Solve the system of equations 3x + y = 3 and 7x + 2y = 1.
1 answer:
Answer:
(x, y) = (-5, 18)
Step-by-step explanation:
You have done the first two steps.
<h3>3.</h3>7x +2(3 -3x) = 1 . . . . . equation with y substituted
7x +6 -6x = 1 . . . . . . . eliminate parentheses using the distributive property
x = -5 . . . . . . . . . . . . . subtract 6 from both sides, collect terms
<h3>4.</h3>y = 3 -3(-5) . . . . . . . . use the substitution equation to find y
y = 18
The solution is (x, y) = (-5, 18).
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Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P, where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ Angus has $3,000 he want to invest
∴ P = 3000
∵ The interest rate is compounded continuously
∵ Angus has $5,500 in 8 years
∴ A = 5500
∴ t = 8
→ Substitute them in the rule above to find r
∵ 5500 = 3000
→ Divide both sides by 3000
∴ =
→ Insert ㏑ in both sides
∵ ㏑( ) = ㏑(
)
→ Remember ㏑() = n
∴ ㏑( ) = 8r
→ Divide both sides by 8
∴ 0.07576697545 = r
→ Multiply it by 100% to change it to a percentage
∴ r = 0.07576697545 × 100%
∴ r = 7.576697545 %
→ Round it to the nearest hundredth
∴ r ≅ 7.58
∴ The interest rate is 7.58%