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slava [35]
3 years ago
5

1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals n

egative 4 x
2.) Which kind of function best models the data in the table? Use differences or ratios.

x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

3.) Solve the system of equations algebraically. Show all of your steps.

y equals x squared plus two x; y equals three x plus twenty



PLEASE HELP!
Mathematics
1 answer:
Andrew [12]3 years ago
7 0
Part 1
We are given x^2-21x=-4x. This can be rewritten as x^2-18x=0.
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
     x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}
     x=\frac{18\pm 18}{2}

The values of x are
     x_1=\frac{18-18}{2}=0
     x_2=\frac{18+18}{2}=18

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function. 

Part 3.
The first equation is y=x^2+2.
The second equation is y=3x+20.

We have 
     x^2+2=3x+20
     x^2-3x-18=0
Factoring, we have 
     \left(x-6\right)\left(x+3\right)=0
Equating both factors to zero.
     x_1-6=0\rightarrow x_1=6
     x_2+3=0\rightarrow x_2=-3

When the value of x is 6, the value of y is 
     y=3\left(6\right)+20=38

When the value of x is -3, the value of y is 
     y=3\left(-3\right)+20=11

Therefore, the solutions are (6,38) or (-3,11)
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