Look at one of the vertices of the heptagon where two squares meet. The angles within the squares are both of measure 90 degrees, so together they make up 180 degrees.
All the angles at one vertex must clearly add up to 360 degrees. If the angles from the squares contribute a total of 180 degrees, then the two remaining angles (the interior angle of the heptagon and the marked angle) must also be supplementary and add to 180 degrees. This means we can treat the marked angles as exterior angles to the corresponding interior angle.
Finally, we know that for any convex polygon, the exterior angles (the angles that supplement the interior angles of the polygon) all add to 360 degrees (recall the exterior angle sum theorem). This means all the marked angles sum to 360 degrees as well, so the answer is B.
Answer:
see below
Step-by-step explanation:
A protractor is usually a transparent measuring device laid intended to be laid over an angle to be measured. The centerpoint of the protractor's scale is made to coincide with the angle's vertex, and the baseline of the protractor is aligned with one of the angle's rays. The appropriate scale is used to read the angle where the other ray crosses the scale. You usually have to visually determine if the angle is acute or obtuse, so you can choose the correct scale to read.
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If you're drawing an angle, first draw one ray and locate the vertex on it. Then do the steps above as you would for measurement. Make a mark on your paper corresponding to the desired angle measure, and connect the vertex to that mark to create the other ray of the angle.
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If you're working with a printed protractor, you may need to do your work on a piece of translucent paper or transparency material, so you can see the protractor scale through the page you're drawing on.
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<em>Comment on a printed protractor</em>
A protractor will only give accurate measurements if its geometry is perfect. Some printers will scale a figure differently in horizontal and vertical directions, so will make the protractor scale be elliptical instead of circular. That will give wrong readings.
Answer:
D = 0; one real root
Step-by-step explanation:
Discriminant Formula:
![\displaystyle \large{D = {b}^{2} - 4ac}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7BD%20%3D%20%20%7Bb%7D%5E%7B2%7D%20%20-%204ac%7D)
First, arrange the expression or equation in ax^2+bx+c = 0.
![\displaystyle \large{ {x}^{2} + 6x = - 9}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%3D%20%20-%209%7D)
Add both sides by 9.
![\displaystyle \large{ {x}^{2} + 6x + 9 = - 9 + 9} \\ \displaystyle \large{ {x}^{2} + 6x + 9 = 0}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%209%20%3D%20%20-%209%20%2B%209%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7B%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%209%20%3D%20%200%7D)
Compare the coefficients so we can substitute in the formula.
![\displaystyle \large{a {x}^{2} + bx + c = {x}^{2} + 6x + 9 }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7Ba%20%7Bx%7D%5E%7B2%7D%20%20%2B%20bx%20%2B%20c%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%209%20%7D)
Substitute a = 1, b = 6 and c = 9 in the formula.
![\displaystyle \large{D = {6}^{2} - 4(1)(9)} \\ \displaystyle \large{D = 36 - 36} \\ \displaystyle \large{D = 0}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7BD%20%3D%20%20%7B6%7D%5E%7B2%7D%20%20-%204%281%29%289%29%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7BD%20%3D%20%2036%20-%2036%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7BD%20%3D%20%200%7D)
Since D = 0, the type of solution is one real root.
Answer:
Option D: Absolute value function
Step-by-step explanation:
The absolute value of a number is the distance of the number from 0 to the left or right on the number line.
We are given the function;
f(x) = |2x³ - 3x| + 5
This function contains an absolute value symbol which is |2x³ - 3x|.
This function is thus illustrated by an an absolute value function because an absolute value function will be one that contains algebraic expressions within absolute value symbols.
Since its a square root then it would be irrational.
Hope this helps you! :)