PLEASEEEEE HELP!! BRAINLIEST!!

the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.

wel

Answer:

$\sqrt{14}$

Step-by-step explanation:

In any square with side length $s$ , the diagonal of the square is equal to $s\sqrt{2}$ . Since the side length of this square is $\sqrt{7}$ , the diagonal is equal to $\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}$ .

Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states $a^2+b^2=c^2$ , where $c$ is the hypotenuse of the triangle, and $a$ and $b$ are the two legs of the triangle.

In this question, both legs are equal to $\sqrt{7}$ , and we're solving for the diagonal, which is the hypotenuse in this case:

$\sqrt{7}^2+\sqrt{7}^2=c^2,\\c^2=14,\\c=\boxed{\sqrt{14}}$

4 0

3 years ago

In , there were immigrants admitted to a country. In 1960, the number was . a. Assuming that the change in immigration is lin

Arisa [49]

Answer:

The answer is below

Step-by-step explanation:

The complete question is:

In 1960, there were 237,794 immigrants admitted to a country. In 2001, the number was 1,150,729.

a. Assuming that the change in immigration is linear, write an equation expressing the number of immigrants, y, in terms of t, the number of years after 1900.

b. Use your result in part a to predict the number of immigrants admitted to the country in 2013.

c. Considering the value of the y-intercept in your answer to part a, discuss the validity of using this equation to model the number of immigrants throughout the entire 20th century.

Answer:

a) From the question, we can get two ordered pairs which are $(t_1,y_1)=(60,237794)\ and\ (t_2,y_2)=(101,1150729)$

Using the equation of a line given two points:

$y-y_1=\frac{y_2-y_1}{t_2-t_1}(t-t_1)\\ \\y-237794=\frac{1150729-237794}{101-60}( t-60)\\\\y-237797=22266.71(t-60)\\\\y=22266.71t-1098205.44$

b) In 2013, t = 2013 - 1900 = 113.

Hence:

$y=22266.71t-1098205.44\\\\y=22266.71(113)-1098205.44\\\\y=1417932.488\\\\y=1417933$

c)

$y=22266.71t-1098205.44\\\\the\ y\ intercept\ is\ at\ t=0,hence:\\\\y=22266.71(0)-1098205.44\\\\y=-1098205.44$

Since the y intercept is negative, that is in 1900 the number of immigrants was -1098206 which can not be possible. Hence this equation is not valid and the growth may or may not be linear.

7 0

3 years ago

The endpoints of `bar(EF)` are E(xE , yE) and F(xF , yF). What are the coordinates of the midpoint of `bar(EF)`?

Hoochie [10]

For a better understanding of the solution provided here please find the diagram attached.

Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.

Thus, if, for example, the end coordinates of a line segment are $(x_{1}, y_1)$ and $(x_2, y_2)$ then the coordinates of the midpoint of this line segment will be the average of the coordinates of the two endpoints and thus, it will be: