So you know that:
2x+y=14+y
and
5x-y=x+13y
Here you have two equations with two unknown variables:
If you isolate x from the second equations you get:
x=(7/2)y
Insert that in the first equations and solve for y:
2*(7/2)y+y=14+y
y=2
Insert that value for y in one of the two equations (i chose the first):
2x+2=14+2
x=7
Therefore x=7
Hope that helped.
Actually you could start with isolating x, and then insert that in one of the two equations.
Answer:
(c) 43.
Step-by-step explanation:
Given:
Margin of error (E) = 2
Sample variance 
= 44
Confidence level = 95%
The z- value at 95% confidence level is 1.96.
The sample using the provided information can be calculated as:
Hence, the correct option is (c) 43.
Answer: She started with $160.
It will take 6 weeks before she has less than half of what she originally invested.
Step-by-step explanation:
If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the investment after t weeks.
t represents the number of weeks.
P represents the initial value of the investment.
r represents rate of depreciation.
From the information given,
A = $142.40
r = 11% = 11/100 = 0.11
t = 1
Therefore
142.40 = P(1 - 0.11)^1
142.40 = P(0.89)
P = 142.4/0.89
P = 160
For her to have half of what she invested originally, then
80 = 160(0.89)^t
80/160 = (0.89)^t
0.5 = (0.89)^t
Taking log of both sides to base 10
Log 0.5 = log0.89^t = tlog0.89
- 0.3010 = - 0.051t
t = - 0.3010/- 0.051
t = 5.9
Approximately 6 weeks
Since -5 and -5 are the same number, they are on the same y axis so the only distance we need to calculate is between the X coordinates.
When looking for distance, you can not have a negative. what |-3|+|9| is looking for is the distance from 0 on the X axis. since distance can't be negative, (you go 3 miles away from your house in one direction, vs 3 miles in the opposite. both ways is positive, even with opposite directions. same with axis, it doesnt matter which way, only the number.) you need the absolute value of -3 to get the distance from the 0 on the x axis.
short version: distance is positive, and its adding the distances from the x axis to get distance from each other
First, we need to find the total fraction of her raisins she used:
1/4 + 3/8 = 2/8 + 3/8
She used 5/8 of her supply.
Knowing this:
5/8x = 5
We multiply by 8 (the LCD)
5x = 40
x = 8
Her supply was 8 pounds, and after making the food, she now has 3 pounds
