Solve the following quadratic-linear system of equations. y=x^2-x-6 and y=2x-2

2 answers:

8 0

You can do substitution 2x-2=x^2 -x -6; isolate all terms on one side 0= x^2 -x-2x -6+2; combine like terms x^2 -3x -4=0; factor the quadratic (x-4)(x+1)=0; each term is zero x-4=0 so x=4 and x+1=0 so x=-1. Now, y=2•4-2=6 and y=2•(-1) -2= -4 ; solutions for the system are ( 4,6) and ( -1, -4)

dimaraw [331]3 years ago

7 0

Answer:

(4,6) or (-1,-4)

Step-by-step explanation:

since both equations about x are equal to y, you can make x^2-x-6=2x-2

solve this quadratic equation, you get x=4 or -1

substitute x into y=2x-2

you get y=6 when x=4, or y= -4 when x=-1

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The volume of a cylindrical soup can is represented by the expression πr3 + 7πr2, where r is the radius of the cylinder. Which s

Ganezh [65]

Answer:

Step-by-step explanation:

Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²

From V = πr³ + 7πr²;

factor out the common variable

V = πr³ + 7πr²

V = πr²(r+7) ... 1

The original volume of a cylinder V = πr²h .... 2 where;

r is the radius of the cylinder

h is the height of the cylinder

Equating equation 1 and 2, we will have;

πr²(r+7) = πr²h

Divide both sides by πr²

πr²(r+7)/ πr² = πr²h/ πr²

r+7 = h

h = r+7

Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r. The statement means that the height of the cylindrical soup is 7 more than its radius.

5 0

3 years ago

X² + y² = 8

ohaa [14]

Answer:

$(2,2)~ \text{and}~ (-2,-2)$

Step by step explanation:

$x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \dfrac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \dfrac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\$