Answer:
![\huge\boxed{(f-g)\left(-\dfrac{1}{3}\right)=-3\dfrac{1}{3}}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%28f-g%29%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%3D-3%5Cdfrac%7B1%7D%7B3%7D%7D)
Step-by-step explanation:
![\text{We have}:\\\\f(x)=x^2-4\ \text{and}\ g(x)=x^2+2x\\\\(f-g)(x)=f(x)-g(x)\\\\\text{therefore}\\\\(f-g)(x)=(x^2-4)-(x^2+2x)=x^2-4-x^2-2x\\\\=(x^2-x^2)-2x-4=-2x-4\\\\(f-g)\left(-\dfrac{1}{3}\right)\to\text{put}\ x=-\dfrac{1}{3}\ \text{to the equation of the function}\ (f-g)(x):\\\\(f-g)\left(-\dfrac{1}{3}\right)=-2\left(-\dfrac{1}{3}\right)-4=\dfrac{2}{3}-4=-3\dfrac{1}{3}](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%7D%3A%5C%5C%5C%5Cf%28x%29%3Dx%5E2-4%5C%20%5Ctext%7Band%7D%5C%20g%28x%29%3Dx%5E2%2B2x%5C%5C%5C%5C%28f-g%29%28x%29%3Df%28x%29-g%28x%29%5C%5C%5C%5C%5Ctext%7Btherefore%7D%5C%5C%5C%5C%28f-g%29%28x%29%3D%28x%5E2-4%29-%28x%5E2%2B2x%29%3Dx%5E2-4-x%5E2-2x%5C%5C%5C%5C%3D%28x%5E2-x%5E2%29-2x-4%3D-2x-4%5C%5C%5C%5C%28f-g%29%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Cto%5Ctext%7Bput%7D%5C%20x%3D-%5Cdfrac%7B1%7D%7B3%7D%5C%20%5Ctext%7Bto%20the%20equation%20of%20the%20function%7D%5C%20%28f-g%29%28x%29%3A%5C%5C%5C%5C%28f-g%29%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%3D-2%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29-4%3D%5Cdfrac%7B2%7D%7B3%7D-4%3D-3%5Cdfrac%7B1%7D%7B3%7D)
Answer:
See the attached
Step-by-step explanation:
When in doubt, draw a diagram.
The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.
The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.
The perpendicular line to BC through A is ...
... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)
The intersection of that line and x=6 is ...
... y = -6/2 +7 = 4
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
Answer:
![5(x+2)(x-2)](https://tex.z-dn.net/?f=5%28x%2B2%29%28x-2%29)
Step-by-step explanation:
Find the greatest common factor (GCF) of the 2 terms:
GCF is 5.
Factor out the GCF:
![5x^2-20\\5(\frac{5x^2}{5} -\frac{20}{5} )\\5(x^2-4)](https://tex.z-dn.net/?f=5x%5E2-20%5C%5C5%28%5Cfrac%7B5x%5E2%7D%7B5%7D%20-%5Cfrac%7B20%7D%7B5%7D%20%29%5C%5C5%28x%5E2-4%29)
Rewrite as a difference of squares (
):
![5(x^2-2^2)\\5(x+2)(x-2)](https://tex.z-dn.net/?f=5%28x%5E2-2%5E2%29%5C%5C5%28x%2B2%29%28x-2%29)