<h2>
Hello!</h2>
The answer is:
![3x^{2} -14x+7](https://tex.z-dn.net/?f=3x%5E%7B2%7D%20-14x%2B7)
<h2>
Why?</h2>
To solve the problem we need to add/subtract like terms. We need to remember that like terms are the terms that share the same variable and the same exponent.
For example, we have:
![x^{2} +2x+3x=x^{2} +(2x+3x)=x^{2}+5x](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B2x%2B3x%3Dx%5E%7B2%7D%20%2B%282x%2B3x%29%3Dx%5E%7B2%7D%2B5x)
We have that we were able to add just the terms that were sharing the same variable and exponenr (x for this case).
So, we are given the expression:
![5x^2-5x+1-(2x^2+9x-6)=5x^{2}-2x^{2}-5x-9x+1-(-6)\\\\(5x^{2}-2x^{2})+(-5x-9x)+(1-(-6))=3x^{2}-14x+7](https://tex.z-dn.net/?f=5x%5E2-5x%2B1-%282x%5E2%2B9x-6%29%3D5x%5E%7B2%7D-2x%5E%7B2%7D-5x-9x%2B1-%28-6%29%5C%5C%5C%5C%285x%5E%7B2%7D-2x%5E%7B2%7D%29%2B%28-5x-9x%29%2B%281-%28-6%29%29%3D3x%5E%7B2%7D-14x%2B7)
Hence, the answer is:
![3x^{2} -14x+7](https://tex.z-dn.net/?f=3x%5E%7B2%7D%20-14x%2B7)
Have a nice day!
Answer:
Angle CAD is 44 degrees
Angle ACD is 44 degrees
Angle ACB is 136 degrees
Angle ABC is 22 degrees
Explanation:
29. Triangle ADC is an isosceles triangle because it has two equal sides.
If segments AD and DC are congruent, then segment AC is the base and the base angles of an isosceles triangle are equal.
Let x be angle CAD.
Let's go ahead x;
![\begin{gathered} 92+x+x=180\text{ (sum of angles in a triangle)} \\ 92+2x=180 \\ 2x=180-92 \\ 2x=88 \\ x=\frac{88}{2} \\ \therefore x=44^{\circ} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2092%2Bx%2Bx%3D180%5Ctext%7B%20%28sum%20of%20angles%20in%20a%20triangle%29%7D%20%5C%5C%2092%2B2x%3D180%20%5C%5C%202x%3D180-92%20%5C%5C%202x%3D88%20%5C%5C%20x%3D%5Cfrac%7B88%7D%7B2%7D%20%5C%5C%20%5Ctherefore%20x%3D44%5E%7B%5Ccirc%7D%20%5Cend%7Bgathered%7D)
Therefore, measure of angle CAD is 44 degrees.
30. Measure of angle ACD is 44 degrees (Base angles of an isosceles triangle are equal)
31. Let angle ACB be y,
Let's go ahead and find measure of angle ACB;
![\begin{gathered} 44+y=180\text{ (angles on a straight line)} \\ y=180-44 \\ \therefore y=136^{\circ} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2044%2By%3D180%5Ctext%7B%20%20%20%20%20%28angles%20on%20a%20straight%20line%29%7D%20%5C%5C%20y%3D180-44%20%5C%5C%20%5Ctherefore%20y%3D136%5E%7B%5Ccirc%7D%20%5Cend%7Bgathered%7D)
So measure of angle ACB is 136 degrees.
32. Let angle ABC be z.
Triangle ACB is also an isosceles triangle so the base angles are the same.
Let's go ahead and find z;
![\begin{gathered} 136+z+z=180_{}\text{ (sum of angles in a triangle)} \\ 138+2z=180 \\ 2z=180-136 \\ 2z=44 \\ z=\frac{44}{2} \\ \therefore z=22^{\circ} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20136%2Bz%2Bz%3D180_%7B%7D%5Ctext%7B%20%20%20%20%28sum%20of%20angles%20in%20a%20triangle%29%7D%20%5C%5C%20138%2B2z%3D180%20%5C%5C%202z%3D180-136%20%5C%5C%202z%3D44%20%5C%5C%20z%3D%5Cfrac%7B44%7D%7B2%7D%20%5C%5C%20%5Ctherefore%20z%3D22%5E%7B%5Ccirc%7D%20%5Cend%7Bgathered%7D)
So measure of angle ABC is 22 degrees.
Answer:
3
Step-by-step explanation:
Answer:
![\frac{ \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
Step-by-step explanation:
To find side x , since it the shortest side. Divide the second longest side by sqr root of 3.
Why?
This is a 30-60-90 triangle so that means the second longest side will be sqr root of 3 times more than the shortest side
![\sqrt{2} \div \sqrt{3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B2%7D%20%20%5Cdiv%20%20%5Csqrt%7B3%7D%20)
![\frac{ \sqrt{2} }{1} \times \frac{1}{ \sqrt{3} } = \frac{ \sqrt{2} }{ \sqrt{3} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B1%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
RATIONALIZE the denominator
![\frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
Sqr root of 6 over 3 is the answer.
This section is extra If you want to.
Since the longest side is twice the shortest side, the longest side is
![\frac{2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
Let proof
using pythagorean theorem,
![( \frac{ \sqrt{6} }{3} ) {}^{2} + (\sqrt{2} ) {}^{2}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20%29%20%7B%7D%5E%7B2%7D%20%20%2B%20%20%28%5Csqrt%7B2%7D%20%29%20%7B%7D%5E%7B2%7D%20)
![\frac{6}{9} + 2 = \frac{24}{9}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B9%7D%20%20%2B%202%20%3D%20%20%5Cfrac%7B24%7D%7B9%7D%20)
![\sqrt{ \frac{ {24} }{9} } = \frac{2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7B%20%7B24%7D%20%7D%7B9%7D%20%7D%20%20%3D%20%20%5Cfrac%7B2%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
So it is right.
Answer:
3
Step-by-step explanation:
Because the slope line is ending on 3