Find the values of a, b, and c such that the equation y=ax2+bx+c has ordered pair solutions (1,16), (−1,−2), and (0,−1). To do so, substitute each ordered pair solution into the equation. Each time, the result is an equation in three unknowns, a, b, and c. Then solve the resulting system of three linear equations in three unknowns, a, b, and c.

  y = 8x² +9x -1

Step-by-step explanation:

The coefficients of the quadratic function can be found from three points by substituting the point values into the equation and solving for the coefficients.

The equation we want to find coefficients for is ...

  y = ax² +bx +c

For point (1, 16), the equation is 16 = a(1²) +b(1) +c

For point (-1, -2), the equation is -2 = a(-1)² +b(-1) +c

For point (0, -1), the equation is -1 = a(0) +b(0) +c

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The last of these equations gives a value for c (c=-1). Substituting that into the other two gives the equations in a and b as ...

  a + b = 17

  a - b = -1

Adding the two equations gives ...

  2a = 16   ⇒   a = 8

Subtracting the second from the first gives ...

  2b = 18   ⇒   b = 9

Then the desired quadratic equation is ...

  y = 8x² +9x -1

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The solution is in the following image

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

The solution is given in the image below

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years