Answer:
It does not intersect the x axis
Step-by-step explanation:
If there are no real roots the quadratic does not intersect the x axis
If there is one root it touches the x axis
2 real roots it crosses twice
Answer:
C. 12m
Explanation:
Let the length of the shorter arm = x
Since the length of the longer arm is equal to twice the length of the shorter arm;
• The length of the longer arm = 2x
• The area of triangle ABD = 18√3 m².
Given a triangle with two sides and the included angle, the area of the triangle is calculated using the formula below:
![\begin{gathered} \text{Area}=\frac{1}{2}ab\sin \theta \\ \implies\text{Area of triangle ABD =}\frac{1}{2}bd\sin A \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BArea%7D%3D%5Cfrac%7B1%7D%7B2%7Dab%5Csin%20%5Ctheta%20%5C%5C%20%5Cimplies%5Ctext%7BArea%20of%20triangle%20ABD%20%3D%7D%5Cfrac%7B1%7D%7B2%7Dbd%5Csin%20A%20%5Cend%7Bgathered%7D)
Therefore:
![18\sqrt[]{3}=\frac{1}{2}(x)(2x)\sin (60\degree)](https://tex.z-dn.net/?f=18%5Csqrt%5B%5D%7B3%7D%3D%5Cfrac%7B1%7D%7B2%7D%28x%29%282x%29%5Csin%20%2860%5Cdegree%29)
We solve for x.
![\begin{gathered} 18\sqrt[]{3}=\frac{2x^2}{2}\times\sin 60\degree \\ 18\sqrt[]{3}=x^2\times\frac{\sqrt[]{3}}{2} \\ \text{Multiply both sides by }\frac{2}{\sqrt[]{3}} \\ 18\sqrt[]{3}\times\frac{2}{\sqrt[]{3}}=x^2\times\frac{\sqrt[]{3}}{2}\times\frac{2}{\sqrt[]{3}} \\ x^2=36 \\ x^2=6^2 \\ x=6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2018%5Csqrt%5B%5D%7B3%7D%3D%5Cfrac%7B2x%5E2%7D%7B2%7D%5Ctimes%5Csin%2060%5Cdegree%20%5C%5C%2018%5Csqrt%5B%5D%7B3%7D%3Dx%5E2%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%20%5C%5C%20%5Ctext%7BMultiply%20both%20sides%20by%20%7D%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%2018%5Csqrt%5B%5D%7B3%7D%5Ctimes%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%3Dx%5E2%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%5Ctimes%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20x%5E2%3D36%20%5C%5C%20x%5E2%3D6%5E2%20%5C%5C%20x%3D6%20%5Cend%7Bgathered%7D)
Multiply x by 2 to get the length of the longer arm:
![2x=2\times6=12m](https://tex.z-dn.net/?f=2x%3D2%5Ctimes6%3D12m)
The length of the longer arm is 12m.
C is the correct option.
The x values stay the same but the y values change to their opposites.
For example: (2,4) reflected across the x-axis would be (2, -4)
and (6, -3) reflected across the x-axis would be (6, 3)
I hope you understand my explanation.
Answer:
122°
Step-by-step explanation:
The formula for finding the sum of all angles in a polygon is:
(n-2) * 180°
n is the number of angles
Here n = 7, so the sum of all angles is
(7-2) * 180° = 900°
x = 900 - 128 - 130 - 120 - 115 - 145 - 140 = 122°
Make me the brainliest ;)