Solve each seperatly
x+1<-3
minus 1 both sides
x<-4
x-2<0
x<2
so
x<-4 or x<2
graph below
'or' means only one at a time can be true, where they intersect, we can't include those points
so since the solution set x<2 includes x<-4 in it,, the solution set is only -4<x<2
to graph it on a line, see below
Answer:
a) 1/24 do total
Step-by-step explanation:
We have that:
The total is 1.
The first friend gets 1/4 of the total.
The second friend gets 1/3 of the total
The third friend gets 3/8 of the total.
The remaining is x.
So
![\frac{1}{4} + \frac{1}{3} + \frac{3}{8} + x = 1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%2B%20%5Cfrac%7B1%7D%7B3%7D%20%2B%20%5Cfrac%7B3%7D%7B8%7D%20%2B%20x%20%3D%201)
The least common multiple between 4, 3 and 8 is 24. So
![\frac{6 + 8 + 3*3 + 24x}{24} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2B%208%20%2B%203%2A3%20%2B%2024x%7D%7B24%7D%20%3D%201)
![23 + 24x = 24](https://tex.z-dn.net/?f=23%20%2B%2024x%20%3D%2024)
![24x = 1](https://tex.z-dn.net/?f=24x%20%3D%201)
![x = \frac{1}{24}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B24%7D)
So the correct answer is:
a) 1/24 do total
Answer:
-0.34772
Step-by-step explanation:
One way of doing this problem is to change the base from 5 to 10.
Use the change of base formula:
log x
log x = ------------
5 log 5
so:
log (4/7) log 4 - log 7
log (4/7) = --------------- = ---------------------
5 log 5 log 5
Note that "log x" above is the common logarithm of x and is to the base 10.
Continuing, we get:
0.60206 - 0.84510 -0.24304
---------------------------- = --------------------- = -0.34772 (This corresponds to
0.69897 0.69897 the second given
answer choice.)
5x - 4y = 42 ------ (1)
x - 6y = 24 ----------(2), multiply eq. 2 by 5 we get
5x - 30y = 120 -----(3),
now use eq. (3) - (1),
5x - 30y = 120
-(5x - 4y = 42)
- 30y + 4y = 120 - 42,
-26y = 78, y = -78/26 = -3,
x = 24 + 6y = 24 + (6*[-3]) = 24 - 18 = 6,
x = 6, y = -3.
,