Answer:
(C) 4|5 -2x| > 68
Step-by-step explanation:
You can solve each of the inequalities to see if their solutions match the given numbers, or you can start with the given numbers and see what sort of inequality you end up with.
If you plot the given "solution" on a number line, you find that the numbers -6 and 11 are the same distance from x=2.5. That distance is 8.5 units. (One way to deterimine this is to average -6 and 11, then subtract that average from 11 to find the distance.
So, we can write an inequality describing values of x that are more than 8.5 units from 2.5:
|x -2.5| > 8.5
and it will have the solution x < -6 or x > 11.
Multiplying this by 2, it can become ...
|2x -5| > 17
Of course, since the absolute value function doesn't care whether its argument is positive or negative, we can also write this as ...
|5 -2x| > 17
This tells you right away which answer choice is appropriate. Further confirmation can be had by multiplying this by 4:
4|5 -2x| > 68 . . . . . . matches selection C
To estimate the unit rate, we should round the 5.79 to 6. This makes it much simpler to solve as 6 is a multiple of 12. The unit rate, in this case, is the price of 1 pair of socks. We can find this by dividing both the price and pairs of socks by 12. When we do this, we can see that each pair of socks is approximately $0.50.
Answer: $725
<u>Step-by-step explanation:</u>
Let x represent the amount invested at 8%, then $13,000 - x is the amount invested at 16%.
0.08(x) + 0.16(13,000 - x) = 1500
0.08x + 2080 - 0.16x = 1500
2080 - 0.08x = 1500
- 0.08x = -580
x = 7250
Answer:
y = (√7)/4
Step-by-step explanation:
The equation of the unit circle is ...
x^2 +y^2 = 1
Putting the given value in for x, we can find y to be ...
(-3/4)^2 +y^2 = 1
y^2 = 1 -(-3/4)^2 = 1 -9/16 = 7/16 . . . . . subtract 9/16
y = √(7/16) . . . . . . . . . . . take the square root; y > 0 here
y = (√7)/4
(-6,2)
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