elimination
X- 2y = 3
3x - y = 2
Answer: x = 1/5 and y= -7/5
Step-by-step explanation: Let's solve your system by elimination.
Multiply the first equation by -3,and multiply the second equation by 1.
-3 (x - 2y = 3)
1 (3x - y = 2)
Becomes:
-3x + 6y = -9
3x -y = 2
Add these equations to eliminate x:
5y = -7
Then solve 5y = -7
5y/7 = -7/5
y = -7/5
Now that we‘ve found y, let’s plug it back in and solve for x.
Write down an original equation:
x - 2y = 3
increasing at a rate that will supply food for an additional 10,000 people per year.
c. At what point does the population exceed the food supply? Justify your response.
Answer:
After 5 years (2015)
Step-by-step explanation:
The population is increasing 5% per year, so the first year it will be 1.05 of the initial, the next year 1.05x1.05 of the initial, and then successively, so, for n years:
P(n) = 600,000*(1.05)ⁿ
The food suply increase 10,000 people per year, so the first year will be 10,000 + the initial, the next year 10,000 + 10,000 + the initial, and then successively, so, for n years:
F(n) = 70,000 + 10,000*n
So
P(n) > F(n)
600,000*(1.05)ⁿ > 70,000 + 10,000*n
(1.05)ⁿ > 1.167 + 0.0167n
Solving in a computer:
n > 4.42
So, after 5 years the population exceed the food supply.
A DVD club charges nonmembers $20. 50 to purchase a DVD. Members pay $18 per DVD for a one-time membership cost of $25. The cost is the same for members and nonmembers on the first purchase is 10.
Let's call the number of DVDs "d". For non-members, the cost of purchasing d DVDs is:
Cost for non-members = 20.50d
For members, the cost of purchasing d DVDs is:
Cost for members = 25 + 18d
We want to find the value of d for which the cost is the same for members and non-members. In other words, we want to find the value of d that satisfies the equation:
20.50d = 25 + 18d
To solve for d, we can start by subtracting 18d from both sides of the equation:
2.50d = 25
Then, we can divide both sides by 2.50:
d = 10
Therefore, the cost will be the same for members and non-members on the first purchase if the number of DVDs purchased is 10.
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Part A
What is an equation that can be used to
solve for x?
Part B
What is the value of x?
Answer:
y = 180 - (36 + 65)
x = 69
Step-by-step explanation:
To solve for x in the given diagram of parallel lines cut by a transversal, use the concept of corresponding angles. The value of x is 60°.
Part A: To solve for x, we can use the corresponding angles formed by the transversal and the parallel lines. One of the corresponding angles is x + 60°. Since the other corresponding angle is 120°, we can set up the equation x + 60° = 120°. Solving for x, we find that x = 60°.
Part B: The value of x is 60°.
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