates of C=(x,y)=(3.6,-0.4)

We will use section formula over here

$x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}$

m:n=3:2

$3.6=\frac{3x_2+2(-6)}{3+2} , -0.4=\frac{3y_2+2(5)}{3+2}3.6 \times 5 = 3x_2-12, -0.4 \times 5 = 3y_2+10\\18+12=3x_2 , -2=3y_2+10\\30=3x_2 , -12=3y_2\\10=x_2, -4=y_2\\$

Coordinates of B = (10,-4)

2)If point D divides in the ratio 4 : 5, the coordinates of point D are ____

(fraction)

Let the coordinates of D be $(x,y)$

Coordinates of A = $(x_1,y_1)=(-6,5)$

Coordinates of B= $(x_2,y_2)=(10,-4)$

We will use section formula over here

$x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}$

m:n=3:2

$x=\frac{3(10)+2(-6)}{3+2} , y=\frac{3(-4)+2(5)}{3+2}\\x=3.6,y=-0.4$

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)

4 0

3 years ago