How many solutions are there to this equation 3x(x-4)+5-x=2x-7
1 answer:
Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
- x = 1
- x = 4
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To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
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<em>Alternate method</em>
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
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Answer:
C. It will increase by about 0.6%
Step-by-step explanation:
Since, the effective interest rate is,
Where, i is the stated interest rate,
n is the number of compounding periods,
Here, i = 11.28 % = 0.1128,
n = 365 ( 1 year = 365 days ),
Hence, the effective interest rate would be,
=0.119388521952
Now, the changes in effective interest rate = Effective interest rate - Stated interest rate
= 0.119388521952 - 0.1128
= 0.006588521952 ≈ 0.006 = 0.6 %
Hence, It will increased by about 0.6 %,
Option A is correct.
Hope this helps :)