Answer:
b we now know that a = 35° and, since the sum of the triangles equal 180° we can find angle b. Angle c and the 95° angle are supplementary; they add up to 180°.
Step-by-step explanation:
The value of x is –3.
Solution:
Given statement:
4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)
Let's convert this into algebraic expression.
![$4\frac{3}{10} -\left(2\frac{2}{5}x+5\frac{1}{2}\right)=\frac{1}{2}\left(-3\frac{3}{5}x+1\frac{1}{5}\right)](https://tex.z-dn.net/?f=%244%5Cfrac%7B3%7D%7B10%7D%20-%5Cleft%282%5Cfrac%7B2%7D%7B5%7Dx%2B5%5Cfrac%7B1%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%28-3%5Cfrac%7B3%7D%7B5%7Dx%2B1%5Cfrac%7B1%7D%7B5%7D%5Cright%29)
First convert mixed fraction into improper fraction.
![$\frac{43}{10} -\left(\frac{12}{5}x+\frac{11}{2}\right)=\frac{1}{2}\left(-\frac{18}{5}x+\frac{6}{5}\right)](https://tex.z-dn.net/?f=%24%5Cfrac%7B43%7D%7B10%7D%20-%5Cleft%28%5Cfrac%7B12%7D%7B5%7Dx%2B%5Cfrac%7B11%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%28-%5Cfrac%7B18%7D%7B5%7Dx%2B%5Cfrac%7B6%7D%7B5%7D%5Cright%29)
![$\frac{43}{10} -\frac{12}{5}x-\frac{11}{2}=-\frac{18}{10}x+\frac{6}{10}](https://tex.z-dn.net/?f=%24%5Cfrac%7B43%7D%7B10%7D%20-%5Cfrac%7B12%7D%7B5%7Dx-%5Cfrac%7B11%7D%7B2%7D%3D-%5Cfrac%7B18%7D%7B10%7Dx%2B%5Cfrac%7B6%7D%7B10%7D)
Now, take LCM and make the denominators same.
LCM of 2, 5, 10 = 10
![$\frac{43}{10} -\frac{12\times2}{5\times2}x-\frac{11\times5}{2\times5}=-\frac{18}{10}x+\frac{6}{10}](https://tex.z-dn.net/?f=%24%5Cfrac%7B43%7D%7B10%7D%20-%5Cfrac%7B12%5Ctimes2%7D%7B5%5Ctimes2%7Dx-%5Cfrac%7B11%5Ctimes5%7D%7B2%5Ctimes5%7D%3D-%5Cfrac%7B18%7D%7B10%7Dx%2B%5Cfrac%7B6%7D%7B10%7D)
![$\frac{43}{10} -\frac{24}{10}x-\frac{55}{10}=-\frac{18}{10}x+\frac{6}{10}](https://tex.z-dn.net/?f=%24%5Cfrac%7B43%7D%7B10%7D%20-%5Cfrac%7B24%7D%7B10%7Dx-%5Cfrac%7B55%7D%7B10%7D%3D-%5Cfrac%7B18%7D%7B10%7Dx%2B%5Cfrac%7B6%7D%7B10%7D)
Arrange like terms one side of the equation.
![$\frac{18}{10}x -\frac{24}{10}x=\frac{6}{10}-\frac{43}{10}+\frac{55}{10}](https://tex.z-dn.net/?f=%24%5Cfrac%7B18%7D%7B10%7Dx%20-%5Cfrac%7B24%7D%7B10%7Dx%3D%5Cfrac%7B6%7D%7B10%7D-%5Cfrac%7B43%7D%7B10%7D%2B%5Cfrac%7B55%7D%7B10%7D)
![$\frac{18x-24x}{10} =\frac{6-43+55}{10}](https://tex.z-dn.net/?f=%24%5Cfrac%7B18x-24x%7D%7B10%7D%20%3D%5Cfrac%7B6-43%2B55%7D%7B10%7D)
![$\frac{-6x}{10} =\frac{18}{10}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-6x%7D%7B10%7D%20%3D%5Cfrac%7B18%7D%7B10%7D)
![$-6x=\frac{18\times10}{10}](https://tex.z-dn.net/?f=%24-6x%3D%5Cfrac%7B18%5Ctimes10%7D%7B10%7D)
![$-6x=18](https://tex.z-dn.net/?f=%24-6x%3D18)
Divide both sides of the expression by –6, we get
⇒ x = –3
Hence the value of x is –3.
Answer: 31°. In this case, this is a rigind rotation or transformation wich means that it preserves angle and lenght measurements. So the answer is 31°.
;)
Answer:
the first 3 is 10 times the value of the second 3
Answer:
A. 1
Step-by-step explanation:
<em>Scale Factor:</em>
<em>The scale factor is the number you multiply the length of a side of the first triangle to get the length of the corresponding side of the other triangle.</em>
Every side that measures 5 in triangle ABC has a corresponding side in triangle DEF that also measures 5. In this case 5 * 1 = 5, so the scale factor is 1.
Answer: A. 1