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3 years ago

13

This step works because of the ______

1 answer:

ikadub [295]3 years ago

5 0

The answer is B( distributive property).

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Find the roots of the quadratic function by completing the square: x^2 + 4x - 1 = 0

Evgen [1.6K]

Answer: x=4.23606797749979 y=0.23606797749979

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

The difference of 2 numbers is 3 and their sum is 25. What are the numbers? 10 and 15 14 and 11 11 and 13 13 and 12

vagabundo [1.1K]

Let the two numbers be x and y

As given, the difference of two numbers is 3, so

$x-y=3$ or $x=3+y$ ....(1)

And their sum is 25, so

$x+y=25$ .....(2)

Putting x=3+y in equation (2)

$3+y+y=25$

$2y=22$

$y=11$

As, x+y=25

$x+11=25$

$x=14$

So the two numbers are = 14 and 11

8 0

3 years ago

Fill in the table so it represents a linear function.

castortr0y [4]

Answer:

2; 5; 8

Step-by-step explanation:

To fill in the table, we need to generate an equation to represent the relationship between x and y.

First, find the slope using the two pairs given, (5, -1) and (25, 11):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 -(-1)}{25 - 5} = \frac{12}{20} = \frac{3}{5}$

m = ⅗.

Next, using the point-slope form, we can use a point/coordinate pair and the slope to derive an equation as follows.

$y - y_1 = m(x - x_1)$

Where,

$x_1 = 5, y_1 = -1$

m = ⅗.

Plug in the values

$y -(-1) = \frac{3}{5}(x - 5)$

$y + 1 = \frac{3}{5}(x - 5)$

$y + 1 = \frac{3x}{5} - 3$

Subtract 1 from both sides

$y + 1 - 1 = \frac{3x}{5} - 3 - 1$

$y = \frac{3x}{5} - 4$

Use the equation above to fill out the table by plugging each value of x into the equation to get the corresponding values of y for each x value.

✔️When x = 10:

$y = \frac{3x}{5} - 4$

$y = \frac{3(10)}{5} - 4 = 6 - 4$

$y = 2$

✔️When x = 15:

$y = \frac{3x}{5} - 4$

$y = \frac{3(15)}{5} - 4 = 9 - 4$

$y = 5$

✔️When x = 20:

$y = \frac{3x}{5} - 4$

$y = \frac{3(20)}{5} - 4 = 12 - 4$

$y = 8$

8 0

3 years ago

Use the following function rule to find f(r+4). simplify your answer .. f(n)=n+4

Fudgin [204]

N=54........................

7 0

4 years ago

Which expression is a cube root of -1+i√3?

Tpy6a [65]

Answer:

<em>The correct option is C.</em>

Step-by-step explanation:

<u>Root Of Complex Numbers</u>

If a complex number is expressed in polar form as

$Z=(r,\theta)$

Then the cubic roots of Z are

$\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)$

$\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)$

$\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)$

We are given the complex number in rectangular components

$Z=-1+i\sqrt{3}$

Converting to polar form

$r=\sqrt{(-1)^2+(\sqrt{3})^2}=2$

$\displaystyle tan\theta=\frac{\sqrt{3}}{-1}=-\sqrt{3}$

It's located in the second quadrant, so

$\theta=120^o$

The number if polar form is

$Z=(2,120^o)$

Its cubic roots are

$\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)$

$\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)$

$\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)$

Converting the first solution to rectangular coordinates

$z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)$

The correct option is C.

8 0

4 years ago