Question

50 POINTS AND WILL MARK BRAINLIEST NEED HELP ASAP

Answer 1

Answer:

Please see attached image and all steps below for both parts

Step-by-step explanation:

Task 1

The following system of equations includes a linear equation and a quadratic one:

$\left \{ {{y=x+2} \atop {y=x^2-8x+2}} \right} \}$

it can be solved by using substitution in the second equation of the variable "y" by the linear expression of the first equation:

$x+2=x^2-8x+2\\x=x^2-8x\\x^2-9x=0\\x\,(x-9)=0$

and this product of two factors will e zero when either factor is zero, that is: when x = 0, or when x = 9 [to make zero the binomial(x - 9)]

There are two solutions: x = 0 and x = 9.

When we graph both expressions in the system, we see that the line intercepts the parabola at the points (0, 2) and (9, 11). See attached image.

Task 2

Part 1:

Let's pick 30 as a number larger than 25. 30 can be written as 40 - 10

So we can use:

$(40 -10)^2=40^2-2\,(40)\,(10)+ 10^2=1600-800+100=900$

to calculate its square.

Part 2:

let's choose a=9 and b=10 so we use:

$9^3+10^3=(9 + 10)\,(9^2-(9)\,(10)+10^2)=(19)\,(81-(90)+100)=19\,(81-180+100)=19\,*\,91=1729$