Answer: ![m=\frac{-30}{79},\ y=5.40](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-30%7D%7B79%7D%2C%5C%20y%3D5.40)
Step-by-step explanation:
Given
Points are ![\left(6\frac{1}{3},3\right),\ \left(19\frac{1}{2},-2\right)](https://tex.z-dn.net/?f=%5Cleft%286%5Cfrac%7B1%7D%7B3%7D%2C3%5Cright%29%2C%5C%20%5Cleft%2819%5Cfrac%7B1%7D%7B2%7D%2C-2%5Cright%29)
Convert mixed numeral to fraction
![\left(6\frac{1}{3},3\right)\Rightarrow \left(\dfrac{19}{3},3\right)\\\\\left(19\frac{1}{2},-2\right)\Rightarrow \left(\dfrac{39}{2},-2\right)](https://tex.z-dn.net/?f=%5Cleft%286%5Cfrac%7B1%7D%7B3%7D%2C3%5Cright%29%5CRightarrow%20%5Cleft%28%5Cdfrac%7B19%7D%7B3%7D%2C3%5Cright%29%5C%5C%5C%5C%5Cleft%2819%5Cfrac%7B1%7D%7B2%7D%2C-2%5Cright%29%5CRightarrow%20%5Cleft%28%5Cdfrac%7B39%7D%7B2%7D%2C-2%5Cright%29)
Slope of the line is
![\Rightarrow m=\dfrac{3-(-2)}{\dfrac{19}{3}-\dfrac{39}{2}}\\\\\Rightarrow m=\dfrac{5}{\dfrac{38-117}{6}}\\\\\Rightarrow m=\dfrac{-30}{79}](https://tex.z-dn.net/?f=%5CRightarrow%20m%3D%5Cdfrac%7B3-%28-2%29%7D%7B%5Cdfrac%7B19%7D%7B3%7D-%5Cdfrac%7B39%7D%7B2%7D%7D%5C%5C%5C%5C%5CRightarrow%20m%3D%5Cdfrac%7B5%7D%7B%5Cdfrac%7B38-117%7D%7B6%7D%7D%5C%5C%5C%5C%5CRightarrow%20m%3D%5Cdfrac%7B-30%7D%7B79%7D)
Equation of line
![\Rightarrow \dfrac{y-3}{x-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow \dfrac{y-3}{0-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\Rightarrow y-3=\dfrac{190}{79}\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7By-3%7D%7Bx-%5Cdfrac%7B19%7D%7B3%7D%7D%3D%5Cdfrac%7B-30%7D%7B79%7D%5C%5C%5C%5C%5Ctext%7Bfor%20y-intercept%2C%20put%20x%3D0%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7By-3%7D%7B0-%5Cdfrac%7B19%7D%7B3%7D%7D%3D%5Cdfrac%7B-30%7D%7B79%7D%5C%5C%5C%5C%5CRightarrow%20y-3%3D%5Cdfrac%7B190%7D%7B79%7D%5C%5C%5C%5C%5CRightarrow%20y%3D3%2B2.40%5C%5C%5CRightarrow%20y%3D5.40)
9514 1404 393
Answer:
FH = 16
Step-by-step explanation:
ΔGHE is a 5-12-13 triangle.
ΔEHF is a 3-4-5 triangle with a scale factor of 4, so side FH is 4·4 = 16 units.
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(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) are all commonly used Pythagorean triples. The first two on the list are used in these triangles.
If you like, you can work out the numbers using the Pythagorean theorem, which tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
For ΔEHG, that is ...
GE² = EH² + HG²
13² = EH² + 5²
EH² = 13² -5² = 169 -25 = 144
And for ΔEHF, ...
FE² = EH² +HF²
20² = 144 + HF²
400 -144 = HF² = 256
HF = √256 = 16
The length of side FH is 16 units.
Click random buttons until you figure it out, or even ask a parent or teacher
To get our answer, we just have to find the least common multiple (LCM) of 8 and 11. In this case, it's 88, because that's the smallest number that 8 and 11 are both factors of.
Hope this helped! :D