Answer:
x = 18
Step-by-step explanation:
Given
6 - x = - 12 ( subtract 6 from both sides )
- x = - 18 ( multiply both sides by - 1 )
x = 18
Answer:
1.5feet
Step-by-step explanation:
The inequality is
![7- \frac{2}{b}\ \textless \ \frac{5}{b}](https://tex.z-dn.net/?f=7-%20%5Cfrac%7B2%7D%7Bb%7D%5C%20%5Ctextless%20%5C%20%5Cfrac%7B5%7D%7Bb%7D)
write 7 as 7b/b to have all the expressions in common denominator:
![\frac{7b}{b} - \frac{2}{b}\ \textless \ \frac{5}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7b%7D%7Bb%7D%20-%20%5Cfrac%7B2%7D%7Bb%7D%5C%20%5Ctextless%20%5C%20%5Cfrac%7B5%7D%7Bb%7D)
![\frac{7b-2}{b} \ \textless \ \frac{5}{b}](https://tex.z-dn.net/?f=%5Cfrac%7B7b-2%7D%7Bb%7D%20%5C%20%5Ctextless%20%5C%20%5Cfrac%7B5%7D%7Bb%7D)
![\frac{7b-2}{b}- \frac{5}{b}\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B7b-2%7D%7Bb%7D-%20%5Cfrac%7B5%7D%7Bb%7D%5C%20%5Ctextless%20%5C%200)
![\frac{7b-2-5}{b}\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B7b-2-5%7D%7Bb%7D%5C%20%5Ctextless%20%5C%200)
![\frac{7b-7}{b}\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B7b-7%7D%7Bb%7D%5C%20%5Ctextless%20%5C%200)
![\frac{7(b-1)}{b}\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B7%28b-1%29%7D%7Bb%7D%5C%20%5Ctextless%20%5C%200)
here b=1 is a root and b=0 is not in the domain of the expression, but it still has an effect in the sign of the expression.
the sign table of
![\frac{7(b-1)}{b}](https://tex.z-dn.net/?f=%5Cfrac%7B7%28b-1%29%7D%7Bb%7D%20)
is :
+++++++[0] --------[1] +++++
this means that for values of b to the left of 0 and to the right of 1, the expression is positive, and for values of b in (0, 1), the expression is negative.
that is
![\frac{7(b-1)}{b}\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B7%28b-1%29%7D%7Bb%7D%5C%20%5Ctextless%20%5C%200%20)
for b∈(0, 1)
Answer: (0, 1)
Answer:
11
Step-by-step explanation:
248/24=10.3
round up to 11
Answer:
![(x,y) = (-4,2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28-4%2C2%29)
Step-by-step explanation:
Given
![x + y = -2](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%20-2)
![y = 2x + 10](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%2010)
Required
Determine the point of intersection of both equations (if graphed)
To do this, we solve for x and y
Substitute 2x + 10 for y in the first equation
![x + 2x + 10 = -2](https://tex.z-dn.net/?f=x%20%2B%202x%20%2B%2010%20%3D%20-2)
![x + 2x = -2 - 10](https://tex.z-dn.net/?f=x%20%2B%202x%20%3D%20-2%20-%2010)
![3x = -12](https://tex.z-dn.net/?f=3x%20%3D%20-12)
![x = -4](https://tex.z-dn.net/?f=x%20%3D%20-4)
Substitute
in the second equation
![y=2x +10](https://tex.z-dn.net/?f=y%3D2x%20%2B10)
![y=2*-4 +10](https://tex.z-dn.net/?f=y%3D2%2A-4%20%2B10)
![y=-8 +10](https://tex.z-dn.net/?f=y%3D-8%20%2B10)
![y = 2](https://tex.z-dn.net/?f=y%20%3D%202)
So, the point of intersection is:
![(x,y) = (-4,2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28-4%2C2%29)
<em>See attachment for graph</em>