Question 147659: Hope someone can help me with this.
a. An financial advisor invested a total of $6,000, part at 4% annual simple interest and part at 6.5% annual simple interest.
The amount of interest earned for 1 year was $335.00. How much was invested at each rate? Show work.
b. Consider the equation 3x2 – 4x + 7 = 0.
1.Find the discriminant, b2 – 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.
2. Use the quadratic formula to find the exact solutions of the equation. Show work.
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a. An financial advisor invested a total of $6,000, part at 4% annual simple interest and part at 6.5% annual simple interest.
Amount EQUATION: x + y = 6000
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The amount of interest earned for 1 year was $335.00. How much was invested at each rate? Show work.
Interest EQUATION: 0.04x + 0.065y = 335
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Rearrange the equations:
40x + 65y = 335000
40x + 40y = 40*6000
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Subtract 2nd from 1st to get:
25y = 95000
y = $3800 (Amt. invested at 6.5%)
x = 6000 - 3800 = $2200 (Amt. invested at 4%)
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Cheers,
Stan H.
b. Consider the equation 3x2 – 4x + 7 = 0.
1.Find the discriminant, b2 – 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.
2. Use the quadratic formula to find the exact solutions of the equation. Show work.
Answer by Fombitz(32388)  (Show Source):
You can put this solution on YOUR website! a.)Let's call the amount invested at 4%, A, and
call the amount invested at 6.5%, B.
What do we know?
The total invested was $6000.
1.
After one year the total interest was $335.
2.
Let's multiply both sides of eq. 2 by 100 to get rid of denominators.
2.
Now we can use eq. 1 to get A in terms of B and substitute into eq. 2,
1.
Now substitute into eq. 2,
2.
From eq. 1,
.
.
.
b1)3x2 – 4x + 7 = 0
The quadratic formula deals with an equation of the form,
in your case,
The discriminant is,
Since the discriminant is negative, there are two imaginary, or complex roots, that solve the equation.
.
.
.
b2) The full quadratic formula is
The exact solution is,
The approximation is,
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