(20*6)+(12*6)+(18*10)=312 500-312=188 colored pencil's left.
To solve this, we would need to figure out the values of
for which an absolute value is negative. From basics, you should know that an absolute value is always greater than or equal to 0.
If we rearrange this equation a little bit, we get,
![|2x+7|\leq 5+k](https://tex.z-dn.net/?f=%7C2x%2B7%7C%5Cleq%205%2Bk)
So
<em>cannot </em>be negative. So,
![5+k\geq 0\\k\geq -5](https://tex.z-dn.net/?f=5%2Bk%5Cgeq%200%5C%5Ck%5Cgeq%20-5)
For this to <em>have </em>a solution, k needs to be greater than or equal to
.
For <em>no solution</em>, k is less than -5. So, values of k which will make the equation to <em>not </em>have any solution is
.
ANSWER: ![k](https://tex.z-dn.net/?f=k%3C-5)
(7 3/4 mi/h)*(2 2/3 h) = 20 2/3
Todd rode 20.667 miles.
_____
A calculator that works with mixed numbers is a handy thing.
Answer:
The attendance was 198 children, 90 students and 99 adults.
Step-by-step explanation:
We define:
c: children attendance
s: students attendance
a: adult attendance
The equation that describes the total ticket sales is:
![5c+7s+12a=2808](https://tex.z-dn.net/?f=5c%2B7s%2B12a%3D2808)
We also know that the children attendance doubles the adult attendance:
![c=2a](https://tex.z-dn.net/?f=c%3D2a)
The third equation is the seating capacity, which we assume is full:
![c+s+a=387](https://tex.z-dn.net/?f=c%2Bs%2Ba%3D387)
We start by replacing variables in two of the equations:
![c=2a\\\\s=387-c-a=387-2a-a=387-3a](https://tex.z-dn.net/?f=c%3D2a%5C%5C%5C%5Cs%3D387-c-a%3D387-2a-a%3D387-3a)
Then, we solve the remaining equation for a:
![5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99](https://tex.z-dn.net/?f=5c%2B7s%2B12a%3D2808%5C%5C%5C%5C5%282a%29%2B7%28387-3a%29%2B12a%3D2808%5C%5C%5C%5C10a%2B%282709-21a%29%2B12a%3D2808%5C%5C%5C%5C10a%2B12a-21a%3D2808-2709%5C%5C%5C%5Ca%3D99)
Then, we solve for the other two equations:
![c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90](https://tex.z-dn.net/?f=c%3D2a%3D2%2A99%3D198%5C%5C%5C%5Cs%3D387-3a%3D387-3%2A99%3D387-297%3D90)
The attendance was 198 children, 90 students and 99 adults.