Answer:
C. x = 3, y = -6
Step-by-step explanation:
You can divide the second equation by 2. Then you have ...
x +2y = -9
This gives you a couple of choices for solution. The x-coefficients match, so subtracting one equation from the other eliminates x:
(x +2y) -(x -2y) = (-9) -(15)
4y = -24 ⇒ y = -6
Adding the two equations eliminates y:
(x -2y) +(x +2y) = (15) +(-9)
2x = 6 ⇒ x = 3
The solution is (x, y) = (3, -6).
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<em>Additional comment</em>
I find it quick and easy to use a graphing calculator to find the solution. Many graphing calculators also make it simple to solve systems of equations in matrix form. Either way, you can obtain a solution in little more than the time it takes to enter the equations (or their coefficients).
3x + 4(x + 1) = 67
7x + 4 = 67
7x = 67-4 = 63
x = 9
The smaller integer is 9.
Sarah rolled a one 3 times and rolled a three 1 time in a total of 20 rolls. She rolled one or three 4 times out of 20. Therefore,
The answer is
A.
Answer:
E = 1.09
Step-by-step explanation:
Elasticity measures the sensitivity of demand with changes in income.
Elasticity of Income has the formula:
[Change in Demand/Demand]/[Change in Income/Income]
So, now, we have:
D_0 = 2
D_1 = 1
I_0 = 8
I_1 = 15
Now, Elasticity (E) is:
E = [(1-2)/(1+2)]/[(15-8)/(15+8)]
E = [1/3]/[7/23]
E = 1.09
Answer:
if the annual interest rate is 7%, then you need to invest:
present value = future value / (1 + i)ⁿ
- future value = $2,200,000
- i = 7%
- n = 28 years
present value = $2,200,000 / (1 + 7%)²⁸ = $330,884.87
if the interest rate is 15%, the you need to deposit a smaller amount:
present value = future value / (1 + i)ⁿ
- future value = $2,200,000
- i = 15%
- n = 28 years
present value = $2,200,000 / (1 + 15%)²⁸ = $43,942.34
